Work out on a separate sheet of paper with pictures, equations and the answer. Attach to the PAK.

6. A train leaves the station at the 0.0 m marker traveling with a constant velocity of 36.0 m/s. How many seconds later
will the train pass the 1620.0 m marker? What is the velocity of the train in km/hr? 45
s, 130 km/h

10. Sketch the position vs. time graphs for these four motions

a. starting at a positive position with a positive velocity.

b. starting at a negative position with a small positive
velocity.

c. remaining at a negative position.

d. starting at a positive position with a negative velocity.

20. From the reference frame of a stationary observer, a car, traveling at a constant speed of 92 km/hr is passed by a
truck moving at 105 km/h.

From the point of view of the car, what is the truck's speed? 13 km/h

From
the point of view of the truck, what is the car's speed? –13 km/h

4. A bus is moving at 25 m/s. The driver steps on the brakes and the bus stops in 3.0 s.

What is the average acceleration
of the bus while braking? –8.3 m/s^{2}Suppose the bus took twice as long to stop.
How would the acceleration compare to the acceleration above? -4.2 m/s^{2}

10. A bus traveling at +30 km/h accelerates at a constant +3.5 m/s^{2} for 6.8 s. What is the final velocity in
km/h? 116 km/h

14. A rocket traveling at +88 m/s is accelerated uniformly to +132 m/s over a 15 s interval. What is the displacement during
this time? 1.7 x 10^{3} m

18. Starting from rest a car moves 110 m in the first 5.0 s of uniform acceleration. What is the car's acceleration? 8.8 m/s^{2}

21. An airplane accelerates from a velocity of 21 m/s at a constant rate of 3.0 m/s^{2} over +535 m. What is the
final velocity? 60 m/s

25. A brick falls freely from a high scaffold. What is its velocity after 4.0 s? How far does the brick fall during the
first 4.0 s? -39 m/s down -78 m down

29. A man falls 1.0 m to the ground. How long does the fall take? How fast is he going when he hits the floor? 0.45 s, -4.4 m/s

20. Engineers are developing new types of guns that might someday be used to launch satellites as if they were bullets.
One such gun can give a small object a velocity of 3.5 km/s moving it through only 2.0 cm.

What acceleration does this
gun give the object? 3 x 10^{8 }m/s^{2}

Over what time interval does this take
place? 1.14 x 10 ^{-5} s

25. A driver of a car going 90.0 km/h suddenly sees the lights of a barrier 40.0 m ahead. It takes the driver 0.75 s to
apply the brakes and the average acceleration of the car is -10.0 m/s^{2}.

Determine if the car hits the barrier.
just

What is the maximum speed at which the car could be moving and not hit the barrier, assuming
the acceleration rate doesn't change? <90 km/h

30. A stone falls freely from rest for 8.0 s

Calculate the stone’s velocity after 8.0 s. 80
m/s

What is the stone's displacement during this time? 320 m

Problems: PAK 3

Work out on a separate sheet of paper with pictures, equations and the answer. Attach to the PAK.

2. Together a motorbike and a rider have a mass of 275 kg. The motorbike is slowed down with an acceleration of -4.50 m/s^{2}.
What is the net force on the motorbike? Describe the direction of this force and the meaning of the negative sign.
-1240 N

7. A 20 N stone rests on a table. What is the force the table exerts on the stone? In what direction?
20N up

8. An astronaut with a mass of 75 kg travels to Mars.

What is his weight on Earth? 740 N

What
is his weight on Mars where g=3.8 m/s^{2}? 290 N

What is the value of g on top of a
mountain if the astronaut weighs 683 N? 9.1 m/s^{2}

9. Suppose Joe, who weighs 625 N, stands on a bathroom scale calibrated in newtons.

What force would the scale exert
on Joe? in what direction? 625 up

If Joe now holds a 50 N cat in his arms, what force would the scale exert on him? 675 N

After
Joe puts down the cat, his father comes up behind him and lifts his elbows with a 72 N force. What force does the scale now
exert on Joe? 553 N up

13. A rubber ball weighs 49 N. What is the mass of the ball? What is the acceleration of the ball if an upward force of
69 N is applied? 5.0 kg , 4.0 m/s^{2}

15. The space shuttle has a mass of 2.0 x 10^{6} kg. At lift-off the engines generate an upward force of 30 x 10^{6}
N.

What is the weight of the shuttle? 20 x 10 ^{6} N

What is the acceleration of
the shuttle when launched? 5.0 m/s^{2}The average acceleration of the shuttle during
its 10 minute launch is 13 m/s^{2}. What velocity does it attain? 7.8 km/s

As the space
shuttle engines burn, the mass of the fuel becomes less and less. Assuming the force by the engines remains the same, would
you expect the acceleration to increase, decrease, or remain the same? Why? It would increase

4. A physics book is motionless on the top of a table. If you give it a hard push with your hand, it slides across the
table and slowly comes to a stop. Use Newton's first law of motion to answer the following questions.

Why is the book motionless before the force is applied?

Why does the book move when the hand pushes on it?

Why does
the book eventually come to a stop?

Under what conditions would the book remain in motion at constant speed?

12. When a strike hits wooden blocks the hand undergoes an acceleration of -6500 m/s^{2}. Medical data indicates
the mass of the forearm and hand to be 0.7 kg. What is the force exerted on the hand by the blocks? What is its direction?
4550 N, back against the hand

A student stands on a bathroom scale in an elevator at rest on the 64th floor of a building . The scale reads 836 N.

