MULTISTEP A 40.0-kg object supported by a vertical rope.

While on a very smooth level transcontinental plane flight, your coffee cup sits motionless on your tray. Are there forces acting on the cup? If so, how do they differ from the forces that would be acting on the cup if it sat on your kitchen table at home?

You are passing another car on a highway and determine that, relative to you, the car you pass has an acceleration toward the west. However, the driver of the other car is maintaining a constant speed and direction relative to the road. Is the reference frame of your car an inertial one? If not, in which direction (east or west) is your car accelerating relative to the other car?

CONTEXT-RICH You are riding in a limousine that has opaque windows that do not allow you to see outside. The car is on a flat horizontal plain, so the car can accelerate by speeding up, slowing down, or turning. Equipped with just a small heavy object on the end of a string, how can you use it to determine if the limousine is changing either speed or direction? Can you determine the limousines velocity?

If only a single nonzero force acts on an object, does the object accelerate relative to all inertial reference frames? Is it possible for such an object to have zero velocity in some inertial reference frame and not in another? If so, give a specific example. SSM

A baseball is acted upon by a single known force. From this information alone, can you tell in which direction the baseball is moving relative to some reference frame? Explain.

A truck moves directly away from you at constant velocity (as observed by you while standing in the middle of the road). It follows that (a) no forces act on the truck, (b) a constant net force acts on the truck in the direction of its velocity, (c) the net force acting on the truck is zero, (d) the net force acting on the truck is its weight.

ENGINEERING APPLICATION Several space probes have been launched that are now far out in space. Pioneer 10, for example, was launched in the 1970s and is still moving away from the Sun and its planets. Is the mass of Pioneer 10 changing? Which of the known fundamental forces continue to act on it? Does it have a net force on it?

ENGINEERING APPLICATION Astronauts in apparent weightlessness during their stay on the International Space Station must carefully monitor their masses because significant loss of body mass is known to cause serious medical problems. Give an example of how you might design equipment to measure the mass of an astronaut on the orbiting space station.

CONTEXT-RICH You are riding in an elevator. Describe two situations in which your apparent weight is greater than your true weight. SSM

Suppose you are in a train moving at constant velocity relative to the ground. You toss a ball to your friend several seats in front of you. Use Newtons second law to explain why you cannot use your observations of the tossed ball to determine the trains velocity relative to the ground.

Explain why, of the fundamental interactions, gravitational interaction is the main concern in our everyday lives. One other on this list also plays an increasingly significant role in our rapidly advancing technology. Which one is that? Why are the others not obviously important?

Give an example of an object that has three forces acting on it, and (a) accelerates, (b) moves at constant (nonzero) velocity, and (c) remains at rest.

Suppose a block of mass rests on a block of mass and the combination rests on a table as shown in Figure 4-33. Tell the name of the force and its category (contact versus actionat- a-distance) for each of the following forces: (a) force exerted by on (b) force exerted by on (c) force exerted by on the table, (d) force exerted by the table on (e) force exerted by Earth on Which, if any, of these forces constitute a Newtons third-law pair of forces? SSM

CONTEXT-RICH You yank a fish you have just caught on your line upward from rest into your boat. Draw a free-body diagram of the fish after it has left the water and as it gains speed as it rises. In addition, tell the type (tension, spring, gravity, normal, friction, etc.) and category (contact versus action-ata- distance) of each force on your diagram. Which, if any, pairs of the forces on your diagram constitute a Newtons third-law pair? Can you tell the relative magnitudes of the forces on your diagram from the information given? Explain.

If you gently set a fancy plate on the table, it will not break. However if you drop it from a height, it might very well break. Discuss the forces that act on the plate (as it contacts the table) in both these situations. Use kinematics and Newtons second law to describe what is different about the second situation that causes the plate to break?

