Two Paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain taking the longer path?

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Two Paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain taking the longer path?
A. The same
B. Twice as much
C. half as much
D. You gain no PE in either case.
A stone is thrown straight up. Compare its kinetic energy KE, to its potential energy GPE as it is going up.
A. KE increases and GPE decreases
B. KE decreases and GPE decreases .
C. KE increases and GPE increases
D. KE decreases and GPE increases
A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the springs potential energy (EPE) and the gravitational potential energy (GPE) of the mass
A. both EPE and GPE decrease
B. EPE increases and GPE decreases
C. both EPE and GPE increase
D. EPE decreases and GPE increases
A marble is placed in a marble launcher. What can you say about the springs potential energy (EPE) and the kinetic energy (GPE) of the marble as the marble is being fired from the launcher.
A. both EPE and KE decrease
B. EPE increases and KE decreases
C. both EPE and KE increase
D. EPE decreases and KE increases

What does it mean to say that momentum is conserved?

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What does it mean to say that momentum is conserved?
12. What is the momentum of a 100-kilogram fullback carrying a football on a play at a velocity of 3.5 m/sec?
13. What is the momentum of a 75.0-kilogram defensive back chasing the fullback at a velocity of 5.00 m/sec.?
14. A 2,000-kilogram railroad car moving at 5 m/sec to the east collides with a 6,000-kilogram railroad car moving at 3 m/sec to the west. If the cars couple together, what is their velocity after the collision?
15. A 4-kilogram ball moving at 8 m/sec to the right collides with a 1-kilogram ball at rest. After the collision, the 4-kilogram ball moves at 4.8 m/sec to the right. What is the velocity of the 1-kilogram ball?
16. A 0.0010-kg pellet is fired at a speed of 50.0m/s at a motionless 0.35-kg piece of balsa wood. When the pellet hits the wood, it sticks in the wood and they slide off together. With what speed do they slide?
17. Terry, a 70-kilogram tailback, runs through his offensive line at a speed of 7.0 m/sec. Jared, a 100-kilogram linebacker, running in the opposite direction at 6.0m/s, meets Jared head-on and “wraps him up.” What is the result of this tackle?
18. Snowboarding cautiously down a steep slope at a speed of 7.0 m/sec, Sarah, whose mass is 50 kilograms, is afraid she won’t have enough speed to travel up a slight uphill grade ahead of her. She extends her hand as her friend Trevor, having a mass of 100 kilograms is about to pass her traveling at 16 m/sec. If Trevor grabs her hand, calculate the speed at which the friends will be sliding.
19. Tex, an 85.0 kilogram rodeo bull rider is thrown from the bull after a short ride. The 520 kilogram bull chases after Tex at 13.0 m/sec. While running away at 3.00 m/sec, Tex jumps onto the back of the bull to avoid being trampled. How fast does the bull run with Tex aboard?
20. Identical twins Kate and Karen are rowing their boat on a hot Summer afternoon when they decide to go for a swim. Kate, whose mass is 45 kilograms, jumps off the front of the boat at a speed of 3.00 m/sec. Karen jumps off the back at a speed of 4.00 m/sec. If the 70-kilogram rowboat is moving at 1.00m/s when the girls jump, what is the speed of the rowboat after the girls jump?
21. A 0.10-kilogram piece of modeling clay is tossed at a motionless 0.10-kilogram block of wood and sticks. The block slides across a frictionless table at 15 m/sec.
a. At what speed was the clay tossed?
b. The clay is replaced with a “bouncy” ball tossed with the same speed. The bouncy ball rebounds from the wooden block at a speed of 10 meters per second. What effect does this have on the wooden block?
Why?

A traveler flies from Spokane to Atlanta by way of Los Angeles. Los Angeles is approximately 1600 km due south of Spokane, and Atlanta is approximately 3200 km due east of Los Angeles (Fig. 1-32). Find the traveler’s total displacement.