As the elevator moves up the scale increases to 935 N then decreases back to 836 N. Find the acceleration of the elevator.
1.2 m/s^{2}

As the elevator of approaches the 74th floor the scale drops as low as 782
N. what is the acceleration of the elevator? .6 m/s^{2}

Using your results from
parts a and b, explain which change in velocity would take longer. Stopping on the way up.

Explain
the changes in the scale you would expect on the ride down. Less force on the scale,
then more.

Problems PAK 4

1. After walking 11 km due north from camp a hiker then walks 11 km due east. What is the total distance walked by the
hiker? Determine the total displacement from the starting point. 22 km, 16 km

4. A motorboat heads due east at 16 m/s across a river that flows due north at 9.0 m/s.

What is the resultant velocity
(speed and direction) of the boat? 18 m/s 29 degrees north of east

If the river is 136 m wide,
how long does it take the motorboat to reach the other side? 8.5 s

How far downstream is the
boat when it reaches the other side of the river? 77 m

7. A 110 N force and a 55 N force act on an object point P. the 110 N force acts at 90° .The 55 N force acts at 0° . What
is the magnitude and direction of the resultant force? 120 N 63 degrees

8. A motorboat travels at 8.5 m/s. It heads straight across a river 110 m wide. If the water flows downstream at
a rate of 3.8 m/s what is the boat's resultant velocity? 9.3 m/s 24 degrees

How long does it
take the boat to reach the opposite shore? 13 s

11. A heavy box is pulled across a wooden floor with a rope. The rope makes an angle of 60° with the floor. A force of
75 N is exerted on the rope. What is the component of the force parallel to the floor? 37.5
N

18. Two forces act on an object. One force is 6.0 N horizontally. The second force is 8.0 N vertically.

Find the magnitude
and direction of the resultant.

If the object is in equilibrium, find the magnitude and direction
of the force that produces equilibrium. 10 N 53 degrees, 233 degrees

10. A ship leaves its home port expecting to travel to a port 500 km due south. Before it can move, a severe storm comes
up and blows the ship 100 km due east. How far is the ship from its destination? What direction must it travel to get there?

18. Sue and Jenny kick a soccer ball at the same time. Sue's foot exerts a force of 66 N north. Jenny's foot exerts a force
of 88 N east. What is the magnitude and direction of the resultant force on the ball?

23. A 40 kg crate is pulled across ice with a rope. A force of 100 N is applied at an angle of 30° with the horizontal.
Neglecting friction, calculate the acceleration of the crate and the upward force the ice exerts.

**2D Motion**

1. A stone is thrown horizontally at a speed of +5.0 m/s from the top of a cliff 78.4 m high.

How long does it take
the stone to reach the bottom of the cliff? 4 s

How far from the base of the cliff does the
stone strike the ground? 20 m

What are the horizontal and vertical components of the velocity
of the stone just before it hits the ground? 5.0 m/s, -39.2 m/s

3. A steel ball rolls with constant velocity across a tabletop 0.950 m high. It rolls off and hits the ground +0.352 m
horizontally from the edge of the table. How fast was the ball rolling? 0.800
m/s

4. An auto, moving too fast on a horizontal stretch of mountain road slides off the road falling into deep snow 43.9 m
below the road and 87.7 m beyond the edge of the road.

How long did the auto take to fall? 2.99 s

How fast was it going when it left the road ( in m/s and km/h) 29.3 m/s,
105 km/h

What was the acceleration 10 m below the edge of the road? –9.80 m/s2 always

8. A rude tourist throws a peach pit horizontally with a 7.0 m/s velocity out of an elevator cage. If the elevator is not
moving, how long will the pit take to reach the ground 17.0 m below?1.86 s

How far horizontally
from the elevator will the pit land? 13 m

He throws the next pit when the elevator is at the same height but moving upward at a constant 8.5 m/s velocity. How long
will it take the pit to land? 2.92 s

How far away will this pit land? 20
m

5. An airplane traveling 1001 m above the ocean at 125 km/h is to drop a box of supplies to shipwrecked victims below.

How
many seconds before being directly overhead should the box be dropped?

What is the horizontal distance between the plane
and the victims when the box is dropped?

6. Divers at Acapulco dive from a cliff that is 61 m high. If the rocks below the cliff extend outward for 23 m, what is
the minimum horizontal velocity a diver must have to clear the rocks?

Problems: PAK 5

Work out on a separate sheet of paper with pictures, equations and the answer. Attach to the PAK.

10. A runner moving at a speed of 8.8 m/s rounds a bend with a radius of 25 m.

Find the centripetal acceleration of the runner. 3.1 m/s2

What supplies the force needed to give this acceleration to the runner? Friction on shoes

11. Racing on a flat track, a car going 32 m/s rounds a curve 56 m in radius.

What is the car's centripetal acceleration? 18 m/s2

What would be the minimum coefficient of static friction between the tires and road that would be needed for the car to
round the curve without skidding? 1.8

12. A racing car rounds a curve that is banked.

Sketch the auto tire on the incline drawing vectors that represent all the forces on the tire.

Components of what two
forces provide the centripetal acceleration fro the auto tire, and therefore, the auto?

13. It takes a 615 kg racing car 14.3 s to travel at a uniform speed around a circular racetrack of 50.0 m radius.

What
is the acceleration of the car? 9.7 m/s^{2}

What average force must the track exert
on the tires to produce this acceleration? 5940 N

15. Sue whirls a yo-yo in a horizontal circle. The yo-yo has a mass of 0.20 kg and is attached to a string 0.80 m long.

If
the yo-yo makes 1.0 complete revolutions each second, what force does the string exert on it?