For each of the following forces, give what produces it, what object it acts on, its direction, and the reaction force. (a) The force you exert on your briefcase as you hold it while standing at the bus stop. (b) The normal force on the soles of your feet as you stand barefooted on a horizontal wood floor. (c) The gravitational force on you as you stand on a horizontal floor. (d) The horizontal force exerted on a baseball by a bat as the ball is hit straight up the middle toward center field for a single.

For each case, identify the force (including its direction) that causes the acceleration. (a) A sprinter at the very start of the race. (b) Ahockey puck skidding freely but slowly coming to rest on the ice. (c) A long fly ball at the top of its arc. (d) A bungee jumper at the very bottom of her descent.

True or false: (a) If two external forces that are both equal in magnitude and opposite in direction act on the same object, the two forces can never be a Newtons third-law pair. (b) The two forces of a Newtons third-law pair are equal only if the objects involved are not accelerating.

An 80-kg man on ice skates is pushing his 40-kg son, also on skates, with a force of 100 N. Together, they move across the ice steadily gaining speed. (a) The force exerted by the boy on his father is (1) 200 N, (2) 100 N, (3) 50 N, or (4) 40 N. (b) How do the magnitudes of the two accelerations compare? (c) How do the directions of the two accelerations compare?

A girl holds a stone in her hand and can move it up or down or keep it still. True or false: (a) The force exerted by her hand on the rock is always the same magnitude as the force of gravity on the stone. (b) The force exerted by her hand on the rock is the reaction force to the force of gravity on the stone. (c) The force exerted by her hand on the stone is always the same magnitude as the force on her hand by the stone, but in the opposite direction. (d) If the girl moves her hand down at a constant speed, then her upward force on the stone is less than the force of gravity on the stone. (e) If the girl moves her hand downward but slows the stone to rest, then the force of the stone on the girls hand is the same magnitude as the force of gravity on the stone.

A 2.5-kg object hangs at rest from a string attached to the ceiling. (a) Draw a free-body diagram of the object, indicate the reaction force to each force drawn and tell what object the reaction force acts on. (b) Draw a free-body diagram of the string, indicate the reaction force to each force drawn, and tell what object each reaction force acts on. Do not neglect the mass of the string.

(a) Which of the free-body diagrams in Figure 4-34 represents a block sliding down a frictionless inclined surface? (b) For the correct diagram, label the forces and tell which are contact forces and which are action-at-a-distance forces. (c) For each force in the correct diagram, identify the reaction force, the object it acts on and its direction.

A wooden box on the floor is pressed against a compressed, horizontal spring that is attached to a wall. The horizontal floor beneath the box is frictionless. Draw the free-body diagram of the box in the following cases. (a) The box is held at rest against the compressed spring. (b) The force holding the box against the spring no longer exists, but the box is still in contact with the spring. (c) When the box no longer has contact with the spring.

Imagine yourself seated on a wheeled desk chair at your desk. Consider friction forces between the chair and the floor to be negligible. However, the friction forces between the desk and the floor are not negligible. When sitting at rest, you decide you need another cup of coffee. You push horizontally against the desk, and the chair rolls backward away from the desk. (a) Draw a free-body diagram of yourself during the push and clearly indicate which force was responsible for your acceleration. (b) What is the reaction force to the force that caused your acceleration? (c) Draw the freebody diagram of the desk and explain why it did not accelerate. Does this violate Newtons third law? Explain.

The same (net) horizontal force F is applied for a fixed time interval to each of two objects, having masses and that sit on a flat, frictionless surface. (Let ) (a) Assuming the two objects are initially at rest, what is the ratio of their accelerations during the time interval, in terms of F, and ? (b) What is the ratio of their speeds and at the end of the time interval? (c) How far apart are the two objects (and which is ahead) at the end of the time interval?

CONCEPTUAL Most cars have four springs attaching the body to the frame, one at each wheel position. Devise an experimental method of estimating the force constant of one of the springs using your known weight and the weights of several of your friends. Assume the 4 springs are identical. Use the method to estimate the force constant of your cars springs.

Estimate the force exerted on the goalies glove by the puck when he catches a hard slap shot for a save.

