Its not the fall that hurts you; its the sudden stop at

Can a body be in equilibrium when only one force acts on it? Explain

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

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

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?

If the two ends of a rope in equilibrium are pulled with forces of equal magnitude and opposite directions, why isnt the total tension in the rope zero?

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

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?

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?

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 toward the rear of the bus. Think of two possible explanations, and devise a way to decide which is correct

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?

Why is the earth only approximately an inertial reference frame?

Does Newtons second law hold true for an observer in a van as it speeds up, slows down, or rounds a corner? Explain.

Some students refer to the quantity ma S 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?

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?

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?

Students sometimes say that the force of gravity on an object is 9.8 m>s 2 . What is wrong with this view?

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

Its not the fall that hurts you; its the sudden stop at the bottom. Translate this saying into the language of Newtons laws of motion.

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?

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

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 Newtons laws of motion

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 Newtons laws of motion

Which feels a greater pull due to the earths gravity: a 10-kg stone or a 20-kg stone? If you drop the two stones, why doesnt the 20-kg stone fall with twice the acceleration of the 10-kg stone? Explain.

Why is it incorrect to say that 1.0 kg equals 2.2 lb

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 doesnt the wagon remain in equilibrium, no matter how hard the horse pull

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

A large truck and a small compact car have a head-on collision. During the collision, the truck exerts a force F S T on C on the car, and the car exerts a force F S C on 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?

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.

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 vehicle has the larger net force on it, or are the net forces the same? Explain.

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.)

Boxes A and B are in contact on a horizontal, frictionless surface. You push on box A with a horizontal 100-N force (Fig. Q4.31). Box A weighs 150 N, and box B weighs 50 N. Is the force that box A exerts on box B equal to 100 N, greater than 100 N, or less than 100 N? Explain

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 planes 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.

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?

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 Newtons laws of motion have to say about why this happens?

When a car is hit from behind, the occupants may experience whiplash. Use Newtons laws of motion to explain what causes this result.

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

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?

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.

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60.0. If Rover exerts a force of 270 N and Fido exerts a force of 300 N, find the magnitude of the resultant force and the angle it makes with Rovers rope.

To extricate an SUV stuck in the mud, workmen 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.

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 mover’s truck. The ramp has a slope angle of \(20.0^{\circ}\), and the man pulls upward with a force \(\overrightarrow{\boldsymbol{F}}\) whose direction makes an angle of \(30.0^{\circ}\) with the ramp (Fig. E4.4). (a) How large a force \(\overrightarrow{\boldsymbol{F}}\) is necessary for the component \(F_{x}\) parallel to the ramp to be 90.0 N? (b) How large will the component Fy perpendicular to the ramp be then?

Forces F S 1 and F S 2 act at a point. The magnitude of F S 1 is 9.00 N, and its direction is 60.0 above the x-axis in the second quadrant. The magnitude of F S 2 is 6.00 N, and its direction is 53.1 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?

An electron (mass = 9.11 * 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 * 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

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?

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 \(2.50 \ \mathrm {m/s}^ 2\) , 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)?

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 2.20 m>s 2 , what is the mass of the box?

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 \(x=\left(9.0 \times 10^{3} \mathrm{\ m} / \mathrm{s}^{2}\right) t^{2}-\left(8.0 \times 10^{4} \mathrm{\ m} / \mathrm{s}^{3}\right) t^{3}\). 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?

. 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?

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?

A 4.50-kg experimental 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 cats 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 timevarying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation F = A + Bt2 . 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 the fuel ignites. (c) Suppose that you were using this rocket in outer space, far from all gravity. What would its acceleration be 3.00 s after fuel ignition?

An astronauts 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?

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 m>s 2 ?

(a) An ordinary flea has a mass of 210 mg. 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 Jupiter’s moon Io, the acceleration due to gravity is \(g=1.81\mathrm{\ m}/\mathrm{s}^2\). 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?

