Download Physics 11 Kinematics Sample Test

Physics 11 Kinematics Sample Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. What must be your average speed in order to travel 350 km in 5.15 h?
a. 0.015 km/h
c. 68 km/h
b. 67 km/h
d. 1800 km/h
2. Convert 125 km/h into m/s
a. 34.7 m/s
c. 2080 m/s
b. 450 m/s
d. 125000 m/s
3. The motion of an object is shown in the following position-time graph. What is the objects speed?
4.
5.
6.
7.
a. 0.5 m/s
c. 1.3 m/s
b. 0.8 m/s
d. 2 m/s
If the position vs time graph of an object is a horizontal line, the object is
a. moving with a constant non-zero speed.
c. at rest.
d. moving with infinite speed.
b. mocing with constant non-zero
acceleration.
If the velocity vs time graph of an object is a horizontal line, the object is
a. moving with a constant non-zero speed.
c. at rest.
b. mocing with constant non-zero
d. moving with infinite speed.
acceleration.
If the velocity vs time graph of an object is a straight line making an angle of 30 degrees with the time axis,
the object is
a. moving with a constant non-zero speed.
c. at rest.
b. mocing with constant non-zero
d. moving with infinite speed.
acceleration.
The slope of a position-time graph always represents
a. displacement
d. change in ve locity
b. distance
e. acceleration
c. velocity
1
Name:
ID: A
8. The area under a velocity-time graph always represents
a. displacement
d. acceleration
b. change in velocity
e. change in acceleration
c. distance
9. The position-time graph pictured below represents the motions of two objects, A and B. Which of the
following statements concerning the objects' motions is true?
a. Object B travels the greater distance.
b. Object A has the greater speed.
c. Object A leaves the reference point at an earlier time.
d. Both objects have the same speed at the point where the lines cross.
e. Object A is travelling for a longer period of time.
10. The position-time graph pictured below depicts a person, P, running to catch a bus, B, that has just begun to
pull away. Which of the following statements is true?
a.
b.
c.
d.
e.
The person has no chance of catching the bus.
The person's acceleration is greater than that of the bus.
The person has two opportunities to catch up to the bus.
The speed of the bus is always greater than that of the person.
The person's speed is always greater than that of the bus.
2
Name:
ID: A
11. Consider the following velocity-time graph and select the statement that is true.
12.
13.
14.
15.
a. At no time can the motion be considered "uniform."
b. The object returns to its original position.
c. The object travels in one direction and then the other.
d. The object is accelerating throughout the entire recorded time.
e. The object speeds up and later slows down.
The expression “per” as in miles per hour or meters per second mathematically indicates:
a. addition.
b. subtraction.
c. multiplication.
d. division.
Many cars are made with an automatic feature called cruise control. When the driver sets a car on cruise
control, a computer adjusts the engine to maintain the car’s speed constant. When a car is on cruise control
on a straight road, the acceleration of the car is best described as:
a. equal to the initial speed when the cruise control was set.
b. equal to zero.
c. greater than it was before the cruise control was set.
d. less than it was before the cruise control was set.
A rocket has an acceleration of 50 m/sec2. How long does it take the rocket to reach a speed of 1,000 m/sec?
a. .05 seconds
b. 20 seconds
c. 50 seconds
d. 50,000 seconds
A sports car reaches a speed of 50 m/sec in 12 seconds after starting from rest. The acceleration of the car is:
a. 0.24 m/sec2.
b. 4.17 m/sec2.
c. 38 m/sec2.
d. 50 m/sec2.
Problem
16. A car is traveling at a constant speed of 55 km/h. How far does the car travel in 12 minutes? [3]
17. A race car makes three complete laps around a 2.5 km race track. The driver travels at 55 km/h for
the first lap, 110 km/h for the second lap, and 95 km/h for the last lap. What is
a. the average speed for all three laps? [5]
b. the average velocity for all three laps? [1]
3
Name:
ID: A
18. Answer the following questions for the position-time graph below:
8
6
d (m)
4
2
1
a.
b.
c.
d.
