Worksheet L: Linear momentum; center of mass
1.
A big, fat asteroid floats happily in space unaware that another asteroid of mass
m
=
200 kg is heading towards it at 150 m/s. The big asteroid is initially at rest. The collision
breaks the big asteroid in two pieces of mass
M
= 500 kg that come out in the directions
indicated in the figure. The incident asteroid bounces back at an angle as shown in the
figure, at 50 m/s.
Find the speeds
v
1
and
v
2
of the two pieces of the big asteroid.
Conservation of linear momentum in the x and y directions:
02
3
13
:
sin30
0
cos30
xm
v M
v m
v
yM
v
m
v
=−
°
°
(where v
0
= 150 m/s and v
3
= 50 m/s)
From the first equation:
()
20
3
200 kg
150 m/s
50 m/s sin30
500 kg
70 m/s
m
vv
v
M
=+
°
=
+°
=
From the second equation
200 kg
(50 m/s)cos30
500 kg
17 m/s
m
M
=°
=
°
=
30
°
M
M
m
v
1
v
2
50 m/s
2
M
m
150 m/s
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2
. Romeo (77 kg) sits in the left end of a 2.7 mlong boat (80 kg) that floats still at some
distance from the shore and plays a romantic song with his guitar to Juliet (55 kg), who
sits in the right end. After the serenade, Juliet carefully moves to Romeo’s side to plant a
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 Fall '08
 HerreraSiklody
 Center Of Mass, Force, Mass, Momentum, Work

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