Name:
Physics 121, Dr. Callahan
Summer I 2008, Midterm #3
Note:
Show your work. Clarity counts. You may use one 8
1
2
×
11 sheet of notes (both sides) and a calculator.
1
2
3
1. A 3.4 kg mass moving north at 1
.
5 m
/
s hits and sticks to a 5.0 kg mass moving southwest
(45
◦
west of south) at 2
.
3 m
/
s. The collision is completely inelastic. Find the magnitude and
direction of the final velocity of the combined masses.
Answer:
Let
x
point east and
y
point north.
The
x
 and
y
components of momentum are
conserved. Thus
m
1
v
10
x
+
m
2
v
20
x
= (
m
1
+
m
2
)
v
fx
,
so
v
fx
=
m
1
v
10
x
+
m
2
v
20
x
m
1
+
m
2
=
(3
.
4 kg)(0 m
/
s)

(5
.
0 kg)(2
.
3 m
/
s) sin 45
◦
(3
.
4 kg) + (5
.
0 kg)
=

0
.
97 m
/
s
.
Similarly,
m
1
v
10
y
+
m
2
v
20
y
= (
m
1
+
m
2
)
v
fy
,
so
v
fy
=
m
1
v
10
y
+
m
2
v
20
y
m
1
+
m
2
=
(3
.
4 kg)(1
.
5 m
/
s)

(5
.
0 kg)(2
.
3 m
/
s) cos 45
◦
(3
.
4 kg) + (5
.
0 kg)
=

0
.
36 m
/
s
.
Thus
v
f
=
radicalBig
v
2
fx
+
v
2
fy
= 1
.
0 m
/
s
,
θ
= Tan

1
parenleftbigg
v
fy
v
fx
parenrightbigg
= 20
◦
south of west.
2. Consider a uniform stick of mass
m
and length
L
, attached at one end to the floor by a hinge, so that it
is free to pivot about that end. The stick starts out motionless and nearly vertical, then gravity pulls
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 Spring '08
 Chamberlin
 Kinetic Energy, Mass, Work, Special Relativity, m/s, m/s. m1

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