2
t (s)
3
4
What is the car’s instantaneous speed at 2.0 s? [3]
What is the car’s average speed from 0 to 2.0 s? [2]
What is the displacement of the car in the graph? [1]
What distance has the car travelled? [1]
19. Answer the following questions on the velocity-time graph below. Consider positive to be to the right and
negative to be to the left.
4
3
2
1
v (m/s)
0
t (s)
1
2
3
4
5
6
7
-1
-2
-3
-4
-5
a) When is the object moving to the left? [1]
b) When is the object speeding up? [1]
c) When is the object slowing down? [1]
d) What is the acceleration for the first 3 seconds? [2]
e) How far did the object travel in the first 5.0 s? [2]
f) What was the object’s average speed in the first 5.0 s? [1]
20. A car travelling at 50.0 km/h is 150.0 m behind a bicycle that is travelling at 10.0 km/h. How far does
the bicycle travel before the car catches up to it? [6]
4
Physics 11 Kinematics Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
A
A
C
A
B
C
A
B
C
E
D
B
B
B
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
PROBLEM
16. ANS:
v = 55 k m / h
∆t = 12 min ×
1h
60 min
= 0.20 h
∆d
v=
55 =
∆t
∆d
0.20
∆d = 11 k m
PTS: 1
1
17. ANS:
a) Lap 1:
d
t=
v
Lap 2:
t=
d
v
Lap 3:
t=
d
v
2.5
t = 55
2.5
t = 110
2.5
t = 95
t = 0.045 h
t = 0.023 h
t = 0.026 h
tt = 0.045 + 0.023 + 0.026
tt = 0.094 h
v=
d
t
7.5
v = 0.094
v = 80. km / h
b) v=0
PTS: 1
2
18. ANS:
a) Using a tangent line, the slope is
v=
d2 − d1
t2 − t1
v = 4.7 − 3.5
3.5 − 0.5
v = 0.40 m / s
∆d
b) v = t
=
4.0 − 1.0
2.0 − 0
3.0
= 2.0
= 1.5m / s
c) ∆ ä
d=ä
df − ä
di
= 3−1
= +2 m
d) ∆d = ∆d 1 + ∆d 2
= 3.1 + 1.1
= 4.2m
PTS: 1
3
19. ANS:
a) from 5.8 s to 8.0 s
b) from 0 to 3.0 s, and from 5.8 s to 7.0 s
c) from 5.0 s to 5.8 s
∆v
d) a = ∆t
a = 2−0
3−0
a = 0.67 m / s 2
e) ∆d = 0.5(2)(3) + (2)(2)
= 3+4
f)v =
= 7.0m
∆d
t
7.0
= 5.0
= 1.4m / s
PTS: 1
20. ANS:
v rel = 50.0 − 10.0
= 40.0k m / h
∆d
v=
t
0.1500
40.0 =
t
t = 0.00375h
v=
10.0 =
∆d
t
∆d
0.00375
∆d = 0.0375k m
= 37.5m
PTS: 1
4
Physics 11 Acceleration Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
b.
1. If an object accelerates at 6.2 m/s2 , how long will it take to reach a velocity of 25 m/s if starting from rest? a.
25 s
c.
0.25 s
4.0 m/s
d. 4.0 s
The graph below represents the speed of a car vs. time.
Figure 4-1
2. Which point on the speed versus time graph in Figure 4-1 has the highest acceleration?
a. A
c. C
b. B
d. D
3. A sports car reaches a speed of 50 m/sec in 12 seconds after starting from rest. The acceleration of the car is:
a. 0.24 m/sec2.
c. 38 m/sec2.
b. 4.17 m/sec2.
d. 50 m/sec2.
Figure 4-2
4. The graph in Figure 4-2 shows an acceleration of:
a. 0 m/sec2.
c. 0.4 m/sec2.
2
b. 0.2 m/sec .
d. 2 m/sec2.
