Two forces have the same magnitude F. What is the angle between the two vectors if their sum has a magnitude of (a) 2F? (b) ? (c) zero? Sketch the three vectors in each case.

Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in Fig. E4.2. (a) Find the x- and y-components of each of the three pulls. (b) Use the components to find the magnitude and direction of the resultant of the three pulls.

BIO Jaw Injury. Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of 5.00 N on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force?

A man is dragging a trunk up the loading ramp of a movers truck. The ramp has a slope angle of \(20.0^{\circ}\), and the man pulls upward with a force \(\vec{F}\) whose direction makes an angle of \(30.0^{\circ}\) with the ramp (Fig. E4.4). (a) How large a force \(\vec{F}\) is necessary for the component \(F_{x}\) parallel to the ramp to be 60.0 N? (b) How large will the component \(F_{y}\) perpendicular to the ramp then be?

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is \(60.0^{\circ}\). If dog A exerts a force of 270 N and dog B exerts a force of 300 N, find the magnitude of the resultant force and the angle it makes with dog A’s rope.

Two forces, and act at a point. The magnitude of is 9.00 N, and its direction is above the x-axis in the second quadrant. The magnitude of is 6.00 N, and its direction is below the x-axis in the third quadrant. (a) What are the x- and y-components of the resultant force? (b) What is the magnitude of the resultant force?

A 68.5-kg skater moving initially at on rough horizontal ice comes to rest uniformly in 3.52 s due to friction from the ice. What force does friction exert on the skater?

You walk into an elevator, step onto a scale, and push the up button. You also recall that your normal weight is 625 N. Start answering each of the following questions by drawing a freebody diagram. (a) If the elevator has an acceleration of magnitude , what does the scale read? (b) If you start holding a 3.85-kg package by a light vertical string, what will be the tension in this string once the elevator begins accelerating?

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.0 N to the box and produces an acceleration of magnitude what is the mass of the box?

A dockworker applies a constant horizontal force of 80.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in 5.00 s. (a) What is the mass of the block of ice? (b) If the worker stops pushing at the end of 5.00 s, how far does the block move in the next 5.00 s?

A hockey puck with mass 0.160 kg is at rest at the origin (x = 0) on the horizontal, frictionless surface of the rink. At time t = 0 a player applies a force of 0.250 N to the puck, parallel to the x-axis; he continues to apply this force until t = 2.00 s. (a) What are the position and speed of the puck at t = 2.00 s. (b) If the same force is again applied at t = 5.00 s, what are the position and speed of the puck at t = 7.00 s?

A crate with mass 32.5 kg initially at rest on a warehouse floor is acted on by a net horizontal force of 140 N. (a) What acceleration is produced? (b) How far does the crate travel in 10.0 s? (c) What is its speed at the end of 10.0 s?

A 4.50-kg toy cart undergoes an acceleration in a straight line (the x-axis). The graph in Fig. E4.13 shows this acceleration as a function of time. (a) Find the maximum net force on this cart. When does this maximum force occur? (b) During what times is the net force on the cart a constant? (c) When is the net force equal to zero?

A 2.75-kg cat moves in a straight line (the x-axis). Figure E4.14 shows a graph of the x-component of this cat’s velocity as a function of time. (a) Find the maximum net force on this cat. When does this force occur? (b) When is the net force on the cat equal to zero? (c) What is the net force at time 8.5 s?

A small 8.00-kg rocket burns fuel that exerts a time-varying upward force on the rocket as the rocket moves upward from the launch pad. This force obeys the equation Measurements show that at the force is 100.0 N, and at the end of the first 2.00 s, it is 150.0 N. (a) Find the constants A and B, including their SI units. (b) Find the net force on this rocket and its acceleration (i) the instant after the fuel ignites and (ii) 3.00 s after fuel ignition. (c) Suppose you were using this rocket in outer space, far from all gravity. What would its acceleration be 3.00 s after fuel ignition?

An electron (mass \(=9.11 \times 10^{-31} \mathrm{k}\)) leaves one end of a TV picture tube with zero initial speed and travels in a straight line to the accelerating grid, which is 1.80 cm away. It reaches the grid with a speed of \(3.00 \times 10^{6} \mathrm{~m} / \mathrm{s}\). If the accelerating force is constant, compute (a) the acceleration; (b) the time to reach the grid; (c) the net force, in newtons. (You can ignore the gravitational force on the electron.)

Superman throws a 2400-N boulder at an adversary. What horizontal force must Superman apply to the boulder to give it a horizontal acceleration of

BIO (a) An ordinary flea has a mass of How many newtons does it weigh? (b) The mass of a typical froghopper is 12.3 mg. How many newtons does it weigh? (c) A house cat typically weighs 45 N. How many pounds does it weigh, and what is its mass in kilograms?

At the surface of Jupiters moon Io, the acceleration due to gravity is A watermelon weighs 44.0 N at the surface of the earth. (a) What is the watermelons mass on the earths surface? (b) What are its mass and weight on the surface of Io?

An astronauts pack weighs 17.5 N when she is on earth but only 3.24 N when she is at the surface of an asteroid. (a) What is the acceleration due to gravity on this asteroid? (b) What is the mass of the pack on the asteroid?

BIO World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude How much horizontal force must a 55-kg sprinter exert on the starting blocks during a start to produce this acceleration? Which body exerts the force that propels the sprinter: the blocks or the sprinter herself?

A small car (mass 380 kg) is pushing a large truck (mass 900 kg) due east on a level road. The car exerts a horizontal force of 1200 N on the truck. What is the magnitude of the force that the truck exerts on the car?

Boxes A and B are in contact on a horizontal, frictionless surface, as shown in Fig. E4.23. Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 100 N is exerted on box A. What is the magnitude of the force that box A exerts on box B?

The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650 N. What are the reaction forces to these two forces? Is the passenger accelerating? If so, what are the magnitude and direction of the acceleration?

A student with mass 45 kg jumps off a high diving board. Using \(6.0\times10^{24}\mathrm{\ kg}\) for the mass of the earth, what is the acceleration of the earth toward her as she accelerates toward the earth with an acceleration of \(9.8\mathrm{\ m}/\mathrm{s}^2\)? Assume that the net force on the earth is the force of gravity she exerts on it.

An athlete throws a ball of mass m directly upward, and it feels no appreciable air resistance. Draw a free-body diagram of this ball while it is free of the athlete’s hand and (a) moving upward; (b) at its highest point; (c) moving downward. (d) Repeat parts (a), (b), and (c) if the athlete throws the ball at a \(60^{\circ}\) angle above the horizontal instead of directly upward

Two crates, A and B, sit at rest side by side on a frictionless horizontal surface. The crates have masses and A horizontal force is applied to crate A and the two crates move off to the right. (a) Draw clearly labeled free-body diagrams for crate A and for crate B. Indicate which pairs of forces, if any, are thirdlaw actionreaction pairs. (b) If the magnitude of force is less than the total weight of the two crates, will it cause the crates to move? Explain.

