Solution: In order to slide a heavy cabinet across the floor

What did Aristotle believe about the relative speeds of fall for heavy and light objects?

Did Aristotle believe that forces are necessary to keep objects moving, or did he believe that, once moving, theyd move of themselves?

What idea of Aristotle did Galileo discredit with his inclined-plane experiments?

Which dominated Galileos method of extending knowledge: philosophical discussion or experiment?

What name is given to the property by which objects resist changes in motion?

Which depends on location: weight or mass?

Where is your weight greater: on Earth or on the Moon? How about your mass?

What are the units of measurement for weight and for mass?

A 1-kg object weighs nearly 10 N on Earth. Would it weigh more or less on the Moon?

What is the net force on a box pushed to the right with 50 N of force while being pushed to the left with 20 N of force?

What two quantities are necessary for a vector quantity?

Name the force that occurs in a rope when both ends are pulled in opposite directions.

How much tension is there in a vertical rope that holds a 20-N bag of apples at rest?

What does F = 0 mean?

Why is the support force on an object often called the normal force?

When you weigh yourself, how does the support force of the scale acting on you compare with the gravitational force between you and Earth?

A bowling ball sits at rest and another bowling ball rolls down a lane at constant speed. Which ball, if either, is in equilibrium? Defend your answer.

If we push an object at constant velocity, how do we know how much friction acts on the object compared to our pushing force?

How does the direction of a friction force compare with the direction of the velocity of a sliding object?

If you push to the right on a heavy piece of furniture and it slides, what is the direction of friction on the furniture?

Suppose you push to the right on a heavy piece of furniture, but not hard enough to make it slide. Does a friction force act on the furniture?

Distinguish between speed and velocity.

Why do we say that velocity is a vector and speed is not?

Does the speedometer on a vehicle show average speed or instantaneous speed?

How can you be both at rest and moving at 100,000 km/h at the same time?

Distinguish between velocity and acceleration.

What is the acceleration of an object that moves at constant velocity? What is the net force on the object in this case?

What is the acceleration of an object in free fall at Earths surface?

Your grandparents are likely interested in your educational progress. Perhaps they have little science background and may be mathematically challenged. Write a letter to them, without using equations, and explain the difference between velocity and acceleration. Explain why some of your classmates confuse the two, and give some examples that clear up the confusion

By any method you choose, determine your average walking speed. How do your results compare with those of your classmates?

Place a coin on top of a sheet of paper on a desk or table. Pull the paper horizontally with a quick snap. What concept of physics does this illustrate?

Place a file card on top of the mouth of a drinking glass. Place a coin over the center of the card. Snap the card horizontally so it flies off the glass. Youll see that the coin drops into the glass. Doesnt this show the same physics concept as in the preceding activity?

Stand flatfooted next to a wall and make a mark at the highest point you can reach. Then jump vertically and make another mark at the highest point. The distance between the marks is your vertical jumping distance. Use this distance to calculate your hang time.

Show that the average speed of a rabbit that runs a distance of 30 m in a time of 2 s is 15 m/s.

Calculate your average walking speed when you step 1.0 m in 0.5 s.

Show that the acceleration of a hamster is 5 m/s2 when it increases its velocity from rest to 10 m/s in 2 s.

Show that the acceleration of a car that can go from rest to 100 km/h in 10 s is 10 km/h # s.

Show that a freely falling rock drops a distance of 45 m when it falls from rest for 3 s.

How far will a freely falling object fall from rest in 5 s? In 10 s?

Find the net force produced by a 30-N force and a 20-N force in each of these cases: (a) Both forces act in the same direction. (b) The two forces act in opposite directions.

Lucy Lightfoot stands with one foot on one bathroom scale and her other foot on a second bathroom scale. Each scale reads 350 N. What is Lucys weight?

Henry Heavyweight weighs 1200 N and stands on a pair of bathroom scales so that one scale reads twice as much as the other. What are the scale readings?

The sketch shows a painters scaffold in mechanical equilibrium. The person in the middle weighs 500 N, and the tension in each rope is 400 N. What is the weight of the scaffold?

A different scaffold that weighs 400 N supports two painters, one 500 N and the other 400 N. The reading in the left scale is 800 N. What is the reading in the righthand scale?

A horizontal force of 120 N is required to push a bookcase across a floor at a constant velocity. (a) What is the net force acting on the bookcase? (b) How much is the friction force that acts on the sliding bookcase? (c) How much friction acts on the bookcase when it is at rest on a horizontal surface without being pushed?

Reckless Rick driving along the road at 90 km/h bumps into Hapless Harry directly in front of him who is driving at 88 km/h. What is the speed of the collision?

An airplane with an airspeed of 60 km/h lands on a runway where the wind speed is 40 km/h. (a) What is the landing speed of the plane if the wind is head-on? (b) What is the landing speed if the wind is a tailwind, coming from behind the plane? (c) What would be the landing speed of the plane in a headwind of 60 km/h?

(a) Show that the average speed of a tennis ball is 48 m/s when it travels the full length of the court, 24 m, in 0.5 s. (b) How would air resistance affect the travel time?