If Sue increases the speed
of the yo-yo to 2.0 revolutions per second, what force does the string now exert? 6.28 N, 25 N

A wrench with a handle 20 cm in length is used to loosen a nut by applying a force of 10 N. What is the value of the applied
torque? 2 Nm

A meter stick has a mass of .5 kg. Where is its center of mass located if the stick is uniform throughout? If the stick
is placed on a pivot at the 30 cm mark, where must a 1 kg mass be placed to balance the stick in equilibrium? 50 cm mark, 20 cm mark

A bridge is 20 m long, has a mass of 2000 kg and is supported on each end by a steel abutment. If a truck parks 5 m from
the end and has a mass of 1000 kg, what is the force in each of the steel abutments (ends)? 12.5 kN, 17.5
kN

Mr. Dunlap, with a mass of 100 kg, walks out to the end of a plank over shark infested waters. The plank is on a pivot
2 m from one end. The total plank length is 10 m. A rope from rigging can apply an upward force of 1000 N on the plank, before
snapping, at the 5 m mark. If a pile of bricks is on the short end keeps the system in equilibrium, what is the minimum mass
of the bricks. Assume the pile acts on the very end and the mass of the plank is negligible. 250 kg

Problems PAK 6:

Work out on a separate sheet of paper with pictures, equations and the answer. Attach to the PAK.

1. A compact car, mass of 725 kg is moving at +100 km/h. Find its momentum. 2.02
x 10 4 kg m/s

At what velocity is the momentum of a larger car, mass 2175 kg, equal to that of the smaller car?

33.4 km/h

3. The brakes exert 6.40 x 10^{2} N force on a car weighing 15680 N and moving at 20.0 m/s. The car finally stops.

What
is the car's mass? 1600 kg

What is its initial momentum? 32000 kg m/s

What
is the change in the car's momentum? –32000 kg m/s

How long does the braking force act
on the car to bring it to a halt? 50 s

5. A 0.105 kg hockey puck moving at 48 m/s is caught by a 75 kg goalie at rest. With what speed does the goalie slide on
the ice? 0.067 m/s

8. A 0.50 kg ball traveling at 6.0 m/s collides head on with a 1.00 kg ball moving in the opposite direction at a velocity
of -12.0 m/s. The 0.50 kg ball moves away at -14 m/s after the collision. Find the velocity of the second ball. –2.0
m/s

10. A thread hold two carts together on a frictionless surface. A compressed spring acts upon the carts. After the
thread burned The spring pushes the two cars apart. The 1.5 kg cart moves with a velocity of 27 cm/s to the left.
What is the velocity of the 4.5 kg cart? 9.0 m/s to the right

12. A colonial gunner sets up his 225 kg canon at the edge of the flat top of a high tower. It shoots a 4.5 kg cannon ball
horizontally. The ball hits the ground 215 m from the base of the tower. The cannon also moves, on frictionless wheels, and
falls of the back of the tower and lands on the ground.

What is the horizontal distance of the cannon's landing, measured
from the base of the tower? 4.3 m

Why do you not need to know the width of the tower? No friction; time in the air is the same

1. Can a bullet have the same momentum as a truck? Explain. yes

8. The white cue ball travels across a pool table and collides with the stationary eight ball. The two balls have equal
mass. After colliding the cue ball is at rest. What must be the speed of the eight ball? Why? the
original speed of the cue

10. Small rockets are used to make adjustments in the speed of satellites. One such rocket has a thrust of 35 N. If it
is fired to change the velocity of a 72000 kg spacecraft by 63 cm/s, how long should it be fired? 22
min

12. A car moving at 10 m/s crashes into a barrier and stops in 0.25 m.

Find the time required to stop the car.
.02 s

If a 20 kg child were to be stopped in the same time as the car, what average force must
be exerted? 10000 N

Approximately what is the mass of an object whose weight equals the force
from part b? Could you lift such a mass with your arm? 1000 kg

What does your answer say about
holding an infant in your lap instead of using a separate infant restraint?

20. A 15 g bullet is shot into a stone a 5085 g wooden block standing on a frictionless surface. The block, with the bullet
in it, acquires a velocity of 1.0 m/s. Calculate the velocity of the bullet before striking the block. 340
m/s

23. Two students on roller skates stand face to face, then push each other away. One student has a mass of 90 kg, the other
60 kg.

Find the ratio of their velocities just after their hands lose contact.

Which student has the greater
speed? 60 kg student

PAK 7 Problems:

Work out on a separate sheet of paper with pictures, equations and the answer. Attach to the PAK.

1. A force of 825 N is needed to push a car across a lot. Two students push the car 35 m.

How much work is done? 29000 J

After a rainstorm, the force needed to push the car doubles because the ground became soft. By what amount does the work
done by the students change? 2x

4. You and a friend each carry identical boxes down the hall. You choose to carry it first up the stairs, then down the
hall. Your friend carries it down the hall then up another stairwell. Who does more work? Same amount

5. How much work does gravity do when a 25-N object falls a distance of 3.5 m? 88 J

8. A worker pushes a crate weighing 93 N up an inclined plane, pushing horizontally parallel to the ground.

The worker
exerts a force of 85 N. How much work does he do? 340 J

How much work is done by gravity? -279 J against gravity

The coefficient of friction is 0.20. How much work is done by friction? 130 J

10. A rock climber wears a 7.50 kg knapsack while scaling a cliff. After 30.0 min the climber is 8.2 m above the starting
point.