5. An object is thrown up in the air with an initial velocity of 5.0 m/s. When the object reaches its highest point,
the velocity of the object is
a. 5.0 m / s
c. 9.8 m / s
b. 0 m / s
d. 9.8 m / s 2
6. An object is thrown up in the air. When the object reaches its highest point, the acceleration of the object is
a. 19.6 m / s 2
c. 9.8 m / s 2
b. 4.9 m / s 2
d. 0 m / s 2
2 of 2
Name:
7. The acceleration of gravity on the moon is about 1.6 m/sec2. A 2-kilogram object on the moon is dropped
from rest. After ten seconds, the speed of the object is:
a. 1.6 m/sec.
c. 16 m/sec.
b. 3.2 m/sec.
d. 32 m/sec.
8. A clever person who knows physics measures the depth of a deep hole by dropping a rock into the hole. The
rock takes 3.2 seconds to hit the bottom. The depth of the hole is approximately:
a. 16 meters.
c. 50 meters.
b. 31 meters.
d. 100 meters.
9. Which of the following statements CANNOT ever be true?
a. An object can have a speed that is changing and still have zero acceleration.
b. An object can have a speed of zero and an acceleration that is not zero.
c. An object can have a speed that is decreasing and still have acceleration.
d. An object can have an acceleration of zero and a speed that is not zero.
10. Under what condition is average velocity equal to the average of the object’s initial and final velocity?
a. This can only occur if there is no
c. This is impossible.
acceleration.
b. The acceleration must be constant.
d. The acceleration must be constantly
changing.
Problem
11. You are going to catch a baseball, which is travelling at 20.0 m/s. It won’t hurt as much if you pull your hand
back while catching the ball. If you want the deceleration of the ball to be -210.0 m/s2, then how far should
you pull your hand back while catching the ball? [3]
12. Two cars leave the same point at the same time, but travel in opposite directions. Car A drives at a constant
speed of 50.0 km/h; Car B starts from rest, accelerating at 1.3 m/s2. How far apart are they after 10.0 s? [4]
13. A rock is thrown upwards on earth and reaches a height of 8.2 m. Planet Xerig has an acceleration due to
gravity of 19.6 m/s2.
a. How high will the rock go on Xerig if it is given the same initial velocity? [4]
b. How high will it go on Xerig if it is given 3 times the initial velocity? [2]
14. You are standing on a bridge that is 9.6 m above a road below. A car is approaching along the road at a
constant speed of 55 km/h and is 13.5 m away. You want to throw an egg so that it hits the car; at what
downward speed should you throw the egg? Ignore the height of the car. [5]
15. You throw a rock off of a bridge into the water below. It takes 3.2 s to hit the water, which is 15.0 m below
the bridge. With what speed, and in what direction, did you throw the rock? [4]
16. A student is thrown upward with some unknown velocity. He is observed to take 0.43 s to go from point A to
B (3.0 m apart) on the way up. How far above B does the student go? [5]
Short Answer
17. A rock is thrown vertically upward with speed v from the edge of a cliff. A second rock is thrown vertically
downward with the same initial speed. Which rock has the greater speed when it reaches the bottom of the
cliff? Explain. (Ignore air resistance) [3]
3 of 2
Physics 11 Acceleration Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
D
B
B
B
B
C
C
C
A
B
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
1
1
1
1
1
1
1
1
1
1
PROBLEM
11. ANS:
∆d =
v f − vi
2
vi = 20.0m / s
2a
vf = 0
a = −210.0m / s
∆d = ?
PTS: 1
12. ANS:
Car A:
2
2
0 − (20.0)2
=
2(−210.0)
= 0.952m
Car B:
d = vt
d = v i t + 0.5at 2
d = (13.9)(10.0)
d = 0 + 0.5(1.3)(10.0)2
d = 139 m
d = 65 m
d = 139 + 65
d = 204 m
PTS: 1
1 of 3
13. ANS:
a) On earth,
On Xerig,
v f − vi
2
d=
v f − vi
2
2
d=
2a
8.2 =
0 − v 2i
d=
2(−9.8)
v i = 12.7 m / s
2
2a
0 − 12.72
2(19.6)
d = 4.1 m
v 2f − v i2
b) d =
2a
0 − 38.1
d = 2(19.6)
2
d = 37 m
PTS: 1
14. ANS:
time for car to arrive:
d = vt
package:
d = v i t + 0.5at 2
13.5 = 15.3t
2
9.6 = v i (0.88) + 0.5(9.8)(0.88)
t = 0.88 s
v i = 6.6 m / s
PTS: 1
15. ANS:
Using down as positive
d = v i t + 0.5at
2
15.0 = v i (3.2) + 0.5(9.8)(3.2) 2
v i = −11 m / s
so 11 m/s upward
PTS: 1
2 of 3
16. ANS:
first find the speed at point A:
d = v i t + 0.5at 2
3.0 = v i (0.43) + 0.5(−9.8)(0.43) 2
v i = 9.1 m / s
next, find out how far above point A he rises:
v 2f − v 2i
2a
0
d = − 9.12
2(−9.8)
d=
d = 4.2 m
therefore, he goes 4.2 − 3.0 = 1.2 m above point B PTS: 1
SHORT ANSWER
17. ANS:
They will both have the same speed when they hit the bottom. The rock that was initially thrown upward will have the
same downward speed when it returns to the height at which it was thrown.