A person pulls horizontally on block B in Fig. E4.28, causing both blocks to move together as a unit. While this system is moving, make a carefully labeled free-body diagram of block A if (a) the table is frictionless and (b) there is friction between block B and the table and the pull is equal to the friction force on block B due to the table

A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labeled free-body diagram for the ball if (a) the train has a uniform velocity, and (b) the train is speeding up uniformly. Is the net force on the ball zero in either case? Explain.

CP A .22 rifle bullet, traveling at strikes a large tree, which it penetrates to a depth of 0.130 m. The mass of the bullet is 1.80 g. Assume a constant retarding force. (a) How much time is required for the bullet to stop? (b) What force, in newtons, does the tree exert on the bullet?

A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force that is directed at an angle of below the horizontal and the chair slides along the floor. (a) Draw a clearly labeled free-body diagram for the chair. (b) Use your diagram and Newtons laws to calculate the normal force that the floor exerts on the chair.

A skier of mass 65.0 kg is pulled up a snow-covered slope at constant speed by a tow rope that is parallel to the ground. The ground slopes upward at a constant angle of above the horizontal, and you can ignore friction. (a) Draw a clearly labeled freebody diagram for the skier. (b) Calculate the tension in the tow rope.

A 4.80-kg bucket of water is accelerated upward by a cord of negligible mass whose breaking strength is 75.0 N. If the bucket starts from rest, what is the minimum time required to raise the bucket a vertical distance of 12.0 m without breaking the cord?

A large box containing your new computer sits on the bed of your pickup truck. You are stopped at a red light. The light turns green and you stomp on the gas and the truck accelerates. To your horror, the box starts to slide toward the back of the truck. Draw clearly labeled free-body diagrams for the truck and for the box. Indicate pairs of forces, if any, that are third-law action reaction pairs. (The bed of the truck is not frictionless.)

Two horses pull horizontally on ropes attached to a stump. The two forces and that they apply to the stump are such that the net (resultant) force has a magnitude equal to that of and makes an angle of with Let and also. Find the magnitude of and its direction (rela

You have just landed on Planet X. You take out a 100-g ball, release it from rest from a height of 10.0 m, and measure that it takes 2.2 s to reach the ground. You can ignore any force on the ball from the atmosphere of the planet. How much does the 100-g ball weigh on the surface of Planet X?

Two adults and a child want to push a wheeled cart in the direction marked x in Fig. P4.37. The two adults push with horizontal forces and as shown in the figure. (a) Find the magnitude and direction of the smallest force that the child should exert. You can ignore the effects of friction. (b) If the child exerts the minimum force found in part (a), the cart accelerates at in the -direction. What is the weight of the cart?

An oil tankers engines have broken down, and the wind is blowing the tanker straight toward a reef at a constant speed of (Fig. P4.38). When the tanker is 500 m from the reef, the wind dies down just as the engineer gets the engines going again. The rudder is stuck, so the only choice is to try to accelerate straight backward away from the reef. The mass of the tanker and cargo is and the engines produce a net horizontal force of on the tanker. Will the ship hit the reef? If it does, will the oil be safe? The hull can withstand an impact at a speed of or less. You can ignore the retarding force of the water on the tankers hull

A Standing Vertical Jump. Basketball player Darrell Griffith is on record as attaining a standing vertical jump of 1.2 m (4 ft). (This means that he moved upward by 1.2 m after his feet left the floor.) Griffith weighed 890 N (200 lb). (a) What is his speed as he leaves the floor? (b) If the time of the part of the jump before his feet left the floor was 0.300 s, what was his average acceleration (magnitude and direction) while he was pushing against the floor? (c) Draw his free-body diagram (see Section 4.6). In terms of the forces on the diagram, what is the net force on him? Use Newton's laws and the results of part (b) to calculate the average force he applied to the ground.

An advertisement claims that a particular automobile can stop on a dime. What net force would actually be necessary to stop a 850-kg automobile traveling initially at in a distance equal to the diameter of a dime, which is 1.8 cm?

Human Biomechanics. The fastest pitched baseball was measured at Typically, a baseball has a mass of 145 g. If the pitcher exerted his force (assumed to be horizontal and constant) over a distance of 1.0 m, (a) what force did he produce on the ball during this record-setting pitch? (b) Draw free-body diagrams of the ball during the pitch and just after it left the pitchers hand.

Human Biomechanics. The fastest served tennis ball, served by Big Bill Tilden in 1931, was measured at The mass of a tennis ball is 57 g, and the ball is typically in contact with the tennis racquet for 30.0 ms, with the ball starting from rest. Assuming constant acceleration, (a) what force did Big Bills tennis racquet exert on the tennis ball if he hit it essentially horizontally? (b) Draw free- body diagrams of the tennis ball during the serve and just after it moved free of the racquet

Two crates, one with mass 4.00 kg and the other with mass 6.00 kg, sit on the frictionless surface of a frozen pond, connected by a light rope (Fig. P4.43). A woman wearing golf shoes (so she can get traction on the ice) pulls horizontally on the 6.00-kg crate with a force F that gives the crate an acceleration of (a) What is the acceleration of the 4.00-kg crate? (b) Draw a free-body diagram for the 4.00-kg crate. Use that diagram and Newtons second law to find the tension T in the rope that connects the two crates. (c) Draw a free-body diagram for the 6.00-kg crate. What is the direction of the net force on the 6.00-kg crate? Which is larger in magnitude, force T or force F? (d) Use part (c) and Newtons second law to calculate the magnitude of the force F.

An astronaut is tethered by a strong cable to a spacecraft. The astronaut and her spacesuit have a total mass of 105 kg, while the mass of the cable is negligible. The mass of the spacecraft is The spacecraft is far from any large astronomical bodies, so we can ignore the gravitational forces on it and the astronaut. We also assume that both the spacecraft and the astronaut are initially at rest in an inertial reference frame. The astronaut then pulls on the cable with a force of 80.0 N. (a) What force does the cable exert on the astronaut? (b) Since , how can a massless cable exert a force? (c) What is the astronauts acceleration? (d) What force does the cable exert on the spacecraft? (e) What is the acceleration of the spacecraft?