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A traveler flies from Spokane to Atlanta by way of Los Angeles. Los Angeles is approximately 1600 km due south of Spokane, and Atlanta is approximately 3200 km due east of Los Angeles (Fig. 1-32). Find the traveler’s total displacement.
18 A traveler first drives 20.0 km east, then 30.0 km southeast, and finally 10.0 km south. Find the trav- eler’s total displacement.
Vector Algebra
Graphical vector addition
19 Four forces each have a magnitude of 50 lb. Their re- spective directions are north, south, east, and west. Find the resultant force.
20 A 40 lb force acts to the right, while a 100 lb force acts at an angle of 458 above the first. Construct the vector sum of the two forces graphically, using a convenient scale.
21 Electric fields are vector quantities whose magnitudes are measured in units of volts/meter (V/m). Find the resultant electric field when there are two fields, E1 and E2, where E1 is directed vertically upward and has magnitude 100 V/m and E2 is directed 458 to the left of E1 and has magnitude 150 V/m.

1 A cyclist moves at a constant speed of 15 mi/h. Ex- press the speed in units of ft/s.

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1 A cyclist moves at a constant speed of 15 mi/h. Ex- press the speed in units of ft/s.
2 How long is required to travel 300 km along a freeway at a constant speed of (a) 50.0 km/h; (b) 60.0 km/h?
3 Light travels at a constant speed of 3.00 3 108 m/s, whereas sound travels through the air at a constant speed of 340 m/s. (a) How long does it take for light to travel from a
lightning stroke to an observer 1.00 km away? (b) How long after the flash is seen is the thunder pro-
duced by the lightning heard? 4 The driver of a car is initially moving at a constant
speed of 72.0 km/h when a traffic light turns red. If 0.500 s reaction time is required before the brakes can be applied, what is the distance in meters traveled by the car before it begins to slow down?
5 A person on earth communicating with an astronaut on the moon asks a question. How long must the per- son on earth wait for a response if the astronaut an- swers 1.00 s after the message is received? The moon is 3.84 3 105 km from the earth, and the speed of ra- dio waves is 3.00 3 108 m/s.
6 External stimuli are communicated to the brain by means of electrical signals propagating along nerve cells at a speed of approximately 30 m/s. Similarly, electrical messages are sent at the same speed from the brain along nerve cells to the muscles. Reflex ac- tions are controlled by a relatively simple nerve circuit from a muscle to the spine and back to the muscle. Es- timate the reflex time for a stimulus at the knee.
7 The world record in the 100 yard dash is 9.1 s. Esti- mate the world record in the 100 m dash.
Average speed 8 Compute the average speed in m/s of a runner who
completes a mile in 4.00 min. 9 Blood circulating from the heart to the hands and back
to the heart travels a distance of about 2.0 m in 40 s. Find the average speed of the blood.
10 You drive from Los Angeles to Portland, a distance of 1.6 3 103 km, in 30 h, including stops. What steady speed would have allowed you to arrive at the same time if you had driven at this speed nonstop?
11 During 5 successive 1.00 min intervals, a runner moves at the following constant speeds: 0.400 km/min, 0.240 km/min, 0.160 km/min, 0.160 km/min, and 0.320 km/min. Compute the total dis- tance traveled and the average speed.
12 A tortoise and a hare race over a course 1.00 km long. The tortoise moves at a constant speed of 2.00 m/s. The hare moves at a speed of 10.0 m/s for 60.0 s, rests for 10.0 min, and continues at 10.0 m/s for 40.0 s. (a) Sketch s versus t for both the tortoise and the hare
on the same graph. (b) Who wins the race? (c) What is the hare’s average speed?
Instantaneous speed 13 A plane accelerates down a runway. Markers beside
the runway are 10.0 m apart. The plane moves be- tween two adjacent markers in 0.200 s. Estimate the instantaneous speed of the plane as it passes the first marker.
14 By analyzing a multiflash photograph of a golfer hit- ting a golf ball, one finds that the head of the club trav- els 50.0 cm in 0.0100 s, just before it strikes the ball. Find the approximate instantaneous speed of the club head at the instant of contact.
15 Let s 5 ct3, where c 5 1.0 m/s3. Compute the average speed over the time intervals Dt1 5 1.0 3 10]1 s, Dt2 5 1.0 3 10]2 s, and Dt3 5 1.0 3 10]3 s, with all time in- tervals starting at the time t 5 1.0000 s. What is the in- stantaneous speed at t 5 1.0000 s?
16 Paradoxes relating to the nature of motion were for- mulated by the ancient Greeks. The paradoxes were not resolved because the Greeks had no clear under- standing of concepts like instantaneous speed. One of Zeno’s paradoxes can be stated as follows: a runner wishing to run 100 meters must first cover half that distance. But before he can cover the 50 meters, he must first travel 25 meters, and so on. It is clear that before the runner can travel 100 meters, or any finite distance, he must first move through an infinite num- ber of shorter distances, and this he can never do in a finite time. Resolve this paradox.