PTS: 1
Physics 11 Dynamics Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. A hockey puck slides along an ice surface shortly after it has left the hockey stick that propelled it. Which of
the following free-body diagrams best represents the hockey puck?
a. A
d. D
b. B
e. E
c. C
2. If the force of gravity that the earth exerts on you is considered to be the action force then, according to
Newton's third law, the corresponding reaction force would be the
a. normal force of the Earth acting upward on you
b. force your feet exert downward on the Earth
c. force of gravity you exert on the Earth
d. force you exert on your feet, pressing them against the Earth
3. The action and reaction forces of Newton's third law
a. act on the same object
b. act as a pair of forces that are "balanced"
3 of 3
c. make the net force zero because they are equal in strength and opposite in direction
d. act on two different objects
4. Your "weight" is properly defined as
a. the amount of material of which you are composed
b. the gravitational force which Earth exerts on you
c. the gravitational force you exert on Earth
d. the force you exert on a set of bathroom scales
5. Study the force system diagram pictured below and select the factor which would NOT influence the amount
of kinetic friction.
a.
b.
object's mass, m
coefficient of kinetic friction, µK
c.
d.
2 of 3
normal force, FN
applied force, FA
Name:
ID: B
6. The coefficient of friction stems from the
a. nature of the two surfaces in contact
c. strength of the applied force
b. mass of the object
d. strength of the normal force
7. If no forces are acting on an object, its motion will:
a. continue in the same direction with the same speed.
b. slow down and eventually stop.
c. continue at the same speed but could change direction.
d. continue in the same direction but could change speed.
8. Which of the following situations MUST have a net force?
a. An object accelerates from 1 m/sec2 to 2 m/sec2.
b. An object is at rest with zero speed.
c. An object is moving with a constant speed of 2 m/sec.
d. An object has a mass of 1 kilogram.
9. An object is observed to have an acceleration of 2 m/sec2 when a net force of 4 newtons is applied. The mass of
the object is:
a. 0.5 kilogram.
c. 2.0 kilograms.
b. 1.0 kilogram.
d. 8.0 kilograms.
10. A ball is thrown straight up in the air. As the ball travels upward, which diagram correctly shows the net
force, speed, and acceleration?
____ 11. Three forces act on the cart shown in the diagram. The acceleration of the cart is:
a. to the left at 1 m/sec2
c. to the right at 1 m/sec2
2
b. to the left at 2 m/sec
d. to the right at 2 m/sec2
12. Two boxes of mass m and 2m are in contact with each other on a frictionless surface. What is the
acceleration of the more massive box?
F
m
a.
b.
F/m
F/(2m)
c.
d.