(a) Show that the average speed of Leslie is 10 km/h when she runs to the store 5 km away in 30 min. (b) How fast is this in m/s?

(a) Show that the acceleration is 7.5 m/s2 for a ball that starts from rest and rolls down a ramp and gains a speed of 30 m/s in 4 s. (b) Would acceleration be greater or less if the ramp were a bit less steep?

Extend Table 1.2 (which gives values from 0 to 5 s) to 6 to 10 s, assuming no air resistance.

Lillian rides her bicycle along a straight road at average velocity v. (a) Write an equation showing the distance she travels in time t. (b) If Lillians average speed is 7.5 m/s for a time of 5.0 min, show that she travels a distance of 2250 m.

A car races on a circular track of radius r. (a) Write an equation for the cars average speed when it travels a complete lap in time t. (b) The radius of the track is 100 m and the time to complete a lap is 14 s. Show that the average speed around the track is 45 m/s.

A ball is thrown straight up with an initial speed of 30 m/s. (a) How much time does it take for the ball to reach the top of its trajectory? (b) Show that the ball will reach a height of 45 m (neglecting air resistance).

A ball is thrown straight up with enough speed so that it is in the air for several seconds. (a) What is the velocity of the ball when it reaches its highest point? (b) What is its velocity 1 s before it reaches its highest point?

A school bus slows to a stop with an average acceleration of -2.0 m/s2. Show that it takes 5.0 s for the bus to slow from 10.0 m/s to a position of rest.

An airplane starting from rest at one end of a runway accelerates uniformly at 4.0 m/s2 for 15 s before takeoff. (a) What is its speed of takeoff? (b) Show that the plane travels along the runway a distance of 450 m before take of (c) What is the change in its velocity, v, during this 1-s interval? (d) What is its velocity 1 s after it reaches its highest point? (e) What is the change in velocity, v, during this 1-s interval? (f) What is the change in velocity, v, during the 2-s interval from 1 s before the highest point to 1 s after the highest point? (Caution: We are talking about velocity, not speed.) (g) What is the acceleration of the ball during any of these time intervals and at the moment the ball has zero velocity?

The weights of Burl, Paul, and the scaffold produce tensions in the supporting ropes. Rank the tension in the left rope, from greatest to least, in the three situations A, B, and C.

Rank the net force on the block from greatest to least in the four situations A, B, C, and D.

Different materials, A, B, C, and D, rest on a table. (a) From greatest to least, rank them by how much they resist being set in motion. (b) From greatest to least, rank them by the support (normal) force the table exerts on them.

Three pucks, A, B, and C, are sliding across ice at the given speeds. Air and ice friction forces are negligible. (a) From greatest to least, rank them by the force needed to keep them moving. (b) From greatest to least, rank them by the force needed to stop them in the same time interval.

Knowledge can be gained by philosophical logic and also by experimentation. Which of these did Aristotle favor, and which did Galileo favor?

Which of Aristotles ideas did Galileo discredit in his fabled Leaning Tower of Pisa experiment? With his inclined-plane experiments?

A bowling ball rolling along a lane gradually slows as it rolls. How would Aristotle likely interpret this observation? How would Galileo interpret it?

A space probe is carried by a rocket into outer space. A friend wonders what keeps the probe moving after the rocket no longer pushes it. What do you say?

When a ball rolls down an inclined plane, it gains speed because of gravity. When a ball rolls up an inclined plane, it loses speed because of gravity. Why doesnt gravity play a role when a ball rolls on a horizontal surface?

What physical quantity is a measure of how much inertia an object has?

Which has more mass: a 2-kg fluffy pillow or a 3-kg small piece of iron? Which has more volume? Why are your answers different?

Does a person on a diet more accurately lose mass or lose weight? Defend your answer.

A favorite class demonstration by Hewitt is lying on his back with a blacksmiths anvil placed on his chest. When an assistant whacks the anvil with a strong sledge-hammer blow, Hewitt is not injured. How is the physics here similar to that illustrated in Figure 1.8?

What is your own mass in kilograms? Your weight in newtons?

Gravitational force on the Moon is only 16 that of the gravitational force on Earth. What would be the weight of a 10-kg object on the Moon and on Earth? What would be its mass on the Moon and on Earth?

A monkey hangs stationary at the end of a vertical vine. What two forces act on the monkey? Which force, if either, is greater?

Can an object be in mechanical equilibrium when only a single force acts on it? Defend your answer.

When you push downward on a book at rest on a table, you feel an upward force. Does this force depend on friction? Defend your answer.

Nellie Newton hangs at rest from the ends of the rope as shown. How does the reading on the scale compare with her weight?

A hockey puck slides across the ice at a constant velocity. Is the sliding puck in equilibrium? Why or why not?

If you push horizontally on a carton that contains your new kitchen appliance and it slides across the floor, slightly gaining speed, how does the friction acting on the carton compare with your push?

In order to slide a heavy cabinet across the floor at constant speed, you exert a horizontal force of 550 N. Is the force of friction between the cabinet and the floor greater than, less than, or equal to 550 N? Defend your answer.

