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.

Can an object 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 isn’t 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 Newton’s 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 \(m \vec{a}\) 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?

The acceleration of a falling object 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 \(9.8 \ \mathrm{m/s}^2\). 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.

“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.

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 Newton’s laws of motion.

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 speeding up or when it is slowing down? In each case, explain in terms of Newton’s laws of motion.

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.

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 doesn’t the wagon remain in equilibrium, no matter how hard the horse pulls?

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.

A large truck and a small compact car have a head-on collision. During the collision, the truck exerts a force \(\vec{F}_{\text{T on C}}\) on the car, and the car exerts a force \(\vec{F}_{\text{C on T}}\) 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 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.

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 Newton’s laws of motion have to say about why this happens?

When a car is hit from behind, the occupants may experience whiplash. Use Newton’s 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 Newton’s laws of motion to explain why this happens.

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.

CP Estimate the average force that a major-league pitcher exerts on the baseball when he throws a fastball. Express your answer in pounds. In your solution, list the quantities for which you estimate values and any assumptions you make. Do a web search to help determine the values you use in making your estimates.

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?

CP 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?

Block A rests on top of block B as shown in Fig. E4.26. The table is frictionless but there is friction (a horizontal force) between blocks A and B. Block B has mass 6.00 kg and block A has mass 2.00 kg. If the horizontal pull applied to block B equals 12.0 N, then block B has an acceleration of \(1.80 \ \mathrm{m/s}^2\). What is the acceleration of block A?

Two adults and a child want to push a wheeled cart in the direction marked x in Fig. P4.35 (next page). The two adults push with horizontal forces \(\vec{F}_1\) and \(\vec{F}_2\) 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 \(2.0 \ \mathrm{m/s}^2\) in the +x-direction. What is the weight of the cart?

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?

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. P4.37). 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 \(2.50 \ \mathrm{m/s}^2\). (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 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 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 Newton’s second law to calculate the magnitude of F.

CP Two blocks connected by a light horizontal rope sit at rest on a horizontal, frictionless surface. Block A has mass 15.0 kg, and block B has mass m. A constant horizontal force F = 60.0 N is applied to block A (Fig. P4.38). In the first 5.00 s after the force is applied, block A moves 18.0 m to the right. (a) While the blocks are moving, what is the tension T in the rope that connects the two blocks? (b) What is the mass of block B?

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 \(x = (9.0 \times 10^3 \ \mathrm{m/s}^2)t^2 - 18.0 \times 10^4 \ \mathrm{m/s}^3)t^3\). 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?

CP On a test flight a rocket with mass 400 kg blasts off from the surface of the earth. The rocket engines apply a constant upward force F until the rocket reaches a height of 100 m and then they shut off. If the rocket is to reach a maximum height of 400 m above the surface of the earth, what value of F is required? Assume the change in the rocket’s mass is negligible.

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

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 \(g = 1.62 \ \mathrm{m/s}^2\)?

CP A batter swings at a baseball (mass 0.145 kg) that is moving horizontally toward him at a speed of 40.0 m/s. He hits a line drive with the ball moving away from him horizontally at 50.0 m/s just after it leaves the bat. If the bat and ball are in contact for 8.00 ms, what is the average force that the bat applies to the ball?

CP CALC An object with mass m is moving along the x-axis according to the equation \(x(t) = \alpha t^2 - 2 \beta t\), where \(\alpha\) and \(\beta\) are positive constants. What is the magnitude of the net force on the object at time t = 0?

CP Boxes A and B are connected to each end of a light vertical rope (Fig. P4.45). 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?

The two blocks in Fig. P4.46 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 object 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?

CP A small rocket with mass 20.0 kg is moving in free fall toward the earth. Air resistance can be neglected. When the rocket is 80.0 m above the surface of the earth, it is moving downward with a speed of 30.0 m/s. At that instant the rocket engines start to fire and produce a constant upward force F on the rocket. Assume the change in the rocket’s mass is negligible. What is the value of F if the rocket’s speed becomes zero just as it reaches the surface of the earth, for a soft landing? (Hint: The net force on the rocket is the combination of the upward force F from the engines and the downward weight of the rocket.)

CP 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?

CP CALC 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?

CP Starting at time t = 0, net force \(F_1\) is applied to an object that is initially at rest. (a) If the force remains constant with magnitude \(F_1\) while the object moves a distance d, the final speed of the object is \(v_1\). What is the final speed \(v_2\) (in terms of \(v_1\) ) if the net force is \(F_2 = 2F_1\) and the object moves the same distance d while the force is being applied? (b) If the force \(F_1\) remains constant while it is applied for a time T, the final speed of the object is \(v_1\). What is the final speed \(v_2\) (in terms of \(v_1\) ) if the applied force is \(F_2 = 2F_1\) and is constant while it is applied for the same time T? In a later chapter we’ll call force times distance work and force times time impulse and associate work and impulse with the change in speed.)

DATA 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?

CALC The position of a training helicopter (weight \(2.75 \times 10^5 \ \mathrm{N}\) ) in a test is given by \(\hat{\rmath= (0.020 \ \mathrm{m/s}^3) t^3 \hat{\imath} + (2.2 \ \mathrm{m/s}) t \hat{\jmath} - (0.060 \ \mathrm{m/s}^2 ) t^2 \hat{\kmath}\). Find the net force on the helicopter at t = 5.0 s.

DATA You are a Starfleet captain going boldly where no one 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: (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.

DATA 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: 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.

CP CALC A block of mass 2.00 kg is initially at rest at x = 0 on a slippery horizontal surface for which there is no friction. Starting at time t = 0, a horizontal force \(F_{x} (t) = \beta - \alpha t\) is applied to the block, where \(\alpha = 6.00 \ \mathrm{N/s}\) anwd \(\beta = 4.00 \ \mathrm{N}\). (a) What is the largest positive value of x reached by the block? How long does it take the block to reach this point, starting from t = 0, and what is the magnitude of the force when the block is at this value of x? (b) How long from t = 0 does it take the block to return to x = 0, and what is its speed at this point

CALC 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 \(F_{x} (t) = k_1 + k_{2} y \quad F_{y} (t) = k_{3} t\) 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.

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 Figure P4.60 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.