Question: If there is a net nonzero force

> It is often said that “friction always opposes motion.” Give at least one example in which (a) static friction causes motion, and (b) kinetic friction causes motion.

> A large wrecking ball is held in place by two light steel cables (Fig. E5.6). If the mass m of the wrecking ball is 3620 kg, what are (a) the tension TB in the cable that makes an angle of 40° with the vertical and (b) the tension TA in the ho

> A picture frame hung against a wall is suspended by two wires attached to its upper corners. If the two wires make the same angle with the vertical, what must this angle be if the tension in each wire is equal to 0.75 of the weight of the frame? (Ignore

> In the treatment of spine injuries, it is often necessary to provide tension along the spinal column to stretch the backbone. One device for doing this is the Stryker frame (Fig. E5.4a). A weight W is attached to the patient (sometimes around a neck coll

> A 75.0-kg wrecking ball hangs from a uniform, heavy-duty chain of mass 26.0 kg. (a) Find the maximum and minimum tensions in the chain. (b) What is the tension at a point three-fourths of the way up from the bottom of the chain?

> A 45.0-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds 313 N. Then you must reduce your push to 208 N to keep it moving at a steady 25.0 cm/s

> A box of bananas weighing 40.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.20. (a) If no horizontal force is applied to the box and the box is a

> A stockroom worker pushes a box with mass 16.8 kg on a horizontal surface with a constant speed of 3.50 m/s. The coefficient of kinetic friction between the box and the surface is 0.20. (a) What horizontal force must the worker apply to maintain the moti

> In a laboratory experiment on friction, a 135-N block resting on a rough horizontal table is pulled by a horizontal wire. The pull gradually increases until the block begins to move and continues to increase thereafter. Figure E5.26 shows a graph of the

> After emergencies with major blood loss, a patient is placed in the Trendelenburg position, in which the foot of the bed is raised to get maximum blood flow to the brain. If the coefficient of static friction between a typical patient and the bed sheets

> A 5.00-kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F1t2 is applied to the end of the rope, and the height of the crate above its initial position is given by y(t)=(2.80 m/s)t +(0.610 m/s3)t3. What is th

> You are pushing a large crate from the back of a freight elevator to the front as the elevator is moving to the next floor. In which situation is the force you must apply to move the crate the least, and in which is it the greatest: when the elevator is

> A 2.00-kg box is moving to the right with speed 9.00 m/s on a horizontal, frictionless surface. At t = 0 a horizontal force is applied to the box. The force is directed to the left and has magnitude F(t)=(6.00 N/s2)t2. (a) What distance does the box move

> A 2540-kg test rocket is launched vertically from the launch pad. Its fuel (of negligible mass) provides a thrust force such that its vertical velocity as a function of time is given by v(t)= At + Bt2, where A and B are constants and time is measured fro

> When jumping straight up from a crouched position, an average person can reach a maximum height of about 60 cm. During the jump, the person’s body from the knees up typically rises a distance of around 50 cm. To keep the calculations simple and yet get a

> A 550-N physics student stands on a bathroom scale in an elevator that is supported by a cable. The combined mass of student plus elevator is 850 kg. As the elevator starts moving, the scale reads 450 N. (a) Find the acceleration of the elevator (magnitu

> In Fig. E5.2 each of the suspended blocks has weight w. The pulleys are frictionless, and the ropes have negligible weight. In each case, draw a free-body diagram and calculate the tension T in the rope in terms of w. Fig. E5.2: Figure E5.2 (a) (b)

> A 750.0-kg boulder is raised from a quarry 125 m deep by a long uniform chain having a mass of 575 kg. This chain is of uniform strength, but at any point it can support a maximum tension no greater than 2.50 times its weight without breaking. (a) What i

> A transport plane takes off from a level landing field with two gliders in tow, one behind the other. The mass of each glider is 700 kg, and the total resistance (air drag plus friction with the runway) on each may be assumed constant and equal to 2500 N

> A light rope is attached to a block with mass 4.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released

> An 8.00-kg block of ice, released from rest at the top of a 1.50-m-long frictionless ramp, slides downhill, reaching a speed of 2.50 m>s at the bottom. (a) What is the angle between the ramp and the horizontal? (b) What would be the speed of the ice at t

> A 15.0-kg load of bricks hangs from one end of a rope that passes over a small, frictionless pulley. A 28.0-kg counterweight is suspended from the other end of the rope (Fig. E5.15). The system is released from rest. (a) Draw two free-body diagrams, one

> Can the total work done on an object during a displacement be negative? Explain. If the total work is negative, can its magnitude be larger than the initial kinetic energy of the object? Explain.

> Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E5.14). The pull is of magnitude 190 N. Find (a) the acceleration of the system and (b) the tension in ropes A and B. Fig. E5.14: Figure E5.14 30.

> On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The 210-kg capsule hit the ground at 311 km>h and penetrated the soil to a depth of 81.0 cm. (a) What was its acceleration (in m>s2 and in g’s), a

> A rocket of initial mass 125 kg (including all the contents) has an engine that produces a constant vertical force (the thrust) of 1720 N. Inside this rocket, a 15.5-N electrical power supply rests on the floor. (a) Find the initial acceleration of the r

> An astronaut is inside a 2.25 × 106 kg rocket that is blasting off vertically from the launch pad. You want this rocket to reach the speed of sound 1331 m/s2 as quickly as possible, but astronauts are in danger of blacking out at an acceleration greater

> In Fig. E5.10 the weight w is 60.0 N. (a) What is the tension in the diagonal string? (b) Find the magnitudes of the horizontal forces

> Two 25.0-N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain from the ceiling. (a) What is the tension in the rope? (b) What is the tension in the chain?

> While a person is walking, his arms swing through approximately a 45° angle in 1 2 s. As a reasonable approximation, assume that the arm moves with constant speed during each swing. A typical arm is 70.0 cm long, measured from the shoulder joint. (a) Wha

> A bowling ball weighing 71.2 N (16.0 lb) is attached to the ceiling by a 3.80-m rope. The ball is pulled to one side and released; it then swings back and forth as a pendulum. As the rope swings through the vertical, the speed of the bowling ball is 4.20

> You tie a cord to a pail of water and swing the pail in a vertical circle of radius 0.600 m. What minimum speed must you give the pail at the highest point of the circle to avoid spilling water?

> An object of mass m is at rest in equilibrium at the origin. At t = 0 a new force

> In a world without friction, which of the following activities could you do (or not do)? Explain your reasoning. (a) Drive around an unbanked highway curve; (b) jump into the air; (c) start walking on a horizontal sidewalk; (d) climb a vertical ladder; (

> An airplane flies in a loop (a circular path in a vertical plane) of radius 150 m. The pilot’s head always points toward the center of the loop. The speed of the airplane is not constant; the airplane goes slowest at the top of the loop and fastest at th

> The Cosmo Clock 21 Ferris wheel in Yokohama, Japan, has a diameter of 100 m. Its name comes from its 60 arms, each of which can function as a second hand (so that it makes one revolution every 60.0 s). (a) Find the speed of the passengers when the Ferris

> A small button placed on a horizontal rotating platform with diameter 0.520 m will revolve with the platform when it is brought up to a speed of 40.0 rev/min, provided the button is no more than 0.220 m from the axis. (a) What is the coefficient of stati

> A small button placed on a horizontal rotating platform with diameter 0.520 m will revolve with the platform when it is brought up to a speed of 40.0 rev>min, provided the button is no more than 0.220 m from the axis. (a) What is the coefficient of stati

> In another version of the “Giant Swing” (see Exercise 5.50), the seat is connected to two cables, one of which is horizontal (Fig. E5.51). The seat swings in a horizontal circle at a rate of 28.0 rpm (rev/min). If the

> The “Giant Swing” at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a cable 5.00 m long, and the upper end of the

> A 1125-kg car and a 2250-kg pickup truck approach a curve on a highway that has a radius of 225 m. (a) At what angle should the highway engineer bank this curve so that vehicles traveling at 65.0 mi/h can safely round it regardless of the condition of th

> A flat (unbanked) curve on a highway has a radius of 170.0 m. A car rounds the curve at a speed of 25.0 m/s. (a) What is the minimum coefficient of static friction that will prevent sliding? (b) Suppose that the highway is icy and the coefficient of stat

> A small model car with mass m travels at constant speed on the inside of a track that is a vertical circle with radius 5.00 m (Fig. E5.45). If the normal force exerted by the track on the car when it is at the bottom of the track (point A) is equal to 2.

> 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

> A crate of books rests on a level floor. To move it along the floor at a constant velocity, why do you exert less force if you pull it at an angle u above the horizontal than if you push it at the same angle below the horizontal?