Consider your desk at rest on a your bedroom floor. (a) As you and your friend start to lift it, does the support force on the desk provided by the floor increase, decrease, or remain unchanged? (b) What happens to the support force on the feet of you and your friend?

An empty jug of weight W is at rest on a table. What is the support force exerted on the jug by the table? What is the support force when water of weight w is poured into the jug?

What is the acceleration of a mouse that moves across a floor at a constant velocity of 2 m/s?

What is the impact speed when a car moving at 100 km/h collides with the rear of another car traveling in the same direction at 98 km/h? When they collide head-on?

Youre in a car traveling at some specified speed limit. You see another car moving at the same speed toward you. How fast is the car approaching you, compared with the speed limit?

Emily Easygo can paddle a canoe in still water at 8 km/h. How successful will she be at canoeing upstream in a river that flows at 8 km/h?

Suppose that an object in free fall were somehow equipped with a speedometer. By how much would its speed readings increase with each second of fall?

Suppose that the freely falling object in the preceding exercise falls from a rest position and is equipped with an odometer. What equation is most appropriate for determining the distance fallen each second? Do the readings indicate equal or unequal distances of fall for successive seconds? Explain.

In the absence of air resistance, a ballplayer tosses a ball straight up. (a) By how much does the speed of the ball decrease each second while it is ascending? (b) By how much does its speed increase each second while it is descending? (c) How does the time of ascent compare with the time of descent?

Gracie says acceleration is how fast you go. Alex says acceleration is how fast you get fast. They look to you for confirmation. Whos correct?

What is the acceleration of a car that moves at a steady velocity of 100 km/h for 100 s? Why is this question an exercise in careful reading as well as in physics?

For a freely falling object dropped from rest, what is its acceleration at the end of 5 s? At the end of 10 s? Defend your answers (and distinguish between velocity and acceleration).

Correct your friend who says, The proposed California Suntrain can easily round a curve at a constant velocity of 160 km/h.

Asteroids have been moving through space for billions of years. A friend says that initial forces from long ago keep them moving. Do you agree with your friend?

In answer to the question What keeps Earth moving around the Sun? a friend asserts that inertia keeps it moving. Correct your friends erroneous answer.

Consider a ball at rest in the middle of a toy wagon. When the wagon is pulled forward, the ball rolls against the back of the wagon. A friend asks what force pushes the ball to the back of the wagon. Interpret this observation in terms of inertia.

In tearing a paper towel or plastic bag from a roll, discuss why a sharp jerk is more effective than a slow pull.

If youre in a car at rest that gets hit from behind, you can suffer a serious neck injury called whiplash. Discuss how whiplash involves the concept of inertia and why cars are equipped with headrests.

Why do you lurch forward in a bus that suddenly slows? Why do you lurch backward when it picks up speed? What law applies here?

Suppose that youre in a moving car and the engine stops running. You step on the brakes and slow the car to half speed. If you release your foot from the brakes, will the car spontaneously speed up a bit, or will it continue at half speed and slow due to friction? Defend your answer.

Harry the painter swings year after year from his bosuns chair. His weight is 500 N, and the rope, unknown to him, has a breaking point of 300 N. Why doesnt the rope break when he is supported as shown on the left? One day, Harry was painting near a flagpole, and, for a change, he tied the free end of the rope to the flagpole instead of to his chair, as shown on the right. Discuss with your friends why Harry took his vacation early.

Place a heavy book on a table and the table pushes up on the book. A friend reasons that the table cant push upward on the book because if it did, the book would rise above the table. What do you say to your friend? Why doesnt this upward push cause the book to rise from the table?

Someone standing at the edge of a cliff (as in Figure 1.24) throws a ball straight up at a certain speed and another ball straight down with the same initial speed. If air resistance is negligible, predict which ball will hit the ground below with greater speed, or whether they will hit at the same speed.

When a ball is tossed straight up, it momentarily comes to a stop at the top of its path. Is it in equilibrium during this brief moment? Why or why not?

Because Earth rotates once every 24 hours, the west wall in your room moves in a direction toward you at a linear speed that is probably more than 1000 km/h (the exact speed depends on your latitude). When you stand facing the wall, you are carried along at the same speed, so you dont notice it. But when you jump upward, with your feet no longer in contact with the floor, why doesnt the high-speed wall slam into you?

If you toss a coin straight upward while riding in a train that travels at uniform and steady motion along a straight-line track, where does the coin land? How about when the train slows while the coin is tossed? When the train rounds a curve?

"Two balls, A and B, are released simultaneously from rest at the left end of equal-length tracks, as shown. Which ball, A or B, will reach the end of its track first?"

Refer to the preceding question. (a) Does ball B roll faster along the lower part of its track than ball A rolls along its straighter track? (b) Is the speed gained by ball B going down the extra dip the same as the speed it loses going up near the right-hand endand doesnt this mean that the speeds of balls A and B will be the same at the ends of both tracks? (c) For ball B, wont the average speed dipping down and up be greater than the average speed of ball A during the same time? (d) So, overall, does ball A or ball B have the greater average speed? (Do you wish to change your answer to the preceding question?)