3 of 3
F/(3m)
F/(4m)
2m
Name:
ID: B
Short Answer
13. Why does a child in a wagon seem to fall backward when you give the wagon a sharp pull? Does he really go
backward? Explain using Newton’s Laws. [2]
4 of 3
Name:
ID: B
Problems - include free body diagrams and show all work to support your answers
14. You are pulling a 35 kg sled horizontally at a constant speed, applying a force of 225 N.
a) What is the coefficient of friction? [3]
b) With what force would you have to pull to give the sled an acceleration of 3.2 m/s2? [3]
15. A high jumper falls on a pad, hitting it with a vertical speed of 4.0 m/s. The pad brings him to rest,
compressing 0.40 m. If the pad exerts an upward force of 1200 N on the high jumper, what is the jumper's
mass? [6]
16. A 71.0 kg person falling through the air experiences a force of air resistance of 425 N. What is his
acceleration? [4]
17. Slimy the Slug (whose mass is 0.050 kg) is kicked along a floor, giving him an initial speed of 5.0 m/s. After
being kicked, he travels 8.0 m before stopping. What is the coefficient of friction between Slimy and the
floor? [6]
18. A person is pushing horizontally with 65.0 N against a 2.0 kg box (initially at rest) that is in contact with a
vertical wall. The coefficient of friction between the box and the wall is 0.40.
Fp
What will the box do? Will it slide down the wall or will it stay still? [4]
5 of 3
Physics 11 Dynamics Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
D
C
D
B
D
A
A
A
C
B
B
C
SHORT ANSWER
13. The child is intially at rest and wants to stay at rest (Newton’s First Law). When the wagon begins to move
forward, the child stays in its original position which makes it look like the child is moving backward relative
to the wagon.
1 of 4
PROBLEM
14. a) At a constant speed, the F f =F p .
F f =µF N
225=µmg
225=µ(35)(9.8)
µ = 0.66
b)
FN
Ff
Fa
Fg
ma = ΣF
ma = F p − F f
35(3.2) = F p − 225
F p = 337N
15.
Fp
Fg
ma =
Using up as positive
2
v f − vi
a=
2d
0 − (4.0)2
2
a=
∑F
2
2(−0.40)
a = 20 m / s2
ma = F p − F g (using up as positive)
m(20) = 1200 − 9.8m
29.8m = 1200
m = 40.3 k g
2 of 4
16.
Fa
Fg
Using down as positive
ma =
∑F
ma = F g − Fa
71.0a = (71.0)(9.8) − 425
a = 3.8 m / s 2
17.
FN
Ff
Fg
2
2
v f − vi
d=
8.0 =
2a
0 − (5.0)2
2a
a = −1.56 m / s 2
ma = ΣF
F f = µF N
ma = −F f
F f = µmg
(0.050)(−1.56) = −F f
0.078 = µ(0.050)(9.8)
F f = 0.078 N
0.078 = µ0.49
µ = 0.16
3 of 4
18.
Ff
FN
Fp
Fg
FN = Fp
Fg = mg
F f = µF N
F N = 65.0 N
Fg = 2.0(9.8)
F f = 0.40(65.0)
Fg = 19.6 N
F f = 26.0 N
Since F f > Fg , the box will not move.
Physics 11 Momentum and Energy Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Air bags help reduce injury in automobile accidents by:
a. reducing the time of collision.
b. reducing the change in momentum.
c. increasing the applied force.
d. increasing the time that force is applied.
2. The amount of work done to stop a bullet travelling through a tree trunk a distance of 50 cm with a force of
2.00 × 102 N is
a. +1.00 × 102 J
c. +4.00 × 102 J
2
b. –1.00 × 10 J
d. –4.00 × 102 J
3. A student pushes a book moving at constant velocity through a horizontal displacement of 10 m. What is the
work done by the student, if the frictional force against the motion is 10 N?
a. 50 J
c. 10 J
b. 100 J
d. zero
4. A construction worker does 450 J of work in lifting a load of bricks from the ground to a support stand 1.50
m from the ground. What was the mass of the bricks she lifted?
a. 30.6 kg
c. 3.06 kg
b. 0.327 kg
d. 68.9 kg
5. The power used in doing 81 joules of work in 9.0 seconds is:
a. 9.0 watts.
c. 729 watts.
b. 0.11 watts.
d. 90 watts.
6. If a 900-watt toaster were rated in horsepower, its rating would be about:
a. 1,210 horsepower.
c. 828 horsepower.
b. 0.830 horsepower.
d. 1.21 horsepower.