CALC To study damage to aircraft that collide with largebirds, you design a test gun that will accelerate chicken-sizedobjects so that their displacement along the gun barrel is givenby The objectleaves the end of the barrel at (a) How long must thegun barrel be? (b) What will be the speed of the objects as theyleave the end of the barrel? (c) What net force must be exerted on a1.50-kg object at (i) and (ii)

.. A spacecraft descends vertically near the surface of Planet X.An upward thrust of 25.0 kN from its engines slows it down at a rate of but it speeds up at a rate of with anupward thrust of 10.0 kN. (a) In each case, what is the direction of the acceleration of the spacecraft? (b) Draw a free-body diagram forthe spacecraft. In each case, speeding up or slowing down, what is thedirection of the net force on the spacecraft? (c) Apply Newtons secondlaw to each case, slowing down or speeding up, and use this tofind the spacecrafts weight near the surface of Planet X.

.. CP A 6.50-kg instrument is hanging by a vertical wireinside a space ship that is blasting off at the surface of the earth.Thisship starts from rest and reaches an altitude of 276 m in 15.0 swith constant acceleration. (a) Draw a free-body diagram for theinstrument during this time. Indicate which force is greater. (b)Find the force that the wire exerts on the instrument.

.. Suppose the rocket in Problem 4.47 is coming in for avertical landing instead of blasting off. The captain adjusts theengine thrust so that the magnitude of the rockets acceleration isthe same as it was during blast-off. Repeat parts (a) and (b).

Insect Dynamics. The froghopper (Philaenus spumarius),the champion leaper of the insect world, has a mass of 12.3 mg and leaves the ground (in the most energetic jumps) at 4.0 m/s from a vertical start. The jump itself lasts a mere 1.0 ms before the insect is clear of the ground. Assuming constant acceleration, (a) draw a free-body diagram of this mighty leaper while the jump is taking place; (b) find the force that the ground exerts on the froghopper during its jump; and (c) express the force in part (b) in terms of the froghopper’s weight.

. A loaded elevator with very worn cables has a total massof 2200 kg, and the cables can withstand a maximum tension of 28,000 N. (a) Draw the free-body force diagram for the elevator. Interms of the forces on your diagram, what is the net force on theelevator? Apply Newtons second law to the elevator and find themaximum upward acceleration for the elevator if the cables are notto break. (b) What would be the answer to part (a) if the elevatorwere on the moon, where

.. CP Jumping to the Ground. A 75.0-kg man steps off aplatform 3.10 m above the ground. He keeps his legs straight as hefalls, but at the moment his feet touch the ground his knees begin tobend, and, treated as a particle, he moves an additional 0.60 mbefore coming to rest. (a) What is his speed at the instant his feettouch the ground? (b) Treating him as a particle, what is his acceleration(magnitude and direction) as he slows down, if the accelerationis assumed to be constant? (c) Draw his free-body diagram(see Section 4.6). In terms of the forces on the diagram, what is thenet force on him? Use Newtons laws and the results of part (b) tocalculate the average force his feet exert on the ground while heslows down. Express this force in newtons and also as a multipleof his weight.

A 4.9-N hammer head is stopped from an initial downward velocity of 3.2 m/s in a distance of 0.45 cm by a nail in a pine board. In addition to its weight, there is a 15-N downward force on the hammer head applied by the person using the hammer. Assume that the acceleration of the hammer head is constant while it is in contact with the nail and moving downward. (a) Draw a free-body diagram for the hammer head. Identify the reaction force to each action force in the diagram. (b) Calculate the downward force \(\overrightarrow{\boldsymbol{F}}\) exerted by the hammer head on the nail while the hammer head is in contact with the nail and moving downward. (c) Suppose the nail is in hardwood and the distance the hammer head travels in coming to rest is only 0.12 cm. The downward forces on the hammer head are the same as in part (b). What then is the force \(\overrightarrow{\boldsymbol{F}}\) exerted by the hammer head on the nail while the hammer head is in contact with the nail and moving downward?

A uniform cable of weight w hangs vertically downward, supported by an upward force of magnitude w at its top end. What is the tension in the cable (a) at its top end; (b) at its bottom end; (c) at its middle? Your answer to each part must include a freebody diagram. (Hint: For each question choose the body to analyze to be a section of the cable or a point along the cable.) (d) Graph the tension in the rope versus the distance from its top end.

The two blocks in Fig. P4.54 are connected by a heavy uniform rope with a mass of 4.00 kg. An upward force of 200 N is applied as shown. (a) Draw three free-body diagrams: one for the 6.00-kg block, one for the 4.00-kg rope, and another one for the 5.00-kg block. For each force, indicate what body exerts that force. (b) What is the acceleration of the system? (c) What is the tension at the top of the heavy rope? (d) What is the tension at the midpoint of the rope?

An athlete whose mass is 90.0 kg is performing weight-lifting exercises. Starting from the rest position, he lifts, with constant acceleration, a barbell that weighs 490 N. He lifts the barbell a distance of 0.60 m in 1.6 s. (a) Draw a clearly labeled free-body force diagram for the barbell and for the athlete. (b) Use the diagrams in part (a) and Newtons laws to find the total force that his feet exert on the ground as he lifts the barbell.

A hot-air balloon consists of a basket, one passenger, and some cargo. Let the total mass be M. Even though there is an upward lift force on the balloon, the balloon is initially accelerating downward at a rate of (a) Draw a free-body diagram for the descending balloon. (b) Find the upward lift force in terms of the initial total weight Mg. (c) The passenger notices that he is heading straight for a waterfall and decides he needs to go up. What fraction of the total weight must he drop overboard so that the balloon accelerates upward at a rate of Assume that the upward lift force remains the same

Two boxes, A and B, are connected to each end of a light vertical rope, as shown in Fig. P4.57. A constant upward force is applied to box A. Starting from rest, box B descends 12.0 m in 4.00 s. The tension in the rope connecting the two boxes is 36.0 N. (a) What is the mass of box B? (b) What is the mass of box A?

The position of a 2.75 * 105 -N training helicopter under test is given by 10.020 m>s 3 2t 3 r n S 12.2 m>s2tn - 10.060 m>s 2 2t 2 k N Find the net force on the helicopter at t = 5.0 s

An object with mass m moves along the x-axis. Its position as a function of time is given by where A and B are constants. Calculate the net force on the object as a function of time

An object with mass m initially at rest is acted on by a force , where and are constants. Calculate the velocity of the object as a function of time.

A mysterious rocket-propelled object of mass 45.0 kg is initially at rest in the middle of the horizontal, frictionless surface of an ice-covered lake. Then a force directed east and with magnitude is applied. How far does the object travel in the first 5.00 s after the force is applied?