How much work does the climber do on the knapsack? 600 J

If the climber weighs 645
N how much work does she do lifting herself and the knapsack? 5900 J

What is the average power
developed by the climber? 3.3 W

11. An electric motor develops 65 kW of power as it lifts a loaded elevator 17.5 m in 35.0 s. How much force does the motor
exert? 1.3 x 10 ^{5 }N

15. A boy exerts a force of 225 N on a lever to raise a 1.25 x 103 N rock a distance of 0.13 m. If the lever is 88.7% efficient,
how far did the boy move his end of the lever? 0.81 m

16. A 60 kg crate is slid up a an inclined ramp 2.0 m long onto a platform 1.0 m above floor level. A 400 N force, parallel
to the ramp is needed to slide the crate up the ramp at a constant speed.

How much work is done in sliding the crate up
the ramp? 800 J

How much work would be done if the crate were simply lifted straight up from
the floor to the platform? 600 J

18. A force of 300 N is used to push a 145 kg mass 30.0 m horizontally in 3.00 s.

Calculate the work done on the mass.
9000 J

Calculate the power. 3000 W

29. Stan raises a 1000 N piano a distance of 5.00 m using a set of pulleys. Stan pulls 20.0 m of rope.

How much effort
force did Stan apply if this was an ideal machine? 250 N

What force is used to overcome
friction if the actual effort is 300 N? 50 N

What is the work output? 5000
J

What is the work input? 6000 J

What is the mechanical advantage? 4
(ideal)

34. What work is required to lift a 215 kg mass a distance of 5.65 m using a machine that is 72.5% efficient?

2. A rifle can shoot a 4.20 g bullet at a speed of 965 m/s.

Find the kinetic energy of the bullet. 1960
J

What work is done on the bullet if it starts from rest? 1960 J

If the work is done
over a distance of 0.75 m, what is the average force on the bullet? 2600 N

If the bullet comes
to rest by pushing 1.5 cm into metal, what is the magnitude and direction of the average force it exerts? 1300
N

7. A person weighing 630 N climbs a ladder to a height of 5.0 m

What work does the person
do? 3200 J

What is the increase in the gravitational potential energy of the person from the
ground to this height? 3200 J

Where does the energy come from to cause this increase in the
gravitational potential energy? Work of person

9. A bike rider approaches a hill with a speed of 8.5 m/s. The total mass of the bike and rider is 85 kg.

Find the kinetic
energy of the bike and rider. 3100 J

The rider coasts up the hill. Assuming there is no friction,
at what height will the bike come to a stop? 3.7 m

Does your answer depend on the mass of the
bike and rider? Explain. no

10. Tarzan, mass 85 kg swings down from a tree limb at the end of a 20 m vine. His feet touch the ground 4.0 m below the
limb.

How fast is Tarzan moving when he reaches the ground? 8.9 m/s

Does your answer
depend on Tarzan's mass? Why or why not? no

Does your answer depend on the length of the vine?
Why or why not? no

11. A skier starts from rest at the top of a 45 m hill, skis down a 30 incline into a valley and continues up a 40 m hill.
Both hill heights are measured from the valley floor. Assume you can neglect friction and the effect of the ski poles.

How
fast is the skier moving at the bottom of the valley? 30 m/s

What is the skier's speed at the
top of the next hill? 10 m/s

15. As everyone knows, bullets bounce off Superman's chest. Suppose Superman, mass 104 kg, while not moving, is struck
by a 4.2 kg bullet moving with a speed of 835 m/s. If the collision is perfectly elastic, find the speed of Superman after
the collision. Assume the bottoms of his super feet are frictionless.

6. Pam has a mass of 40.0 kg and she is at rest on smooth level frictionless ice. Pam straps on a rocket pack. The rocket
supplies a a constant force for 22.0 m and Pam acquires a speed of 62.0 m/s.

What is the magnitude of the force? 3500 N

What is Pam's final kinetic energy? 76.9 kJ

24. Betty weighs 420 N and she is sitting on a playground swing seat that hangs 0.40 m above the ground. Tom pulls the
swing back and releases it when the seat is 1.00 m above the ground.

How fast is Betty moving when the swing passes through
its lowest position?

If Betty moves through the lowest point at 2.0 m/s, how much work was done on the swing by friction?
3.5 m/s, 168 J

29. A railroad car with a mass of 5.0 x 10^{ 5} kg collides with a stationary car of equal mass. After the collision,
the two cars lock together and move of at 4.0 m/s.

Before the collision, the first railroad car was moving at 8.0 m/s.
What was its momentum? 4 x 10^{6} kg m/s

What is the total momentum of the two cars
after the collision? 4 x 10^{6} kg m/s

Find the kinetic energies of the two cars before
and after the collision. 16 x 10^{6} J, 8 x10^{6} J

Account for the loss
of kinetic energy. Friction, sound

30. From what height would a compact car have to be dropped to have the same kinetic energy it has when driven at 100 km/h?
38 m

Term 2 Problems:

PAK 8

1. An asteroid revolves around the sun with a mean (average) orbital radius twice that of
the Earth's. Predict the period of the asteroid in years.

2. You can calculate that on average, Mars is 1.52 times as far from the sun as is Earth.
Predict the time required for Mars to circle the sun in earth days.

3. The moon has a period of 27.3 days and has a mean distance of 3.90x10^{5} km from
the center of Earth. Find the period of an artificial satellite that is 6.70 x 10^{3} km from the center of Earth.

