Exercises and Problems

Exercises

Section 1.1 Motion Diagrams

| A jet plane lands on the deck of an aircraft carrier and quickly comes to a halt. Draw a basic motion diagram, using the images from the video, from the time the jet touches down until it stops.
| You are watching a jet ski race. A racer speeds up from rest to 70 mph in 10 s, then continues at a constant speed. Draw a basic motion diagram of the jet ski, using images from the video, from its start until 10 s after reaching top speed.
| A rocket is launched straight up. Draw a basic motion diagram, using the images from the video, from the moment of liftoff until the rocket is at an altitude of 500 m.

Section 1.2 Models and Modeling

|
1. Write a paragraph describing the particle model. What is it, and why is it important?
2. Give two examples of situations, different from those described in the text, for which the particle model is appropriate.
3. Give an example of a situation, different from those de-scribed in the text, for which it would be inappropriate.

Section 1.3 Position, Time, and Displacement

Section 1.4 Velocity

| A baseball player starts running to the left to catch the ball as soon as the hit is made. Use the particle model to draw a motion diagram showing the position and average velocity vectors of the player during the first few seconds of the run.
| You drop a soccer ball from your third-story balcony. Use the particle model to draw a motion diagram showing the ball’s position and average velocity vectors from the time you release the ball until the instant it touches the ground.
| A car skids to a halt to avoid hitting an object in the road. Use the particle model to draw a motion diagram showing the car’s position and its average velocity from the time the skid begins until the car stops.

Section 1.5 Linear Acceleration

|
1. FIGURE EX1.8 shows the first three points of a motion diagram. Is the object’s average speed between points 1 and 2 greater than, less than, or equal to its average speed between points 0 and 1? Explain how you can tell.
  
  FIGURE EX1.8
2. Use Tactics Box 1.2 to find the average acceleration vector at point 1. Draw the completed motion diagram, showing the velocity vectors and acceleration vector.
| FIGURE EX1.9 shows five points of a motion diagram. Use Tactics Box 1.2 to find the average acceleration vectors at points 1, 2, and 3. Draw the completed motion diagram showing velocity vectors and acceleration vectors.

FIGURE EX1.9

FIGURE EX1.9 Full Alternative Text
|| FIGURE EX1.10 shows two dots of a motion diagram and vector $\vec{v}_{2}$ . Copy this figure, then add dot 4 and the next velocity vector $\vec{v}_{3}$ if the acceleration vector $\vec{a}$ at dot 3 (a) points right and (b) points left.

FIGURE EX 1.10

FIGURE EX Full Alternative Text
|| FIGURE EX1.11 shows two dots of a motion diagram and vector $\vec{v}_{1}$ . Copy this figure, then add dot 3 and the next velocity vector $\vec{v}_{2}$ if the acceleration vector $\vec{a}$ at dot 2 (a) points up and (b) points down.

FIGURE EX1.11

FIGURE EX1.11 Full Alternative Text
| A car travels to the left at a steady speed for a few seconds, then brakes for a stop sign. Draw a complete motion diagram of the car.
| A speed skater accelerates from rest and then keeps skating at a constant speed. Draw a complete motion diagram of the skater.
| A bowling ball rolls up an incline and then onto a smooth, level surface. Draw a complete motion diagram of the bowling ball. Don’t try to find the acceleration vector at the point where the motion changes direction; that’s an issue for Chapter 4.
| You use a long rubber band to launch a paper wad straight up. Draw a complete motion diagram of the paper wad from the moment you release the stretched rubber band until the paper wad reaches its highest point.
| A roof tile falls straight down from a two-story building. It lands in a swimming pool and settles gently to the bottom. Draw a complete motion diagram of the tile.
| Your roommate drops a tennis ball from a third-story balcony. It hits the sidewalk and bounces as high as the second story. Draw a complete motion diagram of the tennis ball from the time it is released until it reaches the maximum height on its bounce. Be sure to determine and show the acceleration at the lowest point.