An object of mass m is at rest in equilibrium at the origin. At t = 0 a new force \(\vec{\boldsymbol{F}}(t)\) is applied that has components \(F_{x}(t)=k_{1}+k_{2} y\) \(F_{y}(t)=k_{3} t\) where \(k_1,\ k_2\) and \(k_3\) are constants. Calculate the position \(\vec{r}(t)\) and velocity \(\vec{v}(t)\) vectors as functions of time.

Problem 1DQ Can a body be in equilibrium when only one force acts on it? Explain.

Two forces have the same magnitude F. What is the angle between the two vectors if their sum has a magnitude of (a) \(2 F^{\prime}\)? (b) \(\sqrt{2} F\)? (c) zero? Sketch the three vectors in each case. Equation Transcription: 2F Text Transcription: 2 F^{\prime} \sqrt{2} F

Problem 2DQ A ball thrown straight up has zero velocity at its highest point. Is the ball in equilibrium at this point? Why or why not?

Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in Fig. E4.2. (a) Find the \(x \text { - and } y \text {-components }\) of each of the three pulls. (b) Use the components to find the magnitude and direction of the resultant of the three pulls. Equation Transcription: Text Transcription: x and y-components

Problem 3DQ A helium balloon hovers in midair, neither ascending nor descending. Is it in equilibrium? What forces act on it?

Problem 3E BIO Jaw Injury. Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of 5.00 N on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force?

Problem 4DQ When you fly in an airplane at night in smooth air, you have no sensation of motion, even though the plane may be moving at 800 km/h (500 mi/h). Why?

BIO Jaw Injury. Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of \(5.00 \mathrm{~N}\) on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force? Equation Transcription: 75.0° Text Transcription: 5.00 N 75.0°

If the two ends of a rope in equilibrium are pulled with forces of equal magnitude and opposite direction, why is the total tension in the rope not zero?

Problem 5E Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60.0°. If dog A exerts a force of 270 N and dog B exerts a force of 300 N. find the magnitude of the resultant force and the angle it makes with dog A’s rope.

Problem 6DQ You tie a brick to the end of a rope and whirl the brick around you in a horizontal circle. Describe the path of the brick after you suddenly let go of the rope.

Two forces,\(\vec{F}_{1} \text { and } \overrightarrow{F_{2}}\), act at a point. The magnitude of \(\vec{F}_{1}\) is 9.00 N, and its direction is 60.0? above the x-axis in the second quadrant. The magnitude of\(\vec{F}_{2}\) is 6.00 N, and its direction is \(53.1^{\circ}\) below the x-axis in the third quadrant. (a) What are the x- and y-components of the resultant force? (b) What is the magnitude of the resultant force? Equation Transcription: and 53.0° Text Transcription: F_1 and F_2 F_1 F_2 53.0^°

Problem 7DQ When a car stops suddenly, the passengers tend to move forward relative to their seats. Why? When a car makes a sharp turn, the passengers tend to slide to one side of the car. Why?

Problem 7E A 68.5-kg skater moving initially at 2.40 m/s on rough horizontal ice comes to rest uniformly in 3.52 s due to friction from the ice. What force does friction exert on the skater?

Problem 8DQ Some people say that the “force of inertia” (or “force of momentum”) throws the passengers forward when a car brakes sharply. What is wrong with this explanation?

Problem 8E You walk into an elevator, step onto a scale, and push the “up” button. You recall that your normal weight is 625 N. Draw a free-body diagram. (a) When the elevator has an upward acceleration of magnitude 2.50 m/s2, what does the scale read? (b) If you hold a 3.85-kg package by a light vertical string, what will be the tension in this string when the elevator accelerates as in part (a)?

Problem 9DQ A passenger in a moving bus with no windows notices that a ball that has been at rest in the aisle suddenly starts to move to-ward the rear of the bus. Think of two possible explanations, and devise a way to decide which is correct.

Problem 9E A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.0 N to the box and produces an acceleration of magnitude 3.00 m/s2, what is the mass of the box?

Problem 10DQ Suppose you chose the fundamental physical quantities to be force, length, and time instead of mass, length, and time. What would be the units of mass in terms of those fundamental quantities?

Problem 10E A dockworker applies a constant horizontal force of 80.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in 5.00 s. (a) What is the mass of the block of ice? (b) If the worker stops pushing at the end of 5.00 s, how far does the block move in the next 5.00 s?

Problem 11DQ Some of the ancient Greeks thought that the “natural state” of an object was to be at rest, so objects would seek their natural state by coming to rest if left alone. Explain why this incorrect view can actually seem quite plausible in the everyday world.

Problem 11E A hockey puck with mass 0.160 kg is at rest at the origin (x = 0) on the horizontal, frictionless surface of the rink. At time t = 0 a player applies a force of 0.250 N to the puck, parallel to the x -axis; she continues to apply this force until t = 2.00 s. (a) What are the position and speed of the puck at t = 2.00 s? (b) If the same force is again applied at t = 5.00 s, what are the position and speed of the puck at t = 7.00 s?

Problem 12DQ Why is the earth only approximately an inertial reference frame?

Problem 12E A crate with mass 32.5 kg initially at rest on a warehouse floor is acted on by a net horizontal force of 14.0 N. (a) What acceleration is produced? (b) How far does the crate travel in 10.0 s? (c) What is its speed at the end of 10.0 s?

Problem 13DQ Does Newton’s second law hold true for an observer in a van as it speeds up, slows down, or rounds a corner? Explain.

A \(\text { 4.50-kg }\) toy cart undergoes an acceleration in a straight line (the x-axis). The graph in Fig. E4.13 shows this acceleration as a function of time. (a) Find the maximum net force on this cart. When does this maximum force occur? (b) During what times is the net force on the cart a constant? (c) When is the net force equal to zero? Equation Transcription: Text Transcription: 4.50-kg

Some students refer to the quantity \(\overrightarrow{m a}\) as “the force of acceleration.” Is it correct to refer to this quantity as a force? If so, what exerts this force? If not, what is a better description of this quantity? Equation Transcription: Text Transcription: overrightarrow{m a}

A \(\text { 2.75-kg }\) cat moves in a straight line (the x-axis). Figure E4.14 shows a graph of the x-component of this cat’s velocity as a function of time. (a) Find the maximum net force on this cat. When does this force occur? (b) When is the net force on the cat equal to zero? (c) What is the net force at time 8.5 s? Equation Transcription: Text Transcription: 2.75-kg

Problem 15DQ The acceleration of a falling body is measured in an elevator that is traveling upward at a constant speed of 9.8 m/s. What value is obtained?