A baseball player slides into second base during a steal attempt. Assuming reasonable values for the length of the slide, the speed of the player at the beginning of the slide, and the speed of the player at the end of the slide, estimate the average force of friction acting on the player.

ENGINEERING APPLICATION A race car skidding out of control manages to slow down to 90 km/h before crashing head-on into a brick wall. Fortunately, the driver is wearing a safety harness. Using reasonable values for the mass of the driver and the stopping distance, estimate the average force exerted on the driver by the safety harness, including its direction. Neglect any effects of frictional forces on the driver by the seat.

A particle is traveling in a straight line at a constant speed of 25.0 m/s. Suddenly, a constant force of 15.0 N acts on it, bringing it to a stop in a distance of 62.5 m. (a) What is the direction of the force? (b) Determine the time it takes for the particle to come to a stop. (c) What is its mass?

An object has an acceleration of when a single force of magnitude acts on it. (a) What is the magnitude of its acceleration when the magnitude of this force is doubled? (b) A second object has an acceleration magnitude of under the influence of a single force of magnitude What is the ratio of the mass of the second object to that of the first object? (c) If the two objects are glued together to form a composite object, what acceleration magnitude will a single force of magnitude acting on the composite object produce?

Atugboat tows a ship with a constant force of magnitude The increase in the ships speed during a 10-s interval is 4.0 km/h. When a second tugboat applies an additional constant force of magnitude in the same direction, the speed increases by 16 km/h during a 10-s interval. How do the magnitudes of and compare? (Neglect the effects of water resistance and air resistance.)

A single constant force of magnitude 12 N acts on a particle of mass m. The particle starts from rest and travels in a straight line a distance of 18 m in 6.0 s. Find m.

A net force of (6.0 N) acts on a 1.5 kg object. Find the acceleration .

A bullet of mass moving at 500 m/s impacts a tree stump and penetrates 6.00 cm into the wood before coming to rest. (a) Assuming that the acceleration of the bullet is constant, find the force (including direction) exerted by the wood on the bullet. (b) If the same force acted on the bullet and it had the same impact speed but half the mass, how far would it penetrate into the wood?

A cart on a horizontal, linear track has a fan attached to it. The cart is positioned at one end of the track, and the fan is turned on. Starting from rest, the cart takes 4.55 s to travel a distance of 1.50 m. The mass of the cart plus fan is 355 g. Assume that the cart travels with constant acceleration. (a) What is the net force exerted on the cartfan combination? (b) Mass is added to the cart until the total mass of the cartfan combination is 722 g, and the experiment is repeated. How long does it take for the cart, starting from rest, to travel 1.50 m now? Ignore the effects due to friction.

Ahorizontal force of magnitude causes an acceleration of magnitude when it acts on an object of mass m sliding on a frictionless surface. Find the magnitude of the acceleration of the same object in the circumstances shown in Figure 4-35a and

Al and Bert stand in the middle of a large frozen lake (frictionless surface). Al pushes on Bert with a force of 20 N for 1.5 s. Berts mass is 100 kg. Assume that both are at rest before Al pushes Bert. (a) What is the speed that Bert reaches as he is pushed away from Al? (b) What speed does Al reach if his mass is 80 kg?

If you push a block whose mass is across a frictionless floor with a horizontal force of a magnitude the block has an acceleration of If you push on a different block whose mass is with a horizontal force of magnitude its acceleration is (a) What acceleration will a horizontal force of magnitude F0 give to a single block with mass (b) What acceleration will a horizontal force of magnitude F0 give to a single block with mass

MULTISTEP To drag a 75.0-kg log along the ground at constant velocity, your tractor has to pull it with a horizontal force of 250 N. (a) Draw the free-body diagram of the log. (b) Use Newtons laws to determine the force of friction on the log. (c) What is the normal force of the ground on the log? (d) What horizontal force must you exert if you want to give the log an acceleration of assuming the force of friction does not change. Redraw the logs free-body diagram for this situation.