A small car of mass 380 kg is pushing a large truck of mass 900 kg due east on a level road. The car exerts a horizontal force of 1600 N on the truck. What is the magnitude of the force that the truck exerts on the car?

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

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?

Boxes A and B are in contact on a horizontal, frictionless surface (Fig. E4.23). Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 250 N is exerted on box A. What is the magnitude of the force that box A exerts on box B?

Boxes A and B are in contact on a horizontal, frictionless surface (Fig. E4.23). Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 250 N is exerted on box A. What is the magnitude of the force that box A exerts on box B?

Crates A and B sit at rest side by side on a frictionless horizontal surface. They have masses mA and mB, respectively. When a horizontal force F S is applied to crate A, 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 actionreaction pairs. (b) If the magnitude of F S is less than the total weight of the two crates, will it cause the crates to move? Explain

You pull horizontally on block B in Fig. E4.26, causing both blocks to move together as a unit. For this moving system, 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 in magnitude 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.

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?

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 37.0 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.

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 5.60-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?

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?

Two adults and a child want to push a wheeled cart in the direction marked x in Fig. P4.33. The two adults push with horizontal forces F S 1 and F S 2 as shown. (a) Find the magnitude and direction of the smallest force that the child should exert. Ignore the effects of friction. (b) If the child exerts the minimum force found in part (a), the cart accelerates at 2.0 m>s 2 in the +x-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 1.5 m>s (Fig. P4.34). 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 * 107 kg, and the engines produce a net horizontal force of 8.0 * 104 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 m>s or less. 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 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 average 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 Newtons 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 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?

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 pitchers 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, which starts from rest, is typically in contact with the tennis racquet for 30.0 ms. Assuming constant acceleration, (a) what force did Big Bills tennis racquet exert on the ball if he hit it essentially horizontally? (b) Draw free-body diagrams of the 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. P4.39). A woman wearing golf shoes (for traction) pulls horizontally on the 6.00-kg crate with a force F that gives the crate an acceleration of 2.50 m>s 2 . (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, T or F? (d) Use part (c) and Newtons second law to calculate the magnitude of F

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. P4.39). A woman wearing golf shoes (for traction) pulls horizontally on the 6.00-kg crate with a force F that gives the crate an acceleration of 2.50 m>s 2 . (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, T or F? (d) Use part (c) and Newtons second law to calculate the magnitude of F

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 \(x=\left(9.0\times 10^3\mathrm{\ m}/\mathrm{s}^2\right)t^2-\left(8.0\times 10^4\mathrm{\ m}/\mathrm{s}^3\right)t^3\). 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?

A 6.50-kg instrument is hanging by a vertical wire inside a spaceship that is blasting off from rest at the earths surface. 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.

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 during the jump; (b) find the force that the ground exerts on the froghopper during the jump; and (c) express the force in part (b) in terms of the froghoppers weight

. 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 Newtons 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>s 2 ?

After an annual checkup, you leave your physicians office, where you weighed 683 N. You then get into an elevator that, conveniently, has a scale. Find the magnitude and direction of the elevators acceleration if the scale reads (a) 725 N and (b) 595 N.

A nail in a pine board stops a 4.9-N hammer head from an initial downward velocity of 3.2 m>s in a distance of 0.45 cm. In addition, the person using the hammer exerts a 15-N downward force on it. 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 for each action force in the diagram. (b) Calculate the downward force F S exerted by the hammer head on the nail while the hammer head is in contact with the nail and moving downward. (c) Suppose that 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 F S exerted by the hammer head on the nail while the hammer head is in contact with the nail and moving downward?

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 freebody diagram. In terms of the forces on the diagram, what is the net force on him? Use Newtons 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

The two blocks in Fig. P4.48 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?

Boxes A and B are connected to each end of a light vertical rope (Fig. P4.49). A constant upward force F = 80.0 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. What are the masses of (a) box B, (b) box A?