A small 8.00-kg rocket burns fuel that exerts a time-varying upward force on the rocket as the rocket moves upward from the launch pad. This force obeys the equation \(F=A+B t^{2}\). Measurements show that at t = 0, the force is 100.0 N, and at the end of the first 2.00 s, it is 150.0 N. (a) Find the constants A and B, including their SI units. (b) Find the net force on this rocket and its acceleration (i) the instant after the fuel ignites and (ii) 3.00 s after fuel ignition. (c) Suppose you were using this rocket in outer space, far from all gravity. What would its acceleration be 3.00 s after fuel ignition?

You can play catch with a softball in a bus moving with constant speed on a straight road, just as though the bus were at rest. Is this still possible when the bus is making a turn at constant speed on a level road? Why or why not?

Problem 16E An electron (mass = 9.11 X 10-31 kg) leaves one end of a TV picture tube with zero initial speed and travels in a straight line to the accelerating grid, which is 1.80 cm away. It reaches the grid with a speed of 3.00 X 106 m/s. If the accelerating force is constant, compute (a) the acceleration; (b) the time to reach the grid; and (c) the net force, in newtons. Ignore the gravitational force on the electron.

Problem 17DQ Students sometimes say that the force of gravity on an object is 9.8 m/s2. What is wrong with this view?

Superman throws a 2400-N boulder at an adversary. What horizontal force must Superman apply to the boulder to give it a horizontal acceleration of \(12.0 \mathrm{~m} / \mathrm{s}^{2}\)?

Problem 18DQ The head of a hammer begins to come loose from its wooden handle. How should you strike the handle on a concrete sidewalk to reset the head? Why does this work?

(a) An ordinary flea has a mass of \(210 \mu \mathrm{g}\). How many newtons does it weigh? (b) The mass of a typical froghopper is 12.3 mg. How many newtons does it weigh? (c) A house cat typically weighs 45 N. How many pounds does it weigh, and what is its mass in kilograms?

Problem 19DQ Why can it hurt your foot more to kick a big rock than a small pebble? Must the big rock hurt more? Explain.

Problem 19E At the surface of Jupiter’s moon Io, the acceleration due to gravity is g = 1.81 m/s2. A watermelon weighs 44.0 N at the surface of the earth. (a) What is the watermelon’s mass on the earth’s surface? (b) What would be its mass and weight on the surface of Io?

Problem 20DQ “It’s not the fall that hurts you; it’s the sudden stop at the bottom.” Translate this saying into the language of Newton’s laws of motion.

An astronaut’s pack weighs 17.5 N when she is on the earth but only 3.24 N when she is at the surface of a moon. (a) What is the acceleration due to gravity on this moon? (b) What is the mass of the pack on this moon?

A person can dive into water from a height of 10 m without injury, but a person who jumps off the roof of a 10-m-tall building and lands on a concrete street is likely to be seriously injured. Why is there a difference?

World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude \(15\mathrm{\ m}/\mathrm{s}^2\). How much horizontal force must a 55-kg sprinter exert on the starting blocks during a start to produce this acceleration? Which body exerts the force that propels the sprinter: the blocks or the sprinter herself?

Why are cars designed to crumple in front and back for safety? Why not for side collisions and rollovers?

Problem 22E A small car (mass 380 kg) is pushing a large truck (mass 900 kg) due east on a level road. The car exerts a horizontal force of 1200 N on the truck. What is the magnitude of the force that the truck exerts on the car?

Problem 23DQ When a bullet is fired from a rifle, what is the origin of the force that accelerates the bullet?

Boxes A and B are in contact on a horizontal, frictionless surface, as shown in Fig. E4.23. Box A has mass \(20.0 \mathrm{~kg}\)and box B has mass \(5.0 \mathrm{~kg}\). A horizontal force of 100 N is exerted on box A. What is the magnitude of the force that box A exerts on box B? Equation Transcription: Text Transcription: 20.0 kg 5.0 kg

Problem 24DQ When a string barely strong enough lifts a heavy weight, it can lift the weight by a steady pull; but if you jerk the string, it will break. Explain in terms of Newton’s laws of motion.

The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650 N. What are the reaction forces to these two forces? Is the passenger accelerating? If so, what are the magnitude and direction of the acceleration?

A large crate is suspended from the end of a vertical rope. Is the tension in the rope greater when the crate is at rest or when it is moving upward at constant speed? If the crate is traveling up-ward, is the tension in the rope greater when the crate is speeding up or when it is slowing down? In each case, explain in terms of Newton’s laws of motion.

Problem 25E A student of mass 45 kg jumps off a high diving board. What is the acceleration of the earth toward her as she accelerates toward the earth with an acceleration of 9.8 m/s? Use 6.0 X 1024 kg for the mass of the earth, and assume that the net force on the earth is the force of gravity she exerts on it.

Problem 26DQ Which feels a greater pull due to the earth’s gravity: a 10-kg stone or a 20-kg stone? If you drop the two stones, why doesn’t the 20-kg stone fall with twice the acceleration of the 10-kg stone? Explain.

Problem 26E An athlete throws a ball of mass m directly upward, and it feels no appreciable air resistance. Draw a free-body diagram of this ball while it is free of the athlete’s hand and (a) moving upward; (b) at its highest point; (c) moving downward. (d) Repeat parts (a), (b), and (c) if the athlete throws the ball at a 60° angle above the horizontal instead of directly upward.

Problem 27DQ Why is it incorrect to say that 1.0 kg equals 2.2 lb?

Two crates, A and B, sit at rest side by side on a frictionless horizontal surface. The crates have masses \(m_A\) and \(m_B\). A horizontal force \(\overrightarrow{\boldsymbol{F}}\) is applied to crate A and the two crates move off to the right. (a) Draw clearly labeled free-body diagrams for crate A and for crate B. Indicate which pairs of forces, if any, are third law action–reaction pairs. (b) If the magnitude of force \(\overrightarrow{\boldsymbol{F}}\) is less than the total weight of the two crates, will it cause the crates to move? Explain.

A horse is hitched to a wagon. Since the wagon pulls back on the horse just as hard as the horse pulls on the wagon, why doesn’t the wagon remain in equilibrium, no matter how hard the horse pulls?

A person pulls horizontally on block B in Fig. E4.28, causing both blocks to move together as a unit. While this system is moving, make a carefully labeled free-body diagram of block A if (a) the table is frictionless and (b) there is friction between block B and the table and the pull is equal to the friction force on block B due to the table.

Problem 29DQ True or false? You exert a push P on an object and it pushes back on you with a force F. If the object is moving at constant velocity, then F is equal to P, but if the object is being accelerated, then P must be greater than F.

Problem 29E A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labeled free-body diagram for the ball if (a) the train has a uniform velocity and (b) the train is speeding up uniformly. Is the net force on the ball zero in either case? Explain.