A 4.0-kg object is subjected to two constant forces, and F The object acceleration? (b) What is its velocity at time (c) Where is the object at time

On the moon, the acceleration due to the effect of gravity is only about 1/6 of that on Earth. An astronaut whose weight on Earth is 600 N travels to the lunar surface. His mass, as measured on the moon, will be (a) 600 kg, (b) 100 kg, (c) 61.2 kg, (d) 9.81 kg, (e) 360 kg.

Find the weight of a 54-kg student in (a) newtons, and (b) pounds.

Find the mass of a 165-lb engineer in kilograms.

ENGINEERING APPLICATION To train astronauts to work on the moon, where the free-fall acceleration is only about 1/6 of that on Earth, NASA submerges them in a tank of water. If an astronaut who is carrying a backpack, air conditioning unit, oxygen supply, and other equipment, has a total mass of 250 kg, determine the following quantities. (a) her weight including backpack, etc. on Earth, (b) her weight on the moon, (c) the required upward buoyancy force of the water during her training for the moons environment on Earth

It is the year 2075 and space travel is common. A physics professor brings his favorite teaching demonstration with him to the moon. The apparatus consists of a very smooth (frictionless) horizontal table and an object to slide on it. On Earth, when the professor attaches a spring (force constant 50 N/m) to the object and pulls horizontally so the spring stretches 2.0 cm, the object accelerates at (a) Draw the free-body diagram of the object and use it and Newtons laws to determine the objects mass. (b) What would the objects acceleration be under identical conditions on the moon?

ENGINEERING APPLICATION, MULTISTEP A35.0-kg traffic light is supported by two wires as in Figure 4-36. (a) Draw the lights free-body diagram and use it to answer the following question qualitatively: Is the tension in wire 2 greater than or less than the tension in wire 1? (b) Verify your answer by applying Newtons laws and solving for the two tensions. 1.5 m>s2. SSM

A 42.6-kg lamp is hanging from wires as shown in Figure 4-37. The ring has negligible mass. The tension in the vertical wire is (a) 209 N, (b) 418 N, (c) 570 N, (d) 360 N, (e) 730 N. T1

In Figure 4-38a, a 0.500-kg block is suspended at the midpoint of a 1.25-m-long string. The ends of the string are attached to the ceiling at points separated by 1.00 m. (a) What angle does the string make with the ceiling? (b) What is the tension in the string? (c) The 0.500-kg block is removed and two 0.250-kg blocks are attached to the string such that the lengths of the three string segments are equal (Figure 4-38b). What is the tension in each segment of the string? SSM

A ball weighing \(100-\mathrm{N}\) is shown suspended from a system of cords (Figure 4-39). What are the tensions in the horizontal and angled cords?

A 10-kg object on a frictionless table is subjected to two horizontal forces, and with magnitudes and as shown in Figure 4-40. Find the third horizontal force that must be applied so that the object is in static equilibrium. SSM

For the systems to be in equilibrium in Figure 4-41a, Figure 4-41b, and Figure 4-41c, find the unknown tensions and masses.

ENGINEERING APPLICATION Your car is stuck in a mud hole. You are alone, but you have a long, strong rope. Having studied physics, you tie the rope tautly to a telephone pole and pull on it sideways, as shown in Figure 4-42. (a) Find the force exerted by the rope on the car when the angle _ is 3.00 and you are pulling with a force of 400 N, but the car does not move. (b) How strong must the rope be if it takes a force of 600 N to move the car when _ is 4.00?