Section 1.6 Motion in One Dimension

|| FIGURE EX1.18 shows the motion diagram of a drag racer. The camera took one frame every 2 s.

FIGURE EX1.18

FIGURE EX1.18 Full Alternative Text
1. Measure the x-value of the racer at each dot. List your data in a table similar to Table 1.1, showing each position and the time at which it occurred.
2. Make a position-versus-time graph for the drag racer. Because you have data only at certain instants, your graph should consist of dots that are not connected together.
| Write a short description of the motion of a real object for which FIGURE EX1.19 would be a realistic position-versus-time graph.

FIGURE EX 1.19

FIGURE EX Full Alternative Text
| Write a short description of the motion of a real object for which FIGURE EX1.20 would be a realistic position-versus-time graph.

FIGURE EX1.20

FIGURE EX1.20 Full Alternative Text

Section 1.7 Solving Problems in Physics

|| Draw a pictorial representation for the following problem. Do not solve the problem. What acceleration does a rocket need to reach a speed of 200 m/s at a height of 1.0 km?
|| Draw a pictorial representation for the following problem. Do not solve the problem. The light turns green, and a bicyclist starts forward with an acceleration of $1.5 m / s^{2}$ . How far must she travel to reach a speed of 7.5 m/s?

Section 1.8 Units and Significant Figures

| How many significant figures are there in each of the following values?
1. $8.263 \times 10^{- 1}$
2. 0.0414
3. 75.0
4. $0.07 \times 10^{8}$
|| Convert the following to basic SI units or a combination of basic SI units:
1. 8.0 in
2. 66 ft/s
3. 60 mph
4. $14 {in}^{2}$
| Convert the following to basic SI units or a combination of basic SI units:
1. 75 in
2. $3.45 \times 10^{6} yr$
3. 62 ft/day
4. $2.2 \times 10^{4} {mi}^{2}$
|| Using the approximate conversion factors in Table 1.5, convert the following to SI units without using your calculator.
1. 20 ft
2. 60 mph
3. 60 mi
4. 8 in
| Using the approximate conversion factors in Table 1.5, convert the following SI units to English units without using your calculator.
1. 30 cm
2. 25 m/s
3. 5 km
4. 0.5 cm
| Perform the following calculations with the correct number of significant figures.
1. $159.31 \times 204.6$
2. $5.1125 + 0.67 + 3.2$
3. $7.662 - 7.425$
4. $16.5 / 3.45$
| Compute the following numbers, applying the significant figure rules adopted in this textbook.
1. $33.3 \times 25.4$
2. $33.3 - 25.4$
3. $\sqrt{33.3}$
4. $333.3 \div 25.4$
| Estimate (don’t measure!) the length of a typical car. Give your answer in both feet and meters. Briefly describe how you arrived at this estimate.
| Estimate the height of a telephone pole. Give your answer in both feet and meters. Briefly describe how you arrived at this estimate.
|| BIO Estimate the average speed with which the hair on your head grows. Give your answer in both m/s and $μ$ m/hour. Briefly describe how you arrived at this estimate.
| BIO Motor neurons in mammals transmit signals from the brain to skeletal muscles at approximately 25 m/s. Estimate how long in ms it takes a signal to get from your brain to your hand.

Problems

For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a complete pictorial representation. Do not solve these problems or do any mathematics.