A large truck and a small compact car have a head-on collision. During the collision, the truck exerts a force \(\vec{F}_{\text {Ton } \mathrm{C}}\) on the car, and the car exerts a force \(\vec{F}_{\operatorname{Con} T}\)on the truck. Which force has the larger magnitude, or are they the same? Does your answer depend on how fast each vehicle was moving before the collision? Why or why not? Equation Transcription: Text Transcription: \vec{F}_{\text {Ton } \{C} \vec{F}_{\operatorname{Con} T}

Problem 30E CP A .22-caliber rifle bullet traveling at 350 m/s strikes a large tree and penetrates it to a depth of 0.130 m. The mass of the bullet is 1.80 g. Assume a constant retarding force. (a) How much time is required for the bullet to stop? (b) What force, in newtons, does the tree exert on the bullet?

Problem 31DQ When a car comes to a stop on a level highway, what force causes it to slow down? When the car increases its speed on the same highway, what force causes it to speed up? Explain.

Problem 31E A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force F = 40.0 N that is directed at an angle of 37.0o below the horizontal, and the chair slides along the floor. (a) Draw a clearly labeled free-body diagram for the chair. (b) Use your diagram and Newton’s laws to calculate the normal force that the floor exerts on the chair.

A small compact car is pushing a large van that has broken down, and they travel along the road with equal velocities and accelerations. While the car is speeding up, is the force it exerts on the van larger than, smaller than, or the same magnitude as the force the van exerts on it? Which object, the car or the van, has the larger net force on it, or are the net forces the same? Explain.

Problem 32E A skier of mass 65.0 kg is pulled up a snow-covered slope at constant speed by a tow rope that is parallel to the ground. The ground slopes upward at a constant angle of 26.0° above the horizontal, and you can ignore friction. (a) Draw a clearly labeled free-body diagram for the skier. (b) Calculate the tension in the tow rope.

Problem 33DQ Consider a tug-of-war between two people who pull in opposite directions on the ends of a rope. By Newton’s third law, the force that A exerts on B is just as great as the force that B exerts on A. So what determines who wins? (Hint: Draw a free-body diagram showing all the forces that act on each person.)

A 4.80-kg bucket of water is accelerated upward by a cord of negligible mass whose breaking strength is 75.0 N. If the bucket starts from rest, what is the minimum time required to raise the bucket a vertical distance of 12.0 m without breaking the cord?

Problem 34DQ On the moon, g = 1.62 m/s2. If a 2-kg brick drops on your foot from a height of 2 m, will this hurt more, or less, or the same if it happens on the moon instead of on the earth? Explain. If a 2-kg brick is thrown and hits you when it is moving horizontally at 6 m/s, will this hurt more, less, or the same if it happens on the moon instead of on the earth? Explain. (On the moon, assume that you are inside a pressurized structure, so you are not wearing a spacesuit.)

A large box containing your new computer sits on the bed of your pickup truck. You are stopped at a red light. The light turns green and you stomp on the gas and the truck accelerates. To your horror, the box starts to slide toward the back of the truck. Draw clearly labeled free-body diagrams for the truck and for the box. Indicate pairs of forces, if any, that are third-law action– reaction pairs. (The bed of the truck is not frictionless.)

Problem 35DQ A manual for student pilots contains this passage: “When an airplane flies at a steady altitude, neither climbing nor descending, the upward lift force from the wings equals the plane’s weight. When the plane is climbing at a steady rate, the upward lift is greater than the weight; when the plane is descending at a steady rate, the upward lift is less than the weight.” Are these statements correct? Explain.

Two horses pull horizontally on ropes attached to a stump. The two forces \(\vec{F}_{1} \text { and } \vec{F}_{2}\) that they apply to the stump are such that the net (resultant) force \(\vec{R}\)has a magnitude equal to that of \(\vec{F}_{1}\) and makes an angle of \(90^{\circ}\) with \(\vec{F}_{1}\). Let \(F_{1}=1300 \mathrm{~N}\) and \(R=1300 \mathrm{~N}\) also. Find the magnitude of \(\vec{F}_{2}\) and its direction (relative to \(\vec{F}_{1}\)). Equation Transcription: and 90° Text Transcription: vec{F}_{1} \text { and } \vec{F}_{2} \vec{R} \vec{F}_{1} 90^{\circ} F_{1}=1300 \{~N} R=1300 \{~N} \vec{F}_{2} \vec{F}_{1}

If your hands are wet and no towel is handy, you can remove some of the excess water by shaking them. Why does this work?

Problem 36P CP You have just landed on Planet X. You release a 100-g ball from rest from a height of 10.0 m and measure that it takes 3.40 s to reach the ground. Ignore any force on the ball from the atmosphere of the planet. How much does the 100-g ball weigh on the surface of Planet X?

Problem 37DQ If you squat down (such as when you examine the books on a bottom shelf) and then suddenly get up, you may temporarily feel light-headed. What do Newton’s laws of motion have to say about why this happens?

Two adults and a child want to push a wheeled cart in the direction marked \(x\) in Fig. P4.37. The two adults push with horizontal forces \(\vec{F}_{1} \text { and } \vec{F}_{2}\) as shown in the figure. (a) Find the magnitude and direction of the smallest force that the child should exert. You can ignore the effects of friction. (b) If the child exerts the minimum force found in part (a), the cart accelerates at \(2.0 \mathrm{~m} / \mathrm{s}^{2}\) in the \(+x\)-direction. What is the weight of the cart? Equation Transcription: and Text Transcription: x \vec{F}_{1} \text { and } \vec{F}_{2} 2.0 \{~m} / \{s}^{2} +x

Problem 38DQ When a car is hit from behind, the occupants may experience whiplash. Use Newton’s laws of motion to explain what causes this result.

An oil tanker’s engines have broken down, and the wind is blowing the tanker straight toward a reef at a constant speed of 1.5 m/s (Fig. P4.38). When the tanker is 500 m from the reef, the wind dies down just as the engineer gets the engines going again. The rudder is stuck, so the only choice is to try to accelerate straight backward away from the reef. The mass of the tanker and cargo is \(3.6 \times 10^{7} \mathrm{~kg}\), and the engines produce a net horizontal force of \(8.0 \times 10^{4} \mathrm{~N}\) on the tanker. Will the ship hit the reef? If it does, will the oil be safe? The hull can withstand an impact at a speed of \(0.2 \mathrm{~m} / \mathrm{s}\) or less. You can ignore the retarding force of the water on the tanker’s hull. Equation Transcription: Text Transcription: 3.6 times 10^7kg 8.0 times 104 N v =1.5 m/s 0.2 m/s 500 m

Problem 39DQ In a head-on auto collision, passengers who are not wearing seat belts may be thrown through the windshield. Use Newton’s laws of motion to explain why this happens.