ENGINEERING APPLICATION, MULTISTEP Balloon arches are often seen at festivals or celebrations; they are made by attaching helium-filled balloons to a rope that is fixed to the ground at each end. The lift from the balloons raises the structure into the arch shape. Figure 4-43a shows the geometry of such a structure: N balloons are attached at equally spaced intervals along a massless rope of length L, which is attached to two supports at its ends. Each balloon provides a lift force of magnitude F. The horizontal and vertical coordinates of the point on the rope where the ith balloon is attached are and and is the tension in the ith segment. (Note segment 0 is the segment between the point of attachment and the first balloon, and segment N is the segment between the last balloon and the other point of attachment). (a) Figure 4-43b shows a free-body diagram for the ith balloon. From this diagram, show that the horizontal component of the force (call it ) is the same for all the string segments. (b) By considering the vertical component of the forces, use Newtons laws to derive the following relationship between the tension in the ith and segments: (c) Show that (d) From the diagram and the two expressions above, show that and that yi _

ENGINEERING APPLICATION, SPREADSHEET (a) Consider a numerical solution to Problem 54. Write a spreadsheet program to make a graph of the shape of a balloon arch. Use the following parameters: (balloons), each providing a lift force and each attached to a rope of length with a horizontal component of tension How far apart are the two points of attachment? How high is the arch at its highest point? (b) Note that we have not specified the spacing between the supportsit is determined by the other parameters. Vary while keeping the other parameters the same until you create an arch that has a spacing of 8.0 m between the supports. What is then? As you increase the arch should get flatter and more spread out. Does your spreadsheet model show this?

A large box whose mass is 20.0 kg rests on a frictionless floor. A mover pushes on the box with a force of 250 N at an angle 35.0 below the horizontal. Draw the boxs free-body diagram and use it to determine the acceleration of the box.

A 20.0 kg box rests on a frictionless ramp with a 15.0 slope. The mover pulls on a rope attached to the box to pull it up the incline (Figure 4-44). If the rope makes an angle of 40.0 with the horizontal, what is the smallest force F the mover will have to exert to move the box up the ramp?

In Figure 4-45, the objects are attached to spring scales calibrated in newtons. Give the reading(s) of the balance(s) in each case, assuming that both the scales and the strings are massless.

A box is held in position on a frictionless incline by a cable (Figure 4-46). (a) If and find the tension in the cable and the normal force exerted by the incline. (b) Find the tension as a function of _ and m, and check your result for plausibility in the special cases of u _ 0 and u _ 90.

A horizontal force of 100 N pushes a 12-kg block up a frictionless incline that makes an angle of 25 with the horizontal. (a) What is the normal force that the incline exerts on the block? (b) What is the magnitude of acceleration of the block?

A 65-kg student weighs himself by standing on a force scale mounted on a skateboard that is rolling down an incline, as shown in Figure 4-47. Assume there is no friction so that the force exerted by the incline on the skateboard is normal to the incline. What is the reading on the scale if _ _ 30? SSM

A block of mass m slides across a frictionless floor and then up a frictionless ramp (Figure 4-48). The angle of the ramp is _ and the speed of the block before it starts up the ramp is The block will slide up to some maximum height h above the floor before stopping. Show that h is independent of m and _ by deriving an expression for h in terms of v and g.

CONCEPTUAL (a) Draw the free-body diagram (with accurate relative force magnitudes) for an object that is hung by a rope from the ceiling of an elevator that is ascending but slowing. (b) Repeat Part (a) but for the situation in which the elevator is descending and speeding up. (c) Can you tell the difference between the two diagrams? Explain why the diagrams do not tell anything about the objects velocity.

A10.0-kg block is suspended from the ceiling of an elevator by a cord rated to withstand a tension of 150 N. Shortly after the elevator starts to ascend, the cord breaks. What was the minimum acceleration of the elevator when the cord broke?

A 2.0-kg block hangs from a spring scale calibrated in newtons that is attached to the ceiling of an elevator (Figure 4-49). What does the scale read when (a) the elevator is ascending with a constant speed of 30 m/s; (b) the elevator is descending with a constant speed of 30 m/s; (c) the elevator is ascending at 20 m/s and gaining speed at a rate of (d) Suppose that from to the elevator ascends at a constant speed of 10 m/s. Its speed is then steadily reduced to zero during the next 4.0 s, so that it is at rest at Describe the reading of the scale during the interval 0 t 9.0 s. t _ 9.0 s. t _ 5.0 s, 3.0 m>s2? t _ 0 SSM

CONCEPTUAL Two boxes of mass and connected by a massless string are being pulled along a horizontal frictionless surface by the tension force in a second string, as shown in Figure 4-50. (a) Draw the free-body diagram of both boxes separately and show that . (b) Is this result plausible? Explain. Does your answer make sense both in the limit that and in the limit that m ? Explain.