4. From data on the period and radius to the moon, find the mean distance from the Earth's
center to an artificial satellite that has a period of 1.00 day.

21. A pendulum has a length of 0.67 m.

Find its period.

How long would the pendulum
have to be to double the period?

Why is your answer not just double the length?

2. Uranus requires 84 years to circle the sun. Find Uranus' orbital radius as a multiple of
Earth's orbital radius.

13. What is the length of a simple pendulum whose period is 1.00 s? Assume normal g.

14. A future astronaut lands on a planet with an unknown value of g. She finds that the period
of a pendulum 0.65 m long is 2.8 s. What is g for the surface of this planet?

5. Calculate the velocity that a satellite shot from Newton's cannon must have in order to
orbit the Earth, 150 km above its surface. How long would it take for the satellite to the cannon in seconds and minutes?

7. Find the velocity with which Mercury moves around the sun. Also, find the velocity of Saturn.
Comment on whether or not it makes sense that Mercury is named after a speedy messenger of the gods, while Saturn is named
after the father of Jupiter.

8. We can consider the sun to be a satellite of our galaxy, the Milky Way. The sun revolves
around the center of the galaxy with a radius of 2.2 x 10 ^{20} m. the period of one rotation is 2.5 x 10^{8}
years.

Find the mass of the galaxy.

Assuming the average star in the galaxy has the mass of the
sun, find the number of stars.

Find the speed with which the sun moves around the center of the galaxy.

8. Tom has a mass of 70.0 kg and Sally has a mass of 50 kg. Tom and Sally are standing
20.0 m apart on the dance floor. Sally looks up and sees him, feeling an attraction. If the attraction is gravitation, find
its size. Assume both can be replaced by spherical masses.

12. The gravitational force between two electrons 1.00 m apart is 5.42 x 10 ^{-71
}N. Find the mass of an electron.

18. Mimas, a moon of Saturn has an orbital radius of 1.87 x 10^{8} m and an
orbital period of 23 h. Use Newton's version of Kepler's third law and these data to find the mass of Saturn.

21. On July 19, 1969 Apollo II s orbit around the moon was adjusted to an average of
111 km. The radius of the moon is 1785 km and the mass of the moon is 7.3 x 10 ^{22} kg.

How many minutes did it
take to orbit once?

At what velocity did it orbit the moon?

What is the period of the following frequencies: 10 Hz, 25 Hz, 300 MHz

What is the frequency for a period of 1000s, 1s, 100ms

PAK 9

Assume the speed of sound in air is 340 m/s.

1. A sound wave produced by a clock chime 515 m away is heard 1.50 s later.

What is the speed of sound in air? 343 m/s

The sound wave has
a frequency of 436 Hz. What is its period? What is its wavelength? .002 s, .78 m

2. A hiker shouts toward a vertical cliff 685 m away. The echo is heard 4.00 s later.

What
is the speed of sound in air? 343 m/s

The wavelength of the sound is 0.750 m. What is
its frequency? What is the period of the wave?

456 Hz, .002 s

4. A typical light wave has a wavelength of 580 nm.

What is the wavelength
of the light in meters? What is the frequency of the wave? 5.8 x 10^{-7} m, 5.2 x 10 ^{-14}
Hz

6. A long spring runs across a floor of a room and out the door. A pulse is sent along the
spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying
loose on the floor? atrtached to wall

3. The human ear can detect sounds with frequencies between 20 Hz and 16 kHz. Fins the largest
and smallest wavelengths the ear can detect, assuming the sound travels through air at 343 m/s at 20° C.

6. The 440 Hz tuning fork is used with a resonating column to determine the velocity of sound
in helium gas. If the spacings between resonances are 110 cm what is the velocity of sound in He?

10. A soprano saxophone is an open pipe. If all the keys are closed it is approximately 65
cm long. Using 340 m/s as the speed of sound, find the lowest frequency that can be played on this instrument.

12. A student has two tuning forks, one with a frequency of 349 Hz and the other with frequency
unknown. When struck together, the tuning forks produce 3 beats per second. What are possible frequencies of the unknown tuning
fork? 352 Hz, 346 Hz

2. An ocean wave has a length of 10.0 m. A wave passes a fixed location every 2.0 s. What
is the speed of the wave? 5 m/s

7. AM radio signals are broadcast at frequencies between 550 kHz and 1600 kHz and travel 3.0
x 10 ^{8} m/s. What is the range of wavelengths for these signals?

FM frequencies range
between 88 MHz and 108 MHz and travel the same speed. What is the range of FM wavelengths?

10. The speed of sound in water is 1498 m/s. A sonar signal is sent from a ship at a point
just below the water and 1.80 s later the reflected signal is detected. How deep is the ocean beneath the ship? 1348 m

11. The equation for the Doppler shift of a sound wave of speed v, reaching a moving detector
is

f' = f(v+v_{d}/v-v_{s})

where v_{d} is the speed of the detector, v_{s} is the speed of the source;f
is the frequencyof the source; f'is the frequency of the detector. If the detector moves toward the source, v_{d}
is positive; if the source moves toward the detector, v_{s} is positive. A train moving toward a detector at 31 m/s
blows a 305 Hz horn. What frequency is detected by a stationary train? By a train moving toward the first train at a speed
of 21 m/s? higher and higher

18. The lowest note on an organ is 16.4 Hz.

What is the shortest open
organ pipe that will resonate with this frequency 10.4 m

What would be the pitch if the
same organ pipe were closed? 5.2 m

PAK 10

What is the frequency of yellow light, wavelength = 556 nm?