Problem 39P CP BIO A Standing Vertical Jump. Basketball player Darrell Griffith is on record as attaining a standing vertical jump of 1.2 m (4 ft). (This means that he moved upward by 1.2 m after his feet left the floor.) Griffith weighed 890 N (200 lb). (a) What was his speed as he left the floor? (b) If the time of the part of the jump before his feet left the floor was 0.300 s, what was his aver-age acceleration (magnitude and direction) while he pushed against the floor? (c) Draw his free-body diagram. In terms of the forces on the diagram, what was the net force on him? Use Newton’s laws and the results of part (b) to calculate the average force he applied to the ground.

Problem 40DQ In a head-on collision between a compact 1000-kg car and a large 2500-kg car, which one experiences the greater force? Explain. Which one experiences the greater acceleration? Explain why. Why are passengers in the small car more likely to be injured than those in the large car, even when the two car bodies are equally strong?

Problem 40P CP An advertisement claims that a particular automobile can “stop on a dime.” What net force would be necessary to stop a 850-kg automobile traveling initially at 45.0 km/h in a distance equal to the diameter of a dime, 1.8 cm?

Solution 41P Suppose you are in a rocket with no windows, traveling in deep space far from other objects. Without looking outside the rocket or making any contact with the outside world, explain how you could determine whether the rocket is (a) moving forward at a constant 80% of the speed of light and (b) accelerating in the forward direction.

Problem 41P BIO Human Biomechanics. The fastest pitched baseball was measured at 46 m/s. A typical baseball has a mass of 145 g. If the pitcher exerted his force (assumed to be horizontal and constant) over a distance of 1.0 m, (a) what force did he produce on the ball during this record-setting pitch? (b) Draw free-body diagrams of the ball during the pitch and just after it left the pitcher’s hand.

Human Biomechanics. The fastest served tennis ball, served by “Big Bill” Tilden in 1931, was measured at 73.14 m/s. The mass of a tennis ball is 57 g, and the ball is typically in contact with the tennis racquet for 30.0 ms, with the ball starting from rest. Assuming constant acceleration, (a) what force did Big Bill’s tennis racquet exert on the tennis ball if he hit it essentially horizontally? (b) Draw free-body diagrams of the tennis ball during the serve and just after it moved free of the racquet.

Two crates, one with mass \(4.00 \mathrm{~kg}\) and the other with mass \(6.00 \mathrm{~kg}\), sit on the frictionless surface of a frozen pond, connected by a light rope (Fig. P4.43). A woman wearing golf shoes (so she can get traction on the ice) pulls horizontally on the \(6.00-\mathrm{kg}\) crate with a force F that gives the crate an acceleration of \(2.50 \mathrm{~m} / \mathrm{s}^{2}\). (a) What is the acceleration of the \(\text { 4.00-kg }\) crate? (b) Draw a free-body diagram for the \(\text { 4.00-kg }\) crate. Use that diagram and Newton’s second law to find the tension T in the rope that connects the two crates. (c) Draw a free-body diagram for the \(6.00-\mathrm{kg}\) crate. What is the direction of the net force on the \(6.00-\mathrm{kg}\) crate? Which is larger in magnitude, force T or force F? (d) Use part (c) and Newton’s second law to calculate the magnitude of the force F. Equation Transcription: Text Transcription: 4.00 kg 6.00 kg 6.00-kg 2.50 m/s2 4.00- kg 4.00- kg 6.00-kg 6.00-kg

An astronaut is tethered by a strong cable to a spacecraft. The astronaut and her spacesuit have a total mass of \(105 \mathrm{~kg}\), while the mass of the cable is negligible. The mass of the spacecraft is \(9.05 \times 10^{4} \mathrm{~kg}\). The spacecraft is far from any large astronomical bodies, so we can ignore the gravitational forces on it and the astronaut. We also assume that both the spacecraft and the astronaut are initially at rest in an inertial reference frame. The astronaut then pulls on the cable with a force of 80.0 N. (a) What force does the cable exert on the astronaut? (b) Since \(\Sigma \vec{F}=m \vec{a}\)how can a “massless” (m = 0) cable exert a force? (c) What is the astronaut’s acceleration? (d) What force does the cable exert on the spacecraft? (e) What is the acceleration of the spacecraft? Equation Transcription: Text Transcription: 105 kg 9.05x104kg Sigma \vec F=ma

Problem 45P CALC To study damage to aircraft that collide with large birds, you design a test gun that will accelerate chicken-sized objects so that their displacement along the gun barrel is given by x = (9.0 X 103 m/s2)t2 – (8.0 X 104 m/s3)t3. The object leaves the end of the barrel at t = 0.025 s. (a) How long must the gun barrel be? (b) What will be the speed of the objects as they leave the end of the barrel? (c) What net force must be exerted on a 1.50-kg object at (i) t = 0 and (ii) t = 0.025 s?

Problem 46P A spacecraft descends vertically near the surface of Planet X. An upward thrust of 25.0 kN from its engines slows it down at a rate of 1.20 m/s2, but it speeds up at a rate of 0.80 m/s2 with an upward thrust of 10.0 kN. (a) In each case, what is the direction of the acceleration of the spacecraft? (b) Draw a free-body diagram for the spacecraft. In each case, speeding up or slowing down, what is the direction of the net force on the spacecraft? (c) Apply Newton’s second law to each case, slowing down or speeding up, and use this to find the spacecraft’s weight near the surface of Planet X.

Problem 47P CP A 6.50-kg instrument is hanging by a vertical wire inside a spaceship that is blasting off from rest at the earth’s sur-face. This spaceship reaches an altitude of 276 m in 15.0 s with constant acceleration. (a) Draw a free-body diagram for the instrument during this time. Indicate which force is greater. (b) Find the force that the wire exerts on the instrument.

Problem 48P Suppose the rocket in Problem is coming in for a vertical landing instead of blasting off. The captain adjusts the engine thrust so that the magnitude of the rocket’s acceleration is the same as it was during blast-off. Repeat parts (a) and (b). A 6.50 kg instrument is hanging by a vertical wire inside a space ship that is blasting offal the surface of the earth. This ship starts from rest and reaches an altitude of 276 m in 15.0 s with constant acceleration. (a) Draw a free-body diagram for the instrument during this time. Indicate which force is greater. (b) Find the force that the wire exerts on the instrument.

