Physics 221.
Exam I
Summer 2003
1. The brightest star in the night sky is α Canis Majoris, also known as Sirius. It lies 8.8 light-years
away. Express this distance in meters. (A light-year is the distance covered by light in one year.
Light travels in vacuum at 3 × 108 m/s).
a.
b.
c.
d.
e.
2.6 × 109 m
7.2 × 1010 m
7.1 × 1012 m
8.3 × 1016 m
3.8 × 1020 m
G
G
2. Let A = 3iˆ + 5kˆ and B = −iˆ + 2 ˆj + α kˆ . Find the value of scalar α that makes these two vectors
perpendicular to each other.
a.
b.
c.
d.
e.
α = 0.3
α = 0.6
α = 0.9
α = 1.2
α = 1.7
3. A box has an initial speed v0 up a frictionless incline. The box moves up the incline and then
returns to its initial position, and continues to move down the incline. Which of the following
velocity versus time graphs corresponds to this motion?
v
v
v
t
A
t
t
C
B
v
v
t
D
t
E
Page 1 of 9
Physics 221.
Exam I
Summer 2003
The situation below refers to the next two questions:
A particle moves along the trajectory shown below at constant speed. The positions of the
particle at t = 0 and at t = 1 s are shown.
t=1s
t=0
4. Which of these vectors best describes the direction of the average velocity of the particle
between t = 0 and t = 1 s?
a. /
b. 2
c. →
d. ←
e. ↑
5. Which of these vectors best describes the direction of the instantaneous acceleration of the
particle at t = 0?
a. /
b. 2
c. →
d. ←
e. ↑
Page 2 of 9
Physics 221.
Exam I
Summer 2003
The situation below refers to the next two questions:
You are standing on the edge of a cliff of height h. You throw a ball at an angle θ = 30° above
the horizontal with an initial speed v0 = 54 m/s. Using a stop watch, you determine that the ball
strikes the ground at the base of the cliff 7 s after release.
θ
h
D
6. What is the horizontal distance D covered by the ball?
a.
b.
c.
d.
e.
D = 203 m
D = 282 m
D = 327 m
D = 482 m
D = 564 m
7. At what time t after the release does the ball reach its maximum height?
a.
b.
c.
d.
e.
t = 1.9 s
t = 2.8 s
t = 3.5 s
t = 4.1 s
t = 4.8 s
Page 3 of 9
Physics 221.
Exam I
Summer 2003
The situation below refers to the next two questions:
A tennis ball of weight W = 0.5 N is attached to a massless rope and swung in a vertical circle.
The rope is L = 2 m long.
L
g
8. What is the minimum speed of the ball at the highest point of the trajectory if the rope is to
stay straight?
a.
b.
c.
d.
e.
vmin
vmin
vmin
vmin
vmin
= 1.0 m/s
= 4.4 m/s
= 8.8 m/s
= 19.6 m/s
= 79.3 m/s
9. Which of the following is the correct expression for the tension in the string T when the ball
is at the lowest point?
a. T = 0
b. T = W
c. T = 2W

v2 
d. T = W 1 +

 gL 

v2 
e. T = W 1 −

 gL 
Page 4 of 9
Physics 221.
Exam I
Summer 2003
10. Two spaceships A and B move toward one another as shown. At time t = 0, spaceship A
launches a shuttle craft toward spaceship B. At time t = tf, the shuttle reaches spaceship B.
B
A
d0
t=0
Shuttle
A
t = tf
df
B
Shuttle
The average speed of the shuttle relative to spaceship A is:
a. vS , A =
b. vS , A
df
tf
d
= 0
tf
c. vS , A =
d. vS , A =
d f − d0
tf
d f + d0
tf
e. None of the above
Page 5 of 9
Physics 221.
Exam I
Summer 2003
The situation below refers to the next two questions:
Block 1 with mass m1 = 1.0 kg and block 2 with mass m2 = 1.6 kg sit atop a frictionless double
inclined plane as shown. The two blocks are connected to one another through a massless string
around an ideal pulley.
m1
θ1 = 30°
m2
θ2 = 60°
11. What is the magnitude of the acceleration of the blocks?
a.
b.
c.
d.
e.
a = 0.35 m/s2
a = 1.6 m/s2
a = 2.5 m/s2
a = 3.0 m/s2
a = 3.3 m/s2
12. Now block 1 is coated with a rough paint so the friction force between this block and the
surface is not negligible (but not strong enough to prevent the blocks from moving). Compare the
tension on the string before and after the coating.
a.
b.
c.
d.
e.
The tension stays the same.
The tension increases only on the side of mass 1 (left side).
The tension decreases only on the side of mass 1 (left side).
The tension increases on both ends.
The tension decreases on both ends.
Page 6 of 9
Physics 221.
Exam I
Summer 2003
The situation below refers to the next two questions:
A box of weight W = 30 N is being pulled across a rough, horizontal surface with a force
T = 10 N exerted by a string that makes an angle θ = 45° with the horizontal. The box moves at a
constant speed v = 3 m/s across the surface.
T
θ
13. Which of the following expressions is correct for the magnitude of the normal force N
exerted by the floor on the box?
a.
b.
c.
d.
e.
N = W + T cos θ
N = W − T cos θ
N = W + T sin θ
N = W − T sin θ
N =W
14. What is the magnitude of the friction force between the box and the surface?
a.
b.
c.
d.
e.
fk = 3.4 N
fk = 5.2 N
fk = 6.9 N
fk = 7.1 N
fk = 10 N
Page 7 of 9
Physics 221.
Exam I
Summer 2003
The situation below refers to the next two questions:
Blocks A and B accelerate on a frictionless horizontal surface while being pushed by your hand with
a force F. The mass of block A is larger than the mass of block B.
F
A
B
15. Compare the acceleration of each block and the net force on each block:
a. a A < aB
Fnet, A < Fnet, B
b. a A = aB
Fnet, A < Fnet, B
c. a A = aB
Fnet, A = Fnet, B
d. a A > aB
Fnet, A = Fnet, B
e. a A = aB
Fnet, A > Fnet, B
16. The force exerted by block B on block A is:
a. 0
b. FA, B = F
mA
F
mA + mB
mB
F
d. FA, B =
mA + mB
mA mB
F
e. FA, B =
mA + mB
c. FA, B =
Page 8 of 9
Physics 221.
Exam I
Summer 2003
17. Two boxes of masses m and 2m are stacked as shown in the figure below on top of a horizontal
frictionless table. The coefficient of static friction between the two boxes is µs. The bottom box is
being pulled with a force F. Find the maximum value of F for which the boxes will move together.
m
µs
2m
F
frictionless
a. Fmax = 3µs mg
b. Fmax = µs mg
3
c. Fmax = µs mg
2
1
d. Fmax = µs mg
2
1
e. Fmax = µs mg
3
Page 9 of 9