The distance to the moon can be found with the help of mirrors left there by astronauts.
A pulse of light is sent to the moon and returns in 2.562 seconds. Calculate the distance to the moon.

Light in air is incident a piece of crown glass at an angle of 45 degrees. What is the
angle of refraction?

A ray of light passes from air into water at an angle of 30 degrees. Find the angle
of refraction.

A ray of light is incident upon a diamond at 45 degrees.

What is the angle of refraction?

Does
diamond or glass bend light more? diamond

A block of unknown material is submerged in water. Light incident on the block at an
angle of 31 degrees. The angle of refraction in the block is 27 degrees. What is the index of refraction for the
material?

A block of material has a critical angle of 45 degrees. What is the index of refraction.

Violet light falls on two slits separated by 1.90 x 10^{-5} m. A first order
line appears 13.2 mm from the central bright line on a screen 0.600 m from the slits. What is the wavelength of the
violet light?

A physics class uses a laser with a known wavelength of 632.8 nm in a double slit experiment.
The slit separation is unknown. A student places a screen 1.00 m in front of the slits and finds the first order line
65.5 mm from the central line. What is the slit separation?

Using the same apparatus with green light, the first order line is at 58.8 mm from the central
line. What is the wavelength of the green light?

Light from a He-Ne Laser with a wavelength of 632.8 nm falls on a slit of unknown width.
A pattern is formed on a screen 1.15 m away where the first dark band is 7.5 mm from the center of the central bright band.
How wide is the slit?

Yellow light falls on a single slit 0.0295 nm wide. On a screen 60.0 cm away, there
is a dark band 12,0 mm from the center of the bright central band. What is the wavelength of the light?

An object 3.0 mm high is 10.0 cm in front of a concave mirror having a 6.0 cm focal length.
Find the image by means of

A ray diagram

The mirror equation

Find the magnification of the mirror

What is the
height of the image?

The image of an object is 30.0 cm from a concave mirror with a 20.0 cm radius of curvature.
Locate the object.

An object is 4.0 cm in front of a concave mirror having a 12.0 cm radius. Locate the
image using the mirror equation and a ray diagram.

A 4.0 cm high candle is placed 10.0 cm from a concave mirror having a focal length of 16.0
cm.

Where is the image located?

What is the height of the candle’s image?

A convex mirror has a focal length of –12 cm. A light bulb with a diameter of 6.0 cm
is placed 60.0 cm in front of the mirror.

Where is the image of the light bulb?

What is the diameter of the image?

Use a ray diagram to find the image position of an object 30 cm to the left of a convex
lens with a +10 cm focal length.

A lens is needed to create an inverted image twice as large as the object when the object
is 7.0 cm from the lens. What focal length is needed?

A newspaper is held 6.0 cm from a convex lens with a 20.0 cm focal length. Find the
image distance for the newsprint.

You are looking at a stamp with a magnifying glass. How do you make the image look larger?

What is the maximum distance you can move and still see a large image?

PAK 11

1. Two positive charges of 6.0 x 10 ^{-6} C are separated by 0.50 m . What force
exists between the charges?

2. A negative charge of -2.0 x 10 ^{-4} C and a positive charge of 8.0 x 10
^{-4} C are separated by 0.30 m. What is the force between the two charges?

3. A negative charge of -6.0 x 10^{ -6 }C exerts an attractive force of 65 N
on a second charge 0.050 m away. What is the magnitude of the second charge?

4. An object with charge +7.5 x 10 ^{-7} C is placed at the origin. The position
of a second object, charge +1.5 x 10 ^{-7 }C is varied from 1.0 cm to 5.0 cm. Draw a graph of the force of the object
at the origin.

7. What potential difference is applied to two metal plates 0.500 m apart if the electric
field between them is 2.5 x 10^{3} N/C?

13. A 27 mF capacitor has a potential difference
of 25 V across it. What is the charge on the capacitor?

16. A 2.2 mF capacitor is first charged so
that the potential difference is 6.0 V. How much additional charge is needed to increase the potential difference to 15.0
V?

12. A force of -4.4 x 10^{3} N exists between a positive charge of 8,.0 x 10
^{-4} C and a negative charge of -3.0 x 10^{-4} C . What distance separates the charges?

19. The two pith balls each have a mass of 1.0 g and equal charges. One pith ball is
suspended by an insulating thread. The other is brought to 3.0 cm from the suspended ball. The suspended ball is now hanging
with the thread forming an angle of 30.0° with the vertical. The ball is in equilibrium
with F_{E}, mg, and T adding vectorially to yield zero. Calculate mg, F_{E} and the charge on the balls.

9. A positive test charge of 8.0 x 10^{-5} C is placed in an electric field
of 50.0 N/C intensity. What is the strength of the force exerted on the test charge?

14. A force 0.053 N is required to move a charge of 37 mC a distance of 25 cm in an
electric field. What is the size of the potential difference between the two points?

1. The current through a light bulb connected across the terminals of a 120 V outlet
is 0.5 A. What is the resistance of the bulb?

3. What current flows through a 120W light
bulb connected to a 120 V outlet?

6. A motor with an operating resistance of 32 ohms is connected to a voltage source.
The current in the circuit is 3.8 A. What is the voltage of the source?

9. What voltage is applied to a 4.0 ohm resistor if the current is 1.5 A?

11. A voltage of 75 V is placed across a 15 ohm resistor. What is the current through
the resistor?

PAK 12:

8. A lamp draws a current of 0.5 A when it is connected to a 120 V source.

What
is the resistance of the lamp?