Insect Dynamics. The froghopper (Philaenus spumarius), the champion leaper of the insect world, has a mass of 12.3 mg and leaves the ground (in the most energetic jumps) at 4.0 m/s from a vertical start. The jump itself lasts a mere 1.0 ms before the insect is clear of the ground. Assuming constant acceleration, (a) draw a free-body diagram of this mighty leaper while the jump is taking place; (b) find the force that the ground exerts on the froghopper during its jump; and (c) express the force in part (b) in terms of the froghopper’s weight.

Problem 50P A loaded elevator with very worn cables has a total mass of 2200 kg, and the cables can withstand a maximum tension of 28,000 N. (a) Draw the free-body force diagram for the elevator. In terms of the forces on your diagram, what is the net force on the elevator? Apply Newton’s second law to the elevator and find the maximum upward acceleration for the elevator if the cables are not to break. (b) What would be the answer to part (a) if the elevator were on the moon, where g = 1.62 m/s2?

Problem 51P CP Jumping to the Ground. A 75.0-kg man steps off a platform 3.10 m above the ground. He keeps his legs straight as he falls, but his knees begin to bend at the moment his feet touch the ground; treated as a particle, he moves an additional 0.60 m before coming to rest. (a) What is his speed at the instant his feet touch the ground? (b) If we treat the man as a particle, what is his acceleration (magnitude and direction) as he slows down, if the acceleration is assumed to be constant? (c) Draw his free- body diagram. In terms of the forces on the diagram, what is the net force on him? Use Newton’s laws and the results of part (b) to calculate the average force his feet exert on the ground while he slows down. Express this force both in newtons and as a multiple of his weight.

A 4.9-N hammer head is stopped from an initial downward velocity of \(3.2 \mathrm{~m} / \mathrm{s}\) in a distance of \(0.45 \mathrm{~cm}\) by a nail in a pine board. In addition to its weight, there is a 15-N downward force on the hammer head applied by the person using the hammer. Assume that the acceleration of the hammer head is constant while it is in contact with the nail and moving downward. (a) Draw a free-body diagram for the hammer head. Identify the reaction force to each action force in the diagram. (b) Calculate the downward force (\vec{F}\) exerted by the hammer head on the nail while the hammer head is in contact with the nail and moving downward. (c) Suppose the nail is in hardwood and the distance the hammer head travels in coming to rest is only 0.12 cm. The downward forces on the hammer head are the same as in part (b). What then is the force (\vec{F}\) exerted by the hammer head on the nail while the hammer head is in contact with the nail and moving downward? Equation Transcription: Text Transcription: 3.2 m/s 0.45 cm vec F Vec F

Problem 53P A uniform cable of weight w hangs vertically downward, supported by an upward force of magnitude w at its top end. What is the tension in the cable (a) at its top end; (b) at its bottom end; (c) at its middle? Your answer to each part must include a free-body diagram. (Hint: For each question choose the body to analyze to be a section of the cable or a pomt along the cable.) (d) Graph the tension in the rope versus the distance from its top end.

The two blocks in Fig. P4.54 are connected by a heavy uniform rope with a mass of \(4.00 \ \mathrm{~kg}\). An upward force of 200 N is applied as shown. (a) Draw three free-body diagrams: one for the \(6.00-\ \mathrm{~kg}\) block, one for the \(4.00-\ \mathrm{~kg}\) rope, and another one for the \(5.00-\ \mathrm{~kg}\) block. For each force, indicate what body exerts that force. (b) What is the acceleration of the system? (c) What is the tension at the top of the heavy rope? (d) What is the tension at the midpoint of the rope?

Problem 55P An athlete whose mass is 90.0 kg is performing weight-lifting exercises. Starting from the rest position, he lifts, with constant acceleration, a barbell that weighs 490 N. He lifts the barbell a distance of 0.60 m in 1.6 s. (a) Draw a clearly labeled free-body force diagram for the barbell and for the athlete. (b) Use the diagrams in part (a) and Newton’s laws to find the total force that his feet exert on the ground as he lifts the barbell.

Problem 56P A hot-air balloon consists of a basket, one passenger, and some cargo. Let the total mass be M. Even though there is an upward lift force on the balloon, the balloon is initially accelerating downward at a rate of g/3. (a) Draw a free-body diagram for the descending balloon. (b) Find the upward lift force in terms of the initial total weight Mg. (c) The passenger notices that he is heading straight for a waterfall and decides he needs to go up. What fraction of the total weight must he drop overboard so that the balloon accelerates upward at a rate of g/2? Assume that the upward lift force remains the same.

Two boxes, A and B, are connected to each end of a light vertical rope, as shown in Fig. P4.57. A constant upward force \(F=80.0 \mathrm{~N}\) is applied to box A. Starting from rest, box B descends 12.0 m in 4.00 s. The tension in the rope connecting the two boxes is 36.0 N. (a) What is the mass of box B? (b) What is the mass of box A? Equation Transcription: Text Transcription: F=80.0 N

The position of a \(2.75 \times 10^{5}-\mathrm{N}\) training helicopter under test is given by \(\overrightarrow{\boldsymbol{r}}=\left(0.020 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3} \hat{\boldsymbol{\imath}}+(2.2 \mathrm{~m} / \mathrm{s}) t \hat{\boldsymbol{j}}-\left(0.060 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2} \hat{\boldsymbol{k}}\). Find the net force on the helicopter at t = 5.0 s.

Problem 59P An object with mass m moves along the x-axis. Its position as a function of time is given by, x(t) = At ? Bt3, where A and B are constants. Calculate the net force on the object as a function of time.

An object with mass m initially at rest is acted on by a force \(\vec{\boldsymbol{F}}=k_{1} \hat{\boldsymbol{\imath}}+k_{2} t^{3} \hat{\boldsymbol{j}}\), where \(k_{1}\) and \(k_{2}\) are constants. Calculate the velocity \(\vec{\boldsymbol{v}}(t)\) of the object as a function of time.

Problem 61P CP CALC A mysterious rocket-propelled object of mass 45.0 kg is initially at rest in the middle of the horizontal, friction-less surface of an ice-covered lake. Then a force directed east and with magnitude F(t) = (16.8 N/s) t is applied. How far does the object travel in the first 5.00 s after the force is applied?

An object of mass m is at rest in equilibrium at the origin. At t = 0 a new force \(\vec{F}\) (t) is applied that has components \( F_{\mathrm{x}}(t)=k_{1}+k_{2} y\) \(F_{\mathrm{y}}(t)=k_{3} t\) where \(k_{1}, k_{2}, \text { and } k_{3}\) are constants. Calculate the position (t) and velocity (t) vectors as functions of time. Equation Transcription: Text Transcription: Vec F Fx(t)=k_1+k_2y F_y(t)=k_3t k_1, k_2 k_3 Vec r Vec v