Question 1 A 2 kg book resting on a flat table requires an applied force of 4 N to make it move. Draw a free body diagram illustrating this situation and find the coefficient of static friction between the book and the table.

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Question 1
A 2 kg book resting on a flat table requires an applied force of 4 N to make it move. Draw a free body diagram illustrating this situation and find the coefficient of static friction between the book and the table.
Question 2
A 30 kg crate is pulled across a flat floor with 80 N of force. The coefficient of kinetic friction between the crate and the floor is 0.15. Draw a free body diagram illustrating this situation and find the acceleration of the crate.
Question 3
An applied force of 100 N causes a 20 kg crate to accelerate across a level floor at 2 m/s2. Draw a free body diagram illustrating this situation and find the coefficient of kinetic friction between the crate and the floor.
Question 4
60 N of force is applied to a 10 kg crate initially at rest on a level floor. The coefficient of friction between the crate and the floor is 0.4. Draw a free body diagram illustrating this situation and find the distance traveled and the velocity of the crate after 3 seconds.
Question 5
Sue and Bill are standing on a frictionless surface of ice. Sue, whose mass is 60 kg, pushes Bill, mass 100 kg, with 300 N of force. Draw a free body diagram illustrating this situation and find the acceleration of both Sue and Bill.

1. Your friend says that what makes one element distinct from another is the number of electrons about the atomic nucleus. Do you agree wholeheartedly, partially, or not at all? Explain.

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1. Your friend says that what makes one element distinct from another is the number of electrons about the atomic nucleus. Do you agree wholeheartedly, partially, or not at all? Explain
2.The atoms that constitute your body are mostly empty space, and structures such as the chair you’re sitting on are composed of atoms that are also mostly empty space. So why don’t you fall through the chair?
3 Your friend says that the primary difference between a solid and a liquid is the kind of atoms in the material. Do you agree or disagree, and why?
4 Why is it easier to start a fire with kindling rather than with large sticks and logs of the same kind of wood?
5.Why is blood pressure measured in the upper arm, at the elevation of your heart?
6. A balloon is weighted so that it is barely able to float in water. If it is pushed beneath the surface, will it return to the surface, stay at the depth to which it is pushed, or sink? Explain.
(Hint: Does the balloon’s density change?)
7. When an air bubble rises in water, what happens to its mass, volume, and density?
8. Why does the weight of an object in air differ from its weight in a vacuum (remembering that weight is the force exerted against a supporting surface)? Cite an example in which this would be an important consideration.
9.In a glass of water at room temperature, do all the molecules have the same speed?
10.Which has the greater amount of internal energy—an iceberg or a cup of hot coffee? Defend your answer.
11.On a cold day, why does a metal doorknob feel colder than the wooden door?
12.Your friend states that the average speed of all hydrogen and nitrogen molecules in a gas is the same. Do you agree or disagree, and why?
13.Place a jar of water on a small stand within a saucepan of water so that the bottom of the jar is held above the bottom of the pan. When the pan is placed on a stove, the water in the pan will boil, but not the water in the jar. Why?
14. Why does the water in a car radiator sometimes boil explosively when the radiator cap is removed?
15.On a chilly 10°C day, your friend who loves cold weather says she wishes it were twice as cold. Taking this literally, show that the temperature she wishes for would be -131.5°C.
16. Imagine a giant dry-cleaner’s bag full of air at a temperature of -35°C floating like a balloon with a string hanging from it 10 km above the ground. Estimate what its temperature would be if you were able to yank it suddenly back to Earth’s surface.