Abox of mass rests on a frictionless horizontal shelf and is attached by strings to boxes of masses and as shown in Figure 4-51. Both pulleys are frictionless and massless. The system is released from rest. After it is released, find (a) the acceleration of each of the boxes, and (b) the

Two blocks are in contact on a frictionless horizontal surface. The blocks are accelerated by a single horizontal force applied to one of them (Figure 4-52). Find the acceleration and the contact force of block 1 on block 2 (a) in terms of F, and and (b) for the specific values and

Repeat Problem 68, but with the two blocks interchanged. Are your answers for this problem the same as in Problem 68? Explain.

Two 100-kg boxes are dragged along a horizontal frictionless surface at a constant acceleration of as shown in Figure 4-53. Each rope has a mass of 1.00 kg. Find the magnitude of the force F and the tension in the ropes at points A, B, and C. S 1.00 m>s2,

A block of mass m is being lifted vertically by a uniform rope of mass M and length L. The rope is being pulled upward by a force applied to its top end, and the rope and block are accelerating upward with an acceleration of magnitude a. Show that the tension in the rope at a distance x (where ) above the block is given by

A chain consists of 5 links, each having a mass of 0.10 kg. The chain is being pulled upward by a force applied by your hand to its top link, giving the chain an upward acceleration of Find (a) the force magnitude F exerted on the top link by your hand; (b) the net force on each link; and (c) the magnitude of the force that each link exerts on the link below it.

MULTISTEP A 40.0-kg object supported by a vertical rope. The rope, and thus the object, is then accelerated from rest upward so that it attains a speed of 3.50 m/s in 0.700 s. (a) Draw the object’s free-body diagram with the relative lengths of the vectors showing the relative magnitudes of the forces. (b) Use the free-body diagram and Newton’s laws to determine the tension in the rope.

ENGINEERING APPLICATION, MULTISTEP A 15000-kg helicopter is lowering a 4000-kg truck to the ground by a cable of fixed length. The truck, helicopter, and cable are descending at 15.0 m/s and must be slowed to 5.00 m/s in the next 50.0 m of descent to prevent damaging the truck. Assume a constant rate of slowing. (a) Draw the free-body diagram of the truck. (b) Determine the tension in the cable. (c) Determine the lift force on the helicopter blades.

Two objects are connected by a massless string, as shown in Figure 4-54. The incline and the massless pulley are frictionless. Find the acceleration of the objects and the tension in the string (a) in terms of _, and m and for (b) u _ 30 and m1 _ m2 _ 5.0kg. 2 m , 1 , SSM

ENGINEERING APPLICATION During a stage production of Peter Pan, the 50-kg actress playing Peter has to fly in vertically (descend). To be in time with the music, she must, starting from rest, be lowered a distance of 3.2 m in 2.2 s at a constant acceleration. Backstage, a smooth surface sloped at 50 supports a counterweight of mass m, as shown in Figure 4-55. Show the calculations that the stage manager must perform to find (a) the mass of the counterweight that must be used and (b) the tension in the wire.

An 8.0-kg block and a 10-kg block, connected by a rope that passes over a frictionless peg, slide on frictionless incline, (Figure 4-56). (a) Find the acceleration of the blocks and the tension in the rope. (b) The two blocks are replaced by two others of masses \(m_1\) and \(m_2\) such that there is no acceleration. Find whatever information you can about the masses of these two new blocks.

