This preview shows pages 1–3. Sign up to view the full content.
Physics 2211
Quiz #4
Solutions
Fall 2007
G
= 6
.
673
×
10

11
N
·
m
2
/
kg
2
g
Earth
= 9
.
8m
/
s
2
Unless otherwise directed, all springs, cords, and pulleys are ideal, and drag should be neglected.
I
. (16 points) Bob, whose mass is 75kg, stands at rest on a stationary 25kg cart. He runs across the cart with
a horizontal velocity of 8.0m/s to the right
with respect to the cart
and jumps oﬀ the end (still at 8.0m/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.
)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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
=
±
75kg
75kg + 25kg
¶
8
.
0m
/
s =

6
.
0m
/
s
The speed is the magnitude of the velocity,
6.0m/s
.
Quiz #4 Solutions Page 1 of 5
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document II
. (16 points) Far in space, where gravity is negligible, a 550kg rocket traveling at 120m/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
= 960N. What is the maximum speed of the rocket during these 60s? (The mass lost by the rocket
is negligible.)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
The impulse on the rocket is the change in its mo
This is the end of the preview. Sign up
to
access the rest of the document.
This homework help was uploaded on 04/09/2008 for the course PHYSICS 2211 taught by Professor Uzer during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 UZER
 Mass

Click to edit the document details