What is the power consumed by the lamp?

9. A 75 W lamp is connected to 120 V.

How much current flows through the lamp?

What
is the resistance of the lamp?

14. A 15 ohm electric heater operates on a 120 V outlet.

What is the current through the heater?

How much energy is used by the heater in 30.0
s?

How much thermal energy is liberated by the heater in this time?

16. A 100.0 W light bulb is 20.0% efficient. That means 20.0% of the electric energy is converted
to light energy.

How many joules does the light bulb convert into light each minute it is in operation?

How
many joules of thermal energy does the light bulb produce each minute?

18. An electric space heater draws 15.0 A from a 120 V source. It is operated on average for
5.0 h each day.

How much power does the heater use?

How much energy in kWh does it consume in 30 days?

At $0.11 per kWh, what does it cost to operate it for 30 days?

5. A 4000 W clothes dryer is connected to a 220 V circuit. How much current does the dryer
draw?

27. A transistor radio operates by means of a 9.0 V battery that supplies it with a 50 mA
current.

If the cost of the battery is $0.90 and it lasts for 300 h, what is the cost per kWh to operate the radio in
this manner?

The same radio, by means of a converter, is plugged into a household circuit by a homeowner
who pays $0.08 per kWh. What does it now cost to operate the radio for 300 h?

2. A 10 ohm resistor, a 15 ohm resistor and a 5 ohm resistor are connected in series across
a 120 V generator.

What is the equivalent resistance of the circuit?

What is the current in the circuit?

5. A 20.0 ohm resistor and a 30.0 ohm resistor are connected in series and placed across a
120 V potential difference.

What is the equivalent resistance of the circuit?

What is the current in the circuit?

What is the voltage drop across each resistor?

What is the voltage drop across the two resistors together?

8. A photoresistor is used in a voltage divider as R2. V = 9.0 V and R1 = 500 ohms.

What is the output voltage V2 across R2 when a bright light strikes the photoresistor and
R2 = 475 ohms?

When the light is dim R2 = 4.0 kilo ohms. What is V2?

When the photoresistor is in total darkness, R2 = 0.4 Megaohms. What is V2?

9. Three 15 ohm resistors are connected in parallel and placed across a 30 V potential difference.

What is the equivalent resistance of the parallel circuit?

What is the current through the entire circuit?

What is the current through each branch of the parallel circuit?

12. Suppose the a 12 ohm and a 15 ohm resistor are connected in parallel and placed across
the terminals of a 15.0 V battery. If the 12 ohm resistor is replaced by a 10 ohm resistor

Does the equivalent resistance become larger, smaller or stay the same?

Does the amount of current through the entire circuit change? In what way?

Does the amount of current through the 15.0 ohm resistor change? In what way?

15. Suppose you are given three 68 ohm resistors . You can use them in a series, parallel,
or series-parallel circuit. Find the three resistances you can produce in the circuit.

5. A lamp having a resistance of 10W is connected across a 15 V battery.

What is the current through the lamp?

What resistance must be connected in series with the lamp to reduce the current to 0.50 A?

4. A string of 18 identical Christmas lights are connected in series to a 120 V source. The
string dissipates 64.0 W.

What is the equivalent resistance of the light string?

What is the resistance of a single light?

What is the power dissipated by each lamp?

14. A 16.0 ohm and a 20.0 ohm resistor are connected in parallel. A difference in potential
of 40.0 V is applied to the combination.

Compute the equivalent resistance of the parallel circuit.

What is the current in the
circuit?

How large is the current through the 16.0 ohm resistor?

PAK 13

1. A student holds a bar magnet in each hand. If both hands are brought close together, will
the force be attractive of repulsive if the magnets are held so that the two N poles are brought close together?

A N pole
and a S pole are brought close together?

5. A long straight current carrying wire runs from north to south.

A compass needle is
placed above the wire and points its N pole toward the east. In what direction is the current flowing?

If a compass is
put underneath the wire, in what direction will the needle point?

6. Suppose you measure the strength of a magnetic field 1 cm from a current carrying wire
. Compare this value with

the strength of the field 2 cm from the wire.

the strength of the field 3 cm from the wire.

10. A wire 0.50 m long carrying a current of 8.0 A is at right angles to a 0.40 T magnetic
field. How strong a force acts on the wire?

12. A copper wire 40 cm long carries a current of 6.0 A and weighs 0.35 N. A certain magnetic
field is strong enough to balance the force of gravity on the wire. What is the strength of the magnetic field?

16. Doubly ionized helium atoms (alpha particles) are traveling at right angles to a magnetic
field at a speed of 4.0 x 10^{-2} m/s. The field strength is 5.0 x 10^{-2}T. What force acts on each particle?

9. The current through a wire 0.80 m long is 5.0 A. The wire is perpendicular to a 0.60 T
magnetic field. What is the magnitude of the force on the wire?

20. A beam of electrons moves at right angles to a 6.0 x 10^{-2}T magnetic field.
The electrons have a velocity of 2.5 x 10^{6} m/s. What is the magnitude of the force on each electron.

1. A straight wire, 0.5 m long is moved straight up through a 0.4 T magnetic field pointed
in the horizontal direction at a speed of 20 m/s.

What EMF is induced in the wire?

The wire is part of a circuit of total resistance of
6.0 ohms. What is the current in the circuit?