> 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 le

> 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?

> 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 t

> To push a box up a ramp, which requires less force: pushing horizontally or pushing parallel to the ramp? Why?

> You drive a car up a steep hill at constant speed. Discuss all of the forces that act on the car. What pushes it up the hill?

> The sign of many physical quantities depends on the choice of coordinates. For example, ay for free-fall motion can be negative or positive, depending on whether we choose upward or downward as positive. Is the same true of work? In other words, can we m

> “In general, the normal force is not equal to the weight.” Give an example in which these two forces are equal in magnitude, and at least two examples in which they are not.

> A man sits in a seat that is hanging from a rope. The rope passes over a pulley suspended from the ceiling, and the man holds the other end of the rope in his hands. What is the tension in the rope, and what force does the seat exert on him? Draw a free

> 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 upward, is the tension in the rope greater when the crate is

> 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.

> A large crate sits on the floor of a warehouse. Paul and Bob apply constant horizontal forces to the crate. The force applied by Paul has magnitude 48.0 N and direction 61.0° south of west. How much work does Paul’s force do during a displacement of the

> 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.

> If the two ends of a rope in equilibrium are pulled with forces of equal magnitude and opposite directions, why isn’t the total tension in the rope zero?

> 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?

> A large truck and a small compact car have a head-on collision. During the collision, the truck exerts a force

> 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.

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

> 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 co

> 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?

> 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.

> 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.

> “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.

> 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?

> 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?

> 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?

> 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?

> Some students refer to the quantity m

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

> 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.

> When a batted baseball moves with air drag, when does the ball travel a greater horizontal distance? (i) While climbing to its maximum height; (ii) while descending from its maximum height back to the ground; (iii) the same for both? Explain in terms of

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

> A ball is dropped from rest and feels air resistance as it falls. Which of the graphs in Fig. Q5.26 best represents its vertical velocity component as a function of time? Fig. Q5.26: (a) (b) (c) (d) (e)

> 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?

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

> 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.

> A car speeds up while the engine delivers constant power. Is the acceleration greater at the beginning of this process or at the end? Explain.

> An advertisement for a portable electrical generating unit claims that the unit’s diesel engine produces 28,000 hp to drive an electrical generator that produces 30 MW of electrical power. Is this possible? Explain.

> To keep the forces on the riders within allowable limits, many loop-the-loop roller coaster rides are designed so that the loop is not a perfect circle but instead has a larger radius of curvature at the bottom than at the top. Explain.

> A professor swings a rubber stopper in a horizontal circle on the end of a string in front of his class. He tells Caroline, in the front row, that he is going to let the string go when the stopper is directly in front of her face. Should Caroline worry?

> The centrifugal force is not included in the free-body diagrams of Figs. 5.34b and 5.35. Explain why not. Figs. 5.34b: Figs. 5.35b: (a) Car rounding banked curve (b) Free-body diagram for car Normal to road is at Y same angle from the vertical as

> Time yourself while running up a flight of steps, and compute the average rate at which you do work against the force of gravity. Express your answer in watts and in horsepower.

> Why is the earth only approximately an inertial reference frame?

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

> If there is a net force on a particle in uniform circular motion, why doesn’t the particle’s speed change?

> A truck speeding down the highway has a lot of kinetic energy relative to a stopped state trooper but no kinetic energy relative to the truck driver. In these two frames of reference, is the same amount of work required to stop the truck? Explain.

> A net force acts on an object and accelerates it from rest to a speed v1. In doing so, the force does an amount of work W1. By what factor must the work done on the object be increased to produce three times the final speed, with the object again startin

> When you stand with bare feet in a wet bathtub, the grip feels fairly secure, and yet a catastrophic slip is quite possible. Explain this in terms of the two coefficients of friction.

> 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?

> Does a car’s kinetic energy change more when the car speeds up from 10 to 15 m/s or from 15 to 20 m/s? 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?

> 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 woman in an elevator lets go of her briefcase, but it does not fall to the floor. How is the elevator moving?

> 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.

> A rope tied to a body is pulled, causing the body to accelerate. But according to Newton’s third law, the body pulls back on the rope with a force of equal magnitude and opposite direction. Is the total work done then zero? If so, how can the body’s kine

> For medical reasons, astronauts in outer space must determine their body mass at regular intervals. Devise a scheme for measuring body mass in an apparently weightless environment.