| A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the jet’s acceleration as it speeds up?
| A Porsche accelerates from a stoplight at $5.0 m / s^{2}$ for five seconds, then coasts for three more seconds. How far has it traveled?
| Sam is recklessly driving 60 mph in a 30 mph speed zone when he suddenly sees the police. He steps on the brakes and slows to 30 mph in three seconds, looking nonchalant as he passes the officer. How far does he travel while braking?
| A car starts from rest at a stop sign. It accelerates at $4.0 m / s^{2}$ for 6.0 s, coasts for 2.0 s, and then slows at a rate of $2.5 m / s^{2}$ for the next stop sign. How far apart are the stop signs?
| Santa loses his footing and slides down a frictionless, snowy roof that is tilted at an angle of $30 °$ . If Santa slides 10 m before reaching the edge, what is his speed as he leaves the roof?
| A speed skater moving across frictionless ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s. What is her acceleration on the rough ice?
| A motorist is traveling at 20 m/s. He is 60 m from a stoplight when he sees it turn yellow. His reaction time, before stepping on the brake, is 0.50 s. What steady deceleration while braking will bring him to a stop right at the light?
| A car traveling at 30 m/s runs out of gas while traveling up a $10 °$ slope. How far up the hill will the car coast before starting to roll back down?
|| A Porsche challenges a Honda to a 400 m race. Because the Porsche’s acceleration of $3.5 m / s^{2}$ is greater than the Honda’s $3.0 m / s^{2}$ , the Honda gets a 1.0 s head start. Who wins?
|| David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady $2.0 m / s^{2}$ at the instant when David passes. How far does Tina drive before passing David?

Problems 44, 45, 46, 47, and 48 show a motion diagram. For each of these problems, write a one or two sentence “story” about a real object that has this motion diagram. Your stories should talk about people or objects by name and say what they are doing. Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43 are examples of motion short stories.

|

FIGURE P1.44

FIGURE P1.44 Full Alternative Text
|

FIGURE P1.45

FIGURE P1.45 Full Alternative Text
|

FIGURE P1.46

FIGURE P1.46 Full Alternative Text
|

FIGURE P1.47

FIGURE P1.47 Full Alternative Text
|

FIGURE P1.48

FIGURE P1.48 Full Alternative Text

Problems 49, 50, 51, and 52 show a partial motion diagram. For each:

Complete the motion diagram by adding acceleration vectors.
Write a physics problem for which this is the correct motion diagram. Be imaginative! Don’t forget to include enough information to make the problem complete and to state clearly what is to be found.
Draw a pictorial representation for your problem.

FIGURE P1.49

FIGURE P1.49 Full Alternative Text
FIGURE P1.50

FIGURE P1.50 Full Alternative Text
FIGURE P1.51

FIGURE P1.51 Full Alternative Text
FIGURE P1.52

FIGURE P1.52 Full Alternative Text
| As an architect, you are designing a new house. A window has a height between 140 cm and 150 cm and a width between 74 cm and 70 cm. What are the smallest and largest areas that the window could be?
| A regulation soccer field for international play is a rectangle with a length between 100 m and 110 m and a width between 64 m and 75 m. What are the smallest and largest areas that the field could be?
|| A 5.4-cm-diameter cylinder has a length of 12.5 cm. What is the cylinder’s volume in basic SI units?

Video Tutor Solution: Problem 1.55
|| BIO An intravenous saline drip has 9.0 g of sodium chloride per liter of water. By definition, $1 mL = 1 {cm}^{3}$ . Express the salt concentration in ${kg/m}^{3}$ .
|| The quantity called mass density is the mass per unit volume of a substance. What are the mass densities in basic SI units of the following objects?
1. A $215 {cm}^{3}$ solid with a mass of 0.0179 kg.
2. $95 {cm}^{3}$ of a liquid with a mass of 77 g.
| FIGURE P1.58 shows a motion diagram of a car traveling down a street. The camera took one frame every 10 s. A distance scale is provided.

FIGURE P1.58

FIGURE P1.58 Full Alternative Text
1. Measure the x-value of the car at each dot. Place your data in a table, similar to Table 1.1, showing each position and the instant of time at which it occurred.
2. Make a position-versus-time graph for the car. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together.
| Write a short description of a real object for which FIGURE P1.59 would be a realistic position-versus-time graph.

FIGURE P1.59

FIGURE P1.59 Full Alternative Text
| Write a short description of a real object for which FIGURE P1.60 would be a realistic position-versus-time graph.

FIGURE P1.60

FIGURE P1.60 Full Alternative Text