7. A 5.00-kg sack of potatoes is raised to a height of 2.00 m and then thrown at a constant velocity of 2.00 m/s
onto a truck. What is the kinetic energy of the potatoes?
a. 5.00 J
c. 103 J
b. 10.0 J
d. 98.0 J
4 of 4
8. A cheerleader is thrown vertically upward into the air. As the cheerleader rises, which one of the following
quantities increases?
a. acceleration
c. gravitational potential energy
b. speed
d. kinetic energy
9. The mechanical advantage of a machine may be calculated as the ratio of:
a. input distance to output force.
c. input force to input distance.
b. input force to output force.
d. input distance to output distance.
10. John uses 1,200 joules of energy to lift a 200-newton crate 5 meters using a pulley system. The efficiency of
the system is:
a. 12%
c. 50%
b. 17%
d. 83%
11. The efficiency of a machine is reduced by:
a. friction.
c. effort.
b. work output.
d. mechanical advantage.
2 of 2
Name:
12. A power generating station burns 100 kg of coal every second. Each kg of coal contains approximately 25 MJ of
chemical energy and the power station generates approximately 750 MJ of electricity. The efficiency of the station is
a.
95%
c. 30%
b.
0.33%
d. 3.0%
13. A 1.0 kg mass, moving at 6.0 m/s[E], collides with a stationary 2.0 kg mass. If the collision is perfectly
inelastic, what is the velocity of the combined masses after the collision?
a.
2.0 m/s[E]
c. 4.0 m/s[E]
b.
3.0 m/s[E]
d. 1.0 m/s[E]
14. A collision between two objects referred to as elastic would be characterized by:
a. no loss of kinetic energy and no permanent change in shape.
b. no loss of kinetic energy and a permanent change in shape.
c. a loss of kinetic energy and a permanent change in shape.
d. a loss of kinetic energy and no permanent change in shape.
Short Answer
15. In many professional auto races, stacks of old tires are placed in front of walls that are close to turns in the
racetrack. Using the concepts of impulse and momentum, explain why the tires are stacked there. Include in
your answer how the impulse would compare with and without the tires in front of the wall. [3]
Problem
16. A 50.0 g bullet is traveling east and hits Superman (82.0 kg), who is traveling west at a speed of 125 km/h. Of
course, the bullet bounces off of Supes with a speed of 950 m/s; Superman maintains his original direction
with a speed of 120 km/h. What was the original speed of the bullet? [4]
17. A 120 kg bicyclist (including the mass of the bike) is coasting at the top of a 4.7 m high hill at a speed of 5.0
m/s.
(a) How fast will he be going at the top of the second hill, which is 3.2 m high. [3]
(b) Ignoring friction, what is the highest hill that the cyclist can climb (while still coasting)? [3]
(c) If he loses 2450 J of energy to friction, what will his speed be at the top of the second hill? [3]
18. A 35.0 g bullet travelling at 348 m/s hits and embeds itself into a 2.6 kg wooden block that is hanging on a
string. The string is 2.78 m long.
(a) How fast is the block moving after the bullet hits it? [2]
(b) Is the collision elastic or inelastic? If elastic, give your reasoning. If inelastic, calculate how much energy
is lost. [3]
(c) To what height does the block rise? [2]
19. A student is sliding down a frictionless water slide at an amusement park. [3]
a) Sketch a graph of gravitational potential energy against height (no numbers are required on the axes).
b) On the same axes, sketch a graph of the toal energy of the student against height.
c) On the same axes, sketch a graph of the kinetic energy of the student against height.
3 of 2
ID: A
Physics 11 Momentum and Energy Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
D
B
B
A
A
D
B
C
D
D
A
C
A
A
SHORT ANSWER
15. The impulse would be the same in each case. The tires increase the time of the collision, decreasing the force
applied on the car and the driver (Since the impulse is a product of the force and the time)..
