Physics 198
Exam I
Fall 2014
1. The graph of position versus time for a car is given below. What can you say about the
velocity of the car over time?
A)
B)
C)
D)
E)
It speeds up all the time
It slows down all the time
It moves at constant velocity
It is not moving
Sometimes it speeds up and sometimes it slows down
x(t)
t
Solution:
The car moves at a constant velocity because the x vs. t plot shows a straight line. The slope of a
straight line is constant. Remember that the slope of x versus t is the velocity!
2. What is the average speed of a car that travels first 9.0 km at an average speed of
and another 9.0 km at an average speed of 90 km/h?
A)
B)
C)
D)
E)
10 km/h
80 km/h
50 km/h
45 km/h
38 km/h
18 km/h
Solution:
x  x1  x 2  9.0km  9.0km  18.0km
t1 
x1
9.0km

 0.90h;
v1
10km/h
t 2 
x 2
9.0km

 0.10h
v2
90km/h
t  t1  t 2  0.90h  0.1h  1.0h
v
x 18.0km

 18km/h
t
1 .0 h
3. A car accelerates from the stationary position with acceleration a  3m / s 2 . What distance
will be covered in 4 s?
A)
B)
C)
D)
E)
24 m
18 m
12 m
16 m
4m
Solution:

3m / s 2 4 s 
at 2
 24m
x  x0  v0 t 
x
2
2
2
Page 1 of 8
Physics 198
Exam I
Fall 2014
4. When throwing a ball straight up, which of the following is true about its velocity v and its
acceleration a at the highest point in its path?
A)
B)
C)
D)
E)
both v = 0 and a = 0
v ≠ 0, but a = 0
v = 0, but a ≠ 0
both v ≠ 0 and a ≠ 0
not enough information to answer the question
Solution: At the top, clearly v = 0 because the ball has “momentarily stopped” - the velocity of
the ball is changing sign (direction). Because velocity is changing the acceleration is definitely
not zero! The acceleration is g  9.8m / s 2 .
5.
Alice and Bill are at the top of a cliff of height H. Both throw a ball with initial speed v0,
Alice straight down and Bill straight up. The speeds of the balls when they hit the ground are
vA and vB. If there is no air resistance, which is true?
A) v A  vB
B)
C)
D)
E)
vA
vA
vA
vA
 2vB
 4vB
 12 v B
 14 v B
Solution: Bill’s ball goes up and comes back down to Bill’s level. At that point, it is moving
downward with v0, the same as Alice’s ball. Thus, it will hit the ground with the same speed as
Alice’s ball.
6. From the same height (and at the same time), one ball is dropped and another ball is fired
horizontally. Which ball has the greater velocity at ground level?
A)
B)
C)
D)
E)
The “dropped” ball
The “fired” ball
Neither – they both have the same velocity on impact
It depends on how hard the ball was thrown
It depends on the initial height
Solution:
Both balls have the same vertical velocity when they
hit the ground (since they are both acted on by gravity
for the same time). However, the “fired” ball also
has a horizontal velocity. When you add the two
components, the “fired” ball has a larger net velocity
when it hits the ground.
Page 2 of 8
Physics 198
Exam I
Fall 2014
7. A box of mass 2 kg has acceleration 4m/s2. What is the net force applied to the box?
A)
B)
C)
D)
E)
2N
4N
6m
8N
9.8 N
Solution:
F  ma  2kg 4m / s 2  8N


8. A box with a mass of 10 kg is given an upward acceleration of 2.2 m/s² by a cable. What is
the tension in the cable?
A)
B)
C)
D)
E)
22 N
44 N
98 m
120 N
240 N
Solution:
Newton’s equation:

T  mg  ma  T  mg  a

T  10kg 9.8m / s 2  2.2m / s 2  120 N
9.
A hockey puck slides on ice at constant velocity. What is the net force acting on the puck?
A)
B)
C)
D)
E)
More than its weight
Equal to its weight
Less than its weight but more than zero
Depends on the speed of the puck
Zero
Solution:
The puck is moving at a constant velocity, and therefore it is not accelerating. Thus, there must
be no net force acting on the puck.
Page 3 of 8
Physics 198
Exam I
Fall 2014
10. What work should be done by an external force to lift a 2.0 kg block up 3.0 m?
A)
B)
C)
D)
E)
20 J
30 J
59 J
120 J
180 J
Solution:
W  Fd cos   mgh  2.0kg 9.8m / s 2 3.0m  58.8J  59 J