A heavy rope of length 5.0 m and mass 4.0 kg lies on a frictionless horizontal table. One end is attached to a 6.0-kg block. The other end of the rope is pulled by a constant horizontal 100-N force. (a) What is the acceleration of the system? (b) Give the tension in the rope as a function of position along the rope

A 60-kg housepainter stands on a 15-kg aluminum platform. The platform is attached to a rope that passes through an overhead pulley, which allows the painter to raise herself and the platform (Figure 4-57). (a) With what force F must she pull down on the rope to accelerate herself and the platform upward at a rate of (b) When her speed reaches 1.0 m/s, she pulls in such a way that she and the platform go up at a constant speed. What force is she exerting on the rope now? (Ignore the mass of the rope.) SSM 0.80m>s2?

Figure 4-58 shows a 20-kg block sliding on a 10-kg block. All surfaces are frictionless and the pulley is massless and frictionless. Find the acceleration of each block and the tension in the string that connects the blocks.

A 20-kg block with a pulley attached slides along a frictionless ledge. It is connected by a massless string to a 5.0-kg block via the arrangement shown in Figure 4-59. Find (a) the acceleration of each block, and (b) the tension in the connecting string.

MULTISTEP The apparatus in Figure 4-60 is called an Atwoods machine and is used to measure the free-fall acceleration g by measuring the acceleration of the two blocks connected by a string over a pulley. Assume a massless, frictionless pulley and a massless string. (a) Draw the free-body diagram of each block. (b) Use the free-body diagrams and Newtons laws to show that the magnitude of the acceleration of either block and the tension in the string are and . (c) Do these expressions give plausible results if in the limit that and in the limit that m ? Explain.

If one of the masses of the Atwoods machine in Figure 4-60 is 1.2 kg, what should be the other mass so that the displacement of either mass during the first second following release is 0.30 m? Assume a massless, frictionless pulley and a massless string.

The acceleration of gravity g can be determined by measuring the time t it takes for a mass in an Atwoods machine described in Problem 82 to fall a distance L, starting from rest. (a) Using the results of Problem 82 (note the acceleration is constant), find an expression for g in terms of L, t, and (b) Show that a small error in the time measurement dt, will lead to an error in g by an amount dg given by (c) Assume that the only significant uncertainty in the experimental measurements is the time of fall. If and is 1.00 kg, find the value of such that g can be measured with an accuracy of percent with a time measurement that is accurate to _0.1 s.

A pebble of mass m rests on the block of mass \(m_2\) of the ideal Atwood's machine in Figure 4-60. Find the force exerted by the pebble on the block of mass \(m_2\).

A simple accelerometer can be made by suspending a small massive object from a string attached to a fixed point on an accelerating object. Suppose such an accelerometer is attached to point P on the ceiling of an automobile traveling in a straight line on a flat surface at constant acceleration. Due to the acceleration, the string will make an angle _ with the vertical. (a) Show that the magnitude of the acceleration a is related to the angle _ by (b) Suppose the automobile brakes steadily to rest from 50 km/h over a distance of 60 m. What angle will the string make with the vertical? Will the suspended object be positioned below and ahead or below and behind point P during the braking?

ENGINEERING APPLICATION The mast of a sailboat is supported at the bow and stern by stainless steel wires, the forestay and backstay, anchored 10 m apart (Figure 4-61). The 12.0-m-long mast weighs 800 N and stands vertically on the deck of the boat. The mast is positioned 3.60 m behind where the forestay is attached. The tension in the forestay is 500 N. Find the tension in the backstay and the force that the mast exerts on the deck. SSM

A50-kg block is suspended from a uniform 1.5-m-long chain that is hanging from the ceiling. The mass of the chain itself is 20 kg. Determine the tension in the chain (a) at the point where the chain is attached to the block, (b) midway up the chain, and (c) at the point where the chain is attached to the ceiling.

The speed of the head of a red headed woodpecker reaches before impact with the tree. If the mass of the head is 0.060 kg and the average force on the head is 6.0 N, find (a) the acceleration of the head (assuming constant acceleration), (b) the depth of penetration into the tree, and (c) the time it takes for the head to come to a stop.

