Physics 2211
Quiz #4
Solutions
Fall 2007
G
= 6
.
673
×
10

11
N
·
m
2
/
kg
2
g
Earth
= 9
.
8 m
/
s
2
Unless otherwise directed, all springs, cords, and pulleys are ideal, and drag should be neglected.
I
. (16 points) Bob, whose mass is 75 kg, stands at rest on a stationary 25 kg cart. He runs across the cart with
a horizontal velocity of 8.0 m/s to the right
with respect to the cart
and jumps off the end (still at 8.0 m/s
horizontally with respect to the cart). If there is no friction between the cart and the level ground, what is
the resulting speed of the cart? (
On Earth.
)
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There are no net external forces on the BobCart system. Linear momentum
in that system is conserved. Let the +
x
direction be toward the right. In
the frame of the ground:
p
xi
g
=
p
xf
g
⇒
m
c
v
ci
g
+
m
b
v
bi
g
=
m
c
v
cf
g
+
m
b
v
bf
g
where
m
c
is the mass of the cart,
m
b
is the mass of Bob,
v
c
is the velocity
of the cart,
v
b
is the velocity of Bob, and
i
and
f
represent initial and final
states, respectively.
“g” indicates that all these velocities are measured
with respect to the ground.
The velocity of Bob with respect to the ground is the velocity of Bob with respect to the cart plus the
velocity of the cart with respect to the ground,
v
b
g
=
v
b
c
+
v
c
g
. Bob and the cart are initially stationary.
0 =
m
c
v
cf
g
+
m
b
v
bf
g
⇒

m
c
v
cf
g
=
m
b
(
v
bf
c
+
v
cf
g
)
=
m
b
v
bf
c
+
m
b
v
cf
g
Solving for the final velocity of the cart with respect to the ground

(
m
c
+
m
b
)
v
cf
g
=
m
b
v
bf
c
⇒
v
cf
g
=
m
b
m
c
+
m
b
¶
v
cf
g
=
75 kg
75 kg + 25 kg
¶
8
.
0 m
/
s =

6
.
0 m
/
s
The speed is the magnitude of the velocity,
6.0 m/s
.
Quiz #4 Solutions Page 1 of 5
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II
. (16 points) Far in space, where gravity is negligible, a 550 kg rocket traveling at 120 m/s in the +
x
direction
fires its engines. The figure shows the thrust force as a function of time, with a maximum thrust magnitude
of
F
max
= 960 N. What is the maximum speed of the rocket during these 60 s? (The mass lost by the rocket
is negligible.)
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 Spring '08
 UZER
 Force, Friction, Mass

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