PROBLEM
16. p i = p f
mb v b + ms v s = mb v ′ + m v ′
b
s
s
(0.050)v b + (82.0)(−34.7) = (0.050)(−950) + (82.0)(−33.3)
v b = 1350 m / s
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ID: A
17. a) Ei = E f
E pi + Eki = E pf + Ekf
2
2
m
/ gh i + 0.5m
/ vi = m
/ gh f + 0.5m
/vf
(9.8)(4.7) + 0.5(5)2 = (9.8)(3.2) + 0.5v 2 f
v f = 7.4 m / s
b) Ei = E f
E pi + Eki = E pf
2
m
/ gh i + 0.5m
/ vi = m
/ gh f
(9.8)(4.7) + 0.5(5.0)2 = 9.8h
f
h f = 6.0 m
c) ∆E = E f − Ei
−2450 = E f − (mgh i + 0.5mv i2)
−2450 = E f − ((120)(9.8)(4.7) + 0.5(120)(5.0) 2)
−2450 = E f − 7030
E f = 4580 J
E f = mgh f + 0.5mv 2f
4580 = 120(9.8)(3.2) + 0.5(120)v 2f
v f = 3.7 m / s
2 of 3
ID: A
pi = p f
18. a)
mb v b = mt v t '
(0.035)(348) = 2.635v t '
v t ' = 4.62 m / s
b) Since the objects stuck together, the collision is inelastic.
Ei = 0.5mb v b2
E f = 0.5mt v t2
Ei = 0.5(0.035)(348) 2
E f = 0.5(2.635)(4.62) 2
Ei = 2120 J
E f = 28.1 J
∆E = E f − Ei
= 28.1 − 2120
= −2090 J
c)
Ei = Et
0.5mv 2i = mgh f
0.5(2.635)(4.62)2 = (2.635)(9.8)h
h = 1.09 m
19.
(b) Et
(a) Ep
Energy
(c) Ek
height
Wave Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. The speed of any mechanical wave as it propagates through a medium is dependent mainly on the
a. frequency of the wave source
b. wavelength
c. period of the wave
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d. type of medium through which the wave travels
2. The shortest time interval in which a wave motion completely repeats itself (i.e., makes one complete
vibration or oscillation) is called the
a. amplitude
c. wavelength
b. period
d. frequency
3. As a wave travels down a spring, the amplitude slowly decreases. Why does this occur?
a. The law of conservation of energy does not apply to waves.
b. The energy is spread out along the entire length of the spring.
c. The wave slows down as it travels along the spring.
d. Some energy is lost due to friction as the particles in the spring rub against each other.
4. Consider the following wave properties:
(i) speed
(ii) frequency
(iii) wavelength
(iv) period
Which of the above quantities does not change as a wave changes mediums?
a. (i) and (iii) only
c. (ii) and (iv) only
b. (i) only
d. (i) and (iv) only
5. A water wave travels from shallow water to deep water and speeds up. Which of the following statements
best describes the wave's behaviour as it changes mediums?
a. The wavelength is shorter in the shallow water and longer in the deeper water.
b. The wavelength is longer in the shallow water and shorter in the deeper water.
c. The wavelength is unaffected.
d. The frequency of the wave is lower in the shallow water and higher in the deeper water.
6. Waves can bend as they travel through small openings or past corners. This is due to the property called
a. diffraction
c. reflection
b. refraction
d. resonance
7. A standing wave with three antinodes is generated in a string. If the wavelength is 10 cm, how far apart are
the nodes created?
a. 2.5 cm
c. 10 cm
b. 5.0 cm
d. 20 cm
2 of 4
Name:
ID: B
8. A student does an experiment by launching two wave pulses from opposite ends of a long spring. The pulses
are the same size and on opposite sides of the spring. Which diagram best describes how the spring looks at the moment
the pulses overlap each other?
a. A
b. B
c. C
d. D
9. Ultrasound is just like ordinary sound EXCEPT:
a. the wavelength is too long to be detected by our ears.
b. the frequency is too high to be detected by our ears.
c. the amplitude is too large to be detected by our ears.
d. the wave has too large a mass to move through air.
10. The wavelength of low frequency sound is:
a. smaller than the wavelength of high frequency sound.
b. about the same as the wavelength of high frequency sound.
c. larger than the wavelength of high frequency sound.
d. proportional to the loudness of the sound in decibels.
