Physics 198
Exam I
Fall 2015
1. While traveling in your car you glance at the speedometer which reads 65mph. This
quantity, 65mph is___
A)
B)
C)
D)
E)
Your average speed
Your average velocity
Your instantaneous speed
Your instantaneous velocity
Your average acceleration
Solution:
Speedometer reads instantaneous speed.
2. What of the following statements is wrong?
A)
B)
C)
D)
E)
An object can have zero velocity and nonzero acceleration at the same time
An object can have a varying speed if its velocity is constant
An object can have a varying velocity if its speed is constant
A rock falling from a cliff has constant acceleration (neglect air resistance)
A dish resting on a table has constant acceleration
Solution:
If an object is at the instant of reversing direction (like an object thrown upward, at the top of its
path), it instantaneously has a zero velocity and a non-zero acceleration at the same time. A
person at the exact bottom of a “bungee” cord plunge also has an instantaneous velocity of zero
but a non-zero (upward) acceleration at the same time.
3. What is the average speed of a car that travels first 4.0 km at an average speed of 20 km/h
and another 5.0 km at an average speed of 50 km/h?
A)
B)
C)
D)
E)
45 km/h
40 km/h
35 km/h
30 km/h
25 km/h
Solution:
x  x1  x 2  4.0km  5.0km  9.0km
t1 
x1
4.0km

 0.20h;
v1
20km/h
t 2 
x 2 5.00km

 0.10h
v2
50km/h
t  t1  t 2  0.20h  0.10h  0.30h
v
x 9.0km

 30km/h
t 0.30h
Page 1 of 7
Physics 198
Exam I
Fall 2015
4. You drop a stone that was initially at rest. What distance will be covered in two seconds?
A)
B)
C)
D)
E)
1.0 m
2.0 m
4.9 m
9.8 m
19.6 m
Solution:
gt 2
y  y 0  v0 t 

2
gt 2
d  y0  y 
 v0 t 
2
9.8 m s 2s 
d
2
2
2
 02s   19.6m
5. A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air
as it moves. (Recall lecture demonstration.) After it is fired, what happens to the ball?
A)
B)
C)
D)
E)
It falls behind the cart
It falls in front of the cart
It falls right back into the cart
It depends on how fast the cart is moving
It remains at rest
Solution:
In the frame of reference of the cart, the ball only has a vertical component of velocity. So it
goes up and comes back down. To a ground observer, both the cart and the ball have the same
horizontal velocity, so the ball still returns into the cart.
6. 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 2 of 7
Physics 198
Exam I
Fall 2015
7. You kick a smooth flat stone out on a frozen pond. The stone slides, slows down and
eventually stops. You conclude that:
A)
B)
C)
D)
E)
The force pushing the stone forward finally stopped pushing on it
No net force acted on the stone
A net force acted on it as it slide until is stopped
The stone simply “ran out of steam”
The stone has a natural tendency to be at rest
Solution:
“Slows down” means it has acceleration. According to the second Newton’s law acceleration is
caused by a force.
8. What work should be done by an external force to lift a 2 kg block up 3 m?
A)
B)
C)
D)
E)
6J
30 J
59 J
120 J
180 J
Solution:
F  mg


W  F|| d  mgd  2kg 9.8m / s 2 3m  58.8J
9. A box of unknown mass and initial speed v0 = 10 m/s moves up a frictionless incline. How
high does the box go before it begins sliding down?
A)
B)
C)
D)
E)
1m
2m
3m
4m
5m
Solution:
K1  U1  K 2  U 2 
1
2
mv02  0  0  mgh 
h
v02
10m / s 2  5.1m

2 g 2  9.8m / s 2
Page 3 of 7
Physics 198
Exam I
Fall 2015
10. A cannon ball is fired at a speed of 70.0 m/s straight up. It proceeds upwards and eventually
falls back down. What is the speed of the cannon ball just before it falls down? Neglect air
resistance.
A)
B)
C)
D)
E)
35 m/s
48 m/s
50 m/s
63 m/s
70 m/s
Solution:
Take into account that h1  h2 .
From conservation of energy: 12 mv12  mgh1  12 mv22  mgh2  12 mv12  12 mv22  v1  v2 .
11. Two identical masses hang from two identical springs. In case 1, the mass is pulled down 2
cm and released. In case 2, the mass is pulled down 4 cm and released. How do the periods
of their motions compare?
A) T1  T2
B) T1  T2
C) T1  T2
D) The answer depends on the ratio of the mass and the spring stiffness constant
E) The answer depends on the spring stiffness constant only
Solution:
For the simple harmonic motion the period is independent from amplitude.
12. Mass m attached to a spring with a spring constant k. If the mass m increases by a factor of
4, the frequency of oscillation of the mass
A)
B)
C)
D)
E)
Doubled
Multiplied by a factor of 4
Halved
Multiplied by a factor of ¼
Remains the same
Solution:
The frequency of mass oscillating on s spring is f 
1
2
k
.
m
Page 4 of 7
Physics 198
Exam I
Fall 2015
13. If the mass m of a simple pendulum increases by a factor of 4, the frequency of small
oscillation of the mass
A)
B)
C)
D)
E)
Doubled
Multiplied by a factor of 4
Halved
Multiplied by a factor of ¼
Remains the same
Solution:
The frequency of small oscillation of a simple pendulum is independent on mass: f 
1
2
g
l
14. A metal string has a mass of 0.020 kg, a length of 40 cm, and is under 80 N tension. What is
the speed of a wave in this metal string?
A)
B)
C)
D)
E)
40 m/s
45 m/s
50 m/s
55 m/s
60 m/s
Solution:
m 0.020kg
 
 0.05 kg m ;
l
0.40m
v
F


80 N
 40 m s
0.05kg / m
15. How many modes has N-mass vibrator?
A)
B)
C)
D)
E)
N
2N
3N
4N
6N
Solution:
N-mass vibrator has N longitudinal and 2N transverse modes of vibration – 3N altogether
Page 5 of 7
Physics 198
Exam I
Fall 2015
16. If a violin string vibrates at 440 Hz as its fundamental frequency, what is the frequency of the
second harmonics?
A)
B)
C)
D)
E)
440 Hz
660 Hz
880 Hz
1320 Hz
None of the above
Solution:
f n  nf1 
f 2  880Hz
17. A string with both ends fixed is vibrating at its 3rd harmonic frequency. The number of
nodes is ___.
A)
B)
C)
D)
E)
1
2
3
4
5
Solution:
The 3rd harmonic has 3antinodes and 4 nodes.
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? 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 
3
2 L   f stopped  m f open
f 2stopped 
400 Hz  f 2stopped  300Hz

m
n
mv 
2n
22
f mstopped 

4L 
Page 6 of 7
Physics 198
Exam I
Fall 2015
19. For what pipes the difference between acoustic length and physical (geometrical) length is
small (could be neglected)?
A)
B)
C)
D)
E)
For very long pipes (length much bigger then radius)
For very short pipes (length much smaller then radius)
If the lengths and the radius are approximately the same
For stopped pipes (one end closed), and it has nothing to do with length and radius
For open pipes (both ends open), and it has nothing to do with length and radius
Solution:
The difference is 0.61r for each open end. If L  r , then this correction can be neglected.
20. To increase twice the frequency of Helmholtz resonator, the volume of the resonator should
be
A)
B)
C)
D)
E)
Increased twice
Decreased twice
Increased four times
Decreased four times
Frequency is independent from the volume
Solution:
v a
follows that if the volume is decreasing four times than the
2 Vl
frequency is increasing two times.
From equation f 
Page 7 of 7