Extraterrestrial Physics. You have landed on an unknown planet, Newtonia, and want to know what objects weigh there. When you push a certain tool, starting from rest, on a frictionless horizontal surface with a 12.0-N force, the tool moves 16.0 m in the first 2.00 s. You next observe that if you release this tool from rest at 10.0 m above the ground, it takes 2.58 s to reach the ground. What does the tool weigh on Newtonia, and what does it weigh on Earth?

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 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?

The position of a training helicopter (weight 2.75 * 105 N) in a test is given by nr = (0.020 m>s 3 )t 3nd + (2.2 m>s) tne (0.060 m>s 2 )t 2 k n. Find the net force on the helicopter at t = 5.0 s.

The table* gives automobile performance data for a few types of cars: (a) During an acceleration of 0 to 60 mph, which car has the largest average net force acting on it? The smallest? (b) During this acceleration, for which car would the average net force on a 72.0-kg passenger be the largest? The smallest? (c) When the Ferrari F430 accelerates from 0 to 100 mph in 8.6 s, what is the average net force acting on it? How does this net force compare with the average net force during the acceleration from 0 to 60 mph? Explain why these average net forces might differ. (d) Discuss why a car has a top speed. What is the net force on the Ferrari F430 when it is traveling at its top speed, 196 mph?

An 8.00-kg box sits on a level floor. You give the box a sharp push and find that it travels 8.22 m in 2.8 s before coming to rest again. (a) You measure that with a different push the box traveled 4.20 m in 2.0 s. Do you think the box has a constant acceleration as it slows down? Explain your reasoning. (b) You add books to the box to increase its mass. Repeating the experiment, you give the box a push and measure how long it takes the box to come to rest and how far the box travels. The results, including the initial experiment with no added mass, are given in the table:Added Mass (kg) Distance (m) Time (s) 0 8.22 2.8 3.00 10.75 3.2 7.00 9.45 3.0 12.0 7.10 2.6 In each case, did your push give the box the same initial speed? What is the ratio between the greatest initial speed and the smallest initial speed for these four cases? (c) Is the average horizontal force f exerted on the box by the floor the same in each case? Graph the magnitude of force f versus the total mass m of the box plus its contents, and use your graph to determine an equation for f as a function of m.

You are a Starfleet captain going boldly where no man has gone before. You land on a distant planet and visit an engineering testing lab. In one experiment a short, light rope is attached to the top of a block and a constant upward force F is applied to the free end of the rope. The block has mass m and is initially at rest. As F is varied, the time for the block to move upward 8.00 m is measured. The values that you collected are given in the table: F (N) Time (s) 250 3.3 300 2.2 350 1.7 400 1.5 450 1.3 500 1.2 (a) Plot F versus the acceleration a of the block. (b) Use your graph to determine the mass m of the block and the acceleration of gravity g at the surface of the planet. Note that even on that planet, measured values contain some experimental error.

An object of mass m is at rest in equilibrium at the origin. At t = 0 a new force F S (t) is applied that has components Fx(t) = k1 + k2y Fy(t) = k3t where k1, k2, and k3 are constants. Calculate the position r S (t) and velocity v S (t) vectors as functions of time.

What is the magnitude of the average force that her neck exerts on her head during the landing? (a) 0 N; (b) 60 N; (c) 120 N; (d) 180 N.

Compared with the force her neck exerts on her head during the landing, the force her head exerts on her neck is (a) the same; (b) greater; (c) smaller; (d) greater during the first half of the landing and smaller during the second half of the landing.

While the dancer is in the air and holding a fixed pose, what is the magnitude of the force her neck exerts on her head? (a) 0 N; (b) 60 N; (c) 120 N; (d) 180 N

The forces on a dancer can be measured directly when a dancer performs a jump on a force plate that measures the force between her feet and the ground. A graph of force versus time throughout a vertical jump performed on a force plate is shown in Fig. P4.60. What is happening at 0.4 s? The dancer is (a) bending her legs so that her body is accelerating downward; (b) pushing her body up with her legs and is almost ready to leave the ground; (c) in the air and at the top of her jump; (d) landing and her feet have just touched the ground.