4. A straight wire, 30.0 m long, moves at 2.0 m/s perpendicularly through a 1.0 T magnetic
field.

What EMF is induced in the wire?

The total resistance of the circuit of which wire is
a part is 15.0 ohms. What is the current?

6. The effective voltage of a particular AC household outlet is 117 V.

What is the maximum voltage across a lamp connected to the outlet?

The effective current through the lamp is 5.5 A. What is the maximum current in the lamp?

9. A step down transformer has 7500 turns on its primary and 125 turns on its secondary.
The voltage across the primary is 7200 V.

What voltage is across the secondary?

The current in the secondary is 36 A. What current
flows in the primary?

2. A proton moves at a speed of 7.5 x 10^{3} m/s as it passes through a 0.6 T magnetic
field. Find the radius of the circular path. The charge carried by the proton is equal to that of the electron, but is positive.

5. A stream of singly ionized lithium atoms is not deflected as it passes through a 1.5 x
10^{-3} T magnetic field perpendicular to a 6.0x10^{-2} V/m electric field.

What is the speed of the lithium atoms as they pass through the crossed fields?

The lithium
atoms move into a 0.18 T magnetic field. They follow a circular path of radius 0.165 m. What is the mass of a lithium atom?

7. A beam of singly ionized oxygen atoms is sent through a mass spectrometer.
The values are B= 7.2 x 10^{-2} T, q= 1.6x10^{-19} C, r = 0.085 m, and V=110 V. Find the mass of an oxygen
atom.

8. The example problem found the mass of a neon isotope. Another neon isotope has a mass of
22 proton masses. How far on the film from the first isotope would these ions land?

5. A 40 cm wire is moved perpendicularly through a magnetic field of 0.32 T with a velocity
of 1.3 m/s. If this wire is connected into a circuit of 10 ohm resistance, how much current is flowing?

8. An EMF of 0.0020 V is induced in a 10 cm wire when it is moving perpendicularly across
a uniform magnetic field at a speed of 4.0 m/s. What is the size of the magnetic field?

15. A step up transformer has 80 turns on its primary. It has 1200 turns on its secondary.
The primary is supplied with an alternating current at 120 V.

What voltage is across the secondary?

The current in the secondary is 2.0 A. What current
flows in the primary circuit?

What is the power input and output of the transformer?

1. A beam of ions passes through a pair of crossed electric and magnetic fields. E is
6.0 x 10 ^{5} N/C and B is 3.0x10^{-3} T. What is the speed of the ions?

4. A proton moves across a 0.36 T magnetic field in a circular path, radius 0.2 m. What
is the speed of the proton?

PAK 14

Find the amount of material left after some time for decay.

1. A patient is administered 20 mg of iodine-131. How much of the iodine is left
after 40 days if the half-life of iodine- 131 is 8 days?

2. A 10 g sample of thorium-234 has a half-life of 25 days. How much thorium will
be left after 50 days?

3. If the half-life of Sr-90 is 28.8 years, how many grams of a 50 g sample will
be left after 86.4 years?

4. Fill in the missing numbers
or symbols for the following atomic equations:

5. A 30.0 g silver rod is heated and then is placed into an insulated vessel containing
100.0 mL of water at 20.0^{o}C. The final temperature after equilibrium is achieved is 23.5^{o}C. What was
the temperature(^{0}K) of the silver rod? The heat capacity of silver is 0.234 J/g^{o}C. The heat capacity
of water is 4.18 J/g^{o}C.

6. A 400.0 g iron rod is heated and then is placed into an insulated vessel containing 1.00 L of
water at 20.0^{o}C. The final temperature after equilibrium is achieved is 33.5^{o}C. What was the temperature
(K) of the iron rod? The heat capacity of iron is 0.444 J/g^{o}C.

7. How
much heat energy (kJ) must be supplied to heat 400.0 g of isopropyl alcohol from 20.0^{o}C to 60.0^{o}C in
a stainless steel vessel weighing 550.0 g. The specific heat of isopropyl alcohol and stainless steel are 2.58 J/g^{o}C
and 0.51 J/g^{o}C respectively.

8. A piece of metal with a mass of 1.50 kilograms, specific heat of 200 J/kg · C°, and initial temperature
of 100° C is dropped into an insulated jar that contains liquid with a mass of 3.00 kilograms, specific heat of l,000 J/kg
· C°, and initial temperature of 0° C. The piece of metal is removed after 5 seconds, at which time its temperature is 20°
C. Neglect any effects of heat transfer to the air or to the insulated jar.

What is the temperature of the liquid after the metal
is removed ?

What is the average rate at which heat is transferred while the piece of metal is in the liquid ?

9. A 100 g aluminum block heated to 100 °C
is placed in 100 g of water at 10.0 °C. The final temperature of the two is 25 °C. What is the specific heat of
the aluminum?

10. If the specific heat of methanol is 2450 J/kg °C, how much
heat must be added to 1 g of methanol to raise its temperature by 15 °C?

11. A block of iron is heated to 200 °C and
tossed into water with a temperature of 20 °C. If the mass of the block is 100 g and the mass of the water is 150 g,
what it he final temperature of the water?

12. A thermometer is to be designed using a long rod of aluminum. The coefficient
of linear expansion a of the rod is 23 x 10^{-6} /°C. If the rod is 30.000 cm long at 32 °F,

a. How long
is the rod at 85 °F?

b. If the
rod is measured to be 30.025 cm long, what is the temperature in Celsius, Fahrenheit, and Kelvin?

from http://www4.alief.isd.tenet.edu/cahowe/Physics/problems.htm