MULTISTEP A frictionless surface is inclined at an angle of 30.0 to the horizontal. A 270-g block on the ramp is attached to a 75.0-g block using a pulley, as shown in Figure 4-62. (a) Draw two free-body diagrams, one for the 270-g block and the other for the 75.0-g block. (b) Find the tension in the string and the acceleration of the 270-g block. (c) The 270-g block is released from rest. surface? Will it slide up the incline, or down the incline?

Abox of mass is pulled along a frictionless horizontal surface by a horizontal force that is applied to the end of a rope of mass (see Figure 4-63). Neglect any sag of the rope. (a) Find the acceleration of the rope and block, assuming them to be one object. (b) What is the net force acting on the rope? (c) Find the tension in the rope at the point where it is attached to the block.

A 2.0-kg block rests on a frictionless wedge that has a 60 incline and an acceleration to the right such that the mass remains stationary relative to the wedge (Figure 4-64). (a) Draw the free-body diagram of the block and use it to determine the magnitude of the acceleration. (b) What would happen if the wedge were given an acceleration larger than this value? Smaller than this value?

The masses attached to each side of an ideal Atwoods machine consist of a stack of five washers, each of mass m, as shown in Figure 4-65. The tension in the string is When one of the washers is removed from the left side, the remaining washers accelerate and the tension decreases by 0.300 N. (a) Find m. (b) Find the new tension and the acceleration of each mass when a second washer is removed from the left side. SSM

Consider the ideal Atwoods machine in Figure 4-65. When N washers are transferred from the left side to the right side, the right side descends 47.1 cm in 0.40 s. Find N.

Blocks of mass m and 2m are on a horizontal frictionless surface (Figure 4-66). The blocks are connected by a horizontal string. In addition, forces and are applied as shown. (a) If the forces shown are constant, find the tension in the connecting string. (b) If the magnitudes of the forces vary with time as and where C equals to 5.00 N/s and t is time, find the time at which the tension in the string equals to 10.0 N.

Elvis Presley has supposedly been sighted numerous times since his death on August 16, 1977. The following is a chart of what Elviss weight would be if he were sighted on the surfaces of other objects in our solar system. Use the chart to determine: (a) Elviss mass on Earth, (b) Elviss mass on Pluto, and (c) the freefall acceleration on Mars. (d) Compare the free-fall acceleration on Pluto to the free-fall acceleration on the moon.

CONTEXT-RICH As a prank, your friends have kidnapped you in your sleep, and transported you out onto the ice covering a local pond. When you wake up you are 30.0 m from the nearest shore. The ice is so slippery (i.e. frictionless) that you cannot seem to get yourself moving. You realize that you can use Newtons third law to your advantage, and choose to throw the heaviest thing you have, one boot, in order to get yourself moving. Take your weight to be 595 N. (a) What direction should you throw your boot so that you will most quickly reach the shore? (b) If you throw your 1.20-kg boot with an average force of 420 N, and the throw takes 0.600 s (the time interval over which you apply the force), what is the magnitude of the force that the boot exerts on you? (Assume constant acceleration.) (c) How long does it take you to reach shore, including the short time in which you were throwing the boot?

The pulley of an ideal Atwoods machine is given an upward acceleration a, as shown in Figure 4-67. Find the acceleration of each mass and the tension in the string that connects them. The speeds of the two blocks are not equal in this situation

ENGINEERING APPLICATION, CONTEXT-RICH, SPREADSHEET You are working for an automotive magazine and putting a certain new automobile (mass 650 kg) through its paces. While accelerating from rest, its onboard computer records its velocity as a function of time as follows: (m/s): 0 10 20 30 40 50 t (s): 0 1.8 2.8 3.6 4.9 6.5 (a) Using a spreadsheet, find the average acceleration of the five time intervals and graph the velocity versus time and acceleration versus time for this car. (b) Where on the graph of velocity versus time is the net force on the car highest and lowest? Explain your reasoning. (c) What is the average net force on the car over the whole trip? (d) From the graph of velocity versus time, estimate the total distance covered by the car.