11. When a wave passes from one medium to another, the ? must stay the same.
a. amplitude
c. speed
b. frequency
d. wavelength
12. The vertical distance from the top of a crest to the bottom of a trough is 34.0 cm. The amplitude of this wave
is
a. 8.5 cm
c. 34.0 cm
b. 17.0 cm
d. 68.0 cm
3 of 4
Name:
ID: B
13. Which of the diagrams below best illustrates the movement of a wave through a small opening?
a. A
b. B
c. C
d. D
14. When two waves interfere with each other, the word interfere means:
a. one wave prevents the other wave from finishing its cycle.
b. one wave stops moving while the other wave passes.
c. the motion we observe is the sum of the motions from each individual wave.
d. the wave with the larger amplitude grows, and the wave with the smaller amplitude
shrinks.
15.
The graph shows the amplitude of a vibrating string as the frequency is changed. The string has a
fundamental frequency of:
a. 10 hertz.
b. 15 hertz.
c. 30 hertz.
d. 90 hertz.
4 of 4
Name:
ID: B
16. The note A has a frequency of 440 hertz. A piano playing the note A sounds different from an electric guitar
playing the same note because the two instruments:
a. create different wavelengths of sound at a frequency of 440 hertz.
b. contain different mixtures of harmonics at multiples of 440 hertz.
c. have different loudness.
d. create sounds of different speeds that reach your ear at different times.
17. The overtones present in a closed air column consist of
a. all of the harmonics
c. only the odd harmonics
b. only the even harmonics
d. none of the harmonics
18. Two tuning forks, one at 256 Hz and the other at 260 Hz are sounded at the same time. How many beats are
heard each second?
a. 1.01
c. 8
b. 4
d. 516
Short Answer
19.
a. Waves go from a slow medium to a faster one. What happens to the frequency and the wavelength? [2]
b. A dripping tap is creating waves as the water drops fall in the sink. Explain what happens to the velocity
and wavelength if the frequency of the falling drops increases. [2]
20. Guitar players can use beats to tune their guitars. Explain how this is done. [3]
Problem
21. A body in a lake bobs up and down 35.0 times in 15.0 s. The waves travel 5.00 m in 24.0 s. Find the
frequency, velocity, and wavelength of these waves. [6]
22. You are standing 2.5 × 102 m from a cliff wall and you clap your hands. The echo of your clap returns 1.45 s
after you clap your hands. What is the air temperature? [3]
23. Three successive resonant lengths for particular tuning fork over an air column are found to be 50 cm, 70 cm,
and 90 cm. The air temperature is 16.0oC.
a) What is the frequency of the tuning fork? [4]
b) Is the air column open or closed? Explain your reasoning. [2]
5 of 4
ID: B
Wave Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
D
B
D
C
A
A
B
A
B
C
B
B
A
C
B
B
C
B
SHORT ANSWER
19. a) The frequency stays the same, the wavelength increases.
b) The velocity stays the same (since it is the same medium), the wavelength decreases.
20. The required frequency is emitted using a known source (such as another string or tuning fork) and, at the
same time, the string being tuned is played. The musician then listens for beats to be produced which indicate
that the string is out of tune. The tension in the string is properly adjusted until the beats disappear which
means that the guitar string has the exact same frequency as the known source.
PROBLEM
21. f =
N
t
v=
d
t
35.0
f = 15.0
5.00
v = 24.0
f = 2.33 Hz
v = 0.208 m / s
v = λf
v
λ=
f
0.208
λ = 2.33
λ = 0.0893 m
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ID: B
22. d wall = 2.5 × 10 2 m = 250 m
techo = 1.45 s (there and back)
t wall = 0.725 s
v sound = ?
d wall
v sound =
t wall
=
250 m
0.725 s
= 345 m/s
v s = 331 + 0.59T
345 = 331 + 0.59T
T = 24°C
23. a) v = 331 + 0.59(16)
v = 340. m / s
Since the difference between each resonance length is 20 cm,
1
∆L = λ
f= v
2
λ
0.2 =
1
2
λ
λ = 0.4 m
340.
f = 0.4
f = 850Hz
f = 900Hz
b) Using each of the 3 lengths in L = xλ with the wavelength found in a),we get values for x of 5/4, 7/4,
and 9/4; therefore, the air column must be closed.
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