PHYS2010 FINAL EXAM, VERSION 0001, SPRING 2006
1
Useful Constants
•
Sea level atmospheric pressure: 101 kPa = 1
.
01
×
10
5
N/m
2
•
Density of water: 1.00 g/cm
3
= 1000 kg/m
3
•
Universal gravitational constant:
G
= 6
.
67
×
10

11
m
3
/
(kg s
2
) = 6
.
67
×
10

11
N m
2
/
kg
2
Problems
For the next two problems, you are ﬂoating in a spacesuit. At ﬁrst you have no velocity
and no forces are acting on you.
1. You throw a ball of mass 1 kg so that it starts moving at 5 m/s. You and the spacesuit
(without the ball) have a mass of 100 kg. What is your speed after you throw the ball?
A)
0.05 m/s
B)
0.5 m/s
C)
0 m/s
D)
5 m/s
E)
15 m/s
Momentum conservation says 0 =
m
1
v
1
+
m
2
v
2
, hence
v
2
=

(
m
1
/m
2
)
v
1
, so
.
05 m/s.
2. You caused the ball to move by applying a constant force for 0.5 s. What is the
magnitude of the force exerted on you by the ball during that time?
A)
0.5 N
B)
1 N
C)
5 N
D)
10 N
E)
Not enough information
given
The force is the change in momentum over the change in time, so
mv/t
= 5
/.
5 = 10
N. By Newton’s third law the magnitudes of the forces (you on the ball or the ball on
you) are the same.
3. Two motors are labeled 1 and 2. Both motors are designed to lift widgets from the
ﬂoor of a warehouse to a high shelf. At its maximum power setting
P
1
, motor 1 is
capable of lifting a mass
m
1
through a height diﬀerence
h
1
in a time
t
1
. Motor 2 can
lift twice the mass of motor 1, but it takes twice as long: at maximum power
P
2
, motor
2 can lift a mass 2
m
1
through a height
h
1
in a time 2
t
1
. What is the relationship
between the power outputs of the two motors?
A)
P
2
=
1
4
P
1
B)
P
2
=
1
2
P
1
C)
P
2
= 4
P
1
D)
P
2
= 2
P
1
E)
P
2
=
P
1
Motor 1 can lift mass
m
1
up
h
1
: the work done in this case is
W
=
m
1
gh
1
, so
P
1
=
W/
Δ
t
=
m
1
gh
1
/t
1
. Similarly,
P
2
= (2
m
1
)
gh
1
/
(2
t
1
) =
m
1
gh
1
/t
1
, so
P
2
=
P
1
.
4. The vector
A
has magnitude

A

= 5
.
6, and makes an angle
θ
= 30
◦
from the left with
the positive
y
axis (see diagram). To twoplace precision, what is
A
x
, the
x
component
of the vector
A
?
x
y
A
=30
o
A)
+2
.
8
B)

2
.
8
C)
+4
.
8
D)

4
.
8
E)
None of these
A
x
=

A
sin
θ
=

(5
.
6)(0
.
5) =

2
.
8
.
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View Full DocumentPHYS2010 FINAL EXAM, VERSION 0001, SPRING 2006
2
5. A penny of mass
m
is resting on a box that is accelerating to the right, as shown
below. The coeﬃcient of static friction between the penny and the box is
μ
S
. When
the acceleration of the box is slowly increased, the penny begins to slide just when the
magnitude of the acceleration reaches
a
max
= 15 m/s
2
. However, when the acceleration
is maintained at
a
0
= 10 m/s
2
, the penny stays in place on the box no matter what
the velocity is.
box
a
penny
mass m
"
S
Which of the following statements are true when the box’s acceleration is
a
=
a
0
and
the penny stays in place?
I. The magnitude of the force of static friction is
F
fric
=
μ
S
mg
.
II. The magnitude of the acceleration of the penny is
a
0
= 10 m/s
2
.
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 '06
 DUBSON
 Physics

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