11. An object of unknown mass is projected with an initial speed, v0 = 10 m/s at an unknown
angle above the horizontal. If air resistance could be neglected, what would be the speed of
the object at height, h = 4.4 m above the starting point?
A)
B)
C)
D)
E)
3.7 m/s
4.2 m/s
4.9 m/s
6.2 m/s
10 m/s
Solution:
mv 2
mv02
 mgh 
 mg 0 
2
2
v  v02  2 gh 
10m / s 2  2  9.8m / s 2  4.4m  3.7m / s
12. Mass m is attached to a spring with a spring constant k. What happens with the frequency of
oscillation if the spring constant k increases by a factor of 4?
A)
B)
C)
D)
E)
Multiplies by a factor of 4
Doubles
Halves
Multiplies by a factor of ¼
Remains the same
Solution:
1 k
f 

2 m
f 4k

fk
4k
2
k
Page 4 of 8
Physics 198
Exam I
Fall 2014
13. A 2.0 kg mass attached to a spring with a spring constant of 200 N/m. What is the frequency
of oscillation of the mass?
A) 1.6Hz
B)
C)
D)
E)
2.4Hz
3.1Hz
6.3Hz
10Hz
Solution:
f 
1
2
k

m
f 
1
2
200 N / m 10

Hz  1.6 Hz
2.0kg
2
14. N-mass vibrator (N masses connected with springs) has:
A)
B)
C)
D)
E)
N longitudinal and N transverse modes of vibration
N longitudinal and 2N transverse modes of vibration
N longitudinal and 3N transverse modes of vibration
2N longitudinal and N transverse modes of vibration
2N longitudinal and 2N transverse modes of vibration
Solution:
15. A sinusoidal wave has a wavelength of 5.00 m and a period of 0.02s. What is the speed of
the wave?
A)
B)
C)
D)
E)
0.10 m/s
5.00m/s
10.0 m/s
250 m/s
340 m/s
Solution:
v T 
v  5.00m 0.02s  250m / s
Page 5 of 8
Physics 198
Exam I
Fall 2014
16. A stretched string has one free end and one fixed end, and is vibrating at its 3rd harmonic
frequency. The number of nodes is ___.
A)
B)
C)
D)
E)
1
2
3
4
5
Solution:
Nodes
17. Two speakers S1 and S2 are driven by the same signal generator and are different distances
from a microphone P as shown. The minimum frequency for constructive interference to
occur at P is __ Hz. (The speed of sound is v = 340 m/s.)
A)
B)
C)
D)
E)
100
200
300
400
500
Solution:
For constructive interference:
r2  r1   n
n  0,1,2,...
f  v /   f min 
v
340m / s

 200Hz
r 2 r1 3.40m  1.70m
18. When both ends of a pipe are open the frequency of the first overtone is 400 Hz. What is the
frequency of the first overtone if one end is open and another end is closed (stopped pipe)?
The pipe is sufficiently narrow so you can neglect its diameter, i.e. neglect end effects.
A)
B)
C)
D)
E)
800 Hz
600 Hz
400 Hz
300 Hz
200 Hz
Solution:
First overtone for the open pipe – second harmonic
First overtone for the one end open one end closed pipe – third harmonic
nv 
f nopen 
m open
3
2 L 
stopped

fn
f 2stopped 
400 Hz  f 2stopped  300Hz
  fm
2n
22
mv 
f mstopped 

4L 
Page 6 of 8
Physics 198
Exam I
Fall 2014
19. If the linear mass density of a rope is 0.150 g/m and the tension is 6.00 N, what is the speed
of waves in the rope?
A)
B)
C)
D)
E)
100 m/s
120 m/s
200 m/s
220 m/s
240 m/s
Solution:
  0.150g/m  1.50  10 -4 kg/m
v
F


6.00N
 200m / s
1.50  10 -4 kg/m
20. A 4.00 m long string is connected to a vibrator with frequency 120 Hz. The string is
oscillating in its 4 th harmonic. Find the speed of waves in the string.
A)
B)
C)
D)
E)
100 m/s
120 m/s
200 m/s
220 m/s
240 m/s
Solution:
2L
2  4.00m
n 
 4 
 2.00m
n
4
v  f  2.00m120Hz   240m / s
Page 7 of 8
Physics 198
Exam I
Fall 2014
Record Sheet
You may fill in this sheet with your choices, detach it and take it with you after the exam for
comparison with the posted answers
1
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2
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3
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4
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5
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10
20
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