Physics 53
Summer 2010
Quiz 4
Solutions
Check the best answer.
1.
A pair of blocks, with m2 = 2m1 , have a spring between them
to which they are not attached. They are pushed together to
compress the spring and then released from rest. When they
have left the expanded spring:
m1
m2
They have the same speed.
m2 has greater kinetic energy than m1 .
√
They have the same magnitude of momentum.
None of the above is true.
Check T or F depending on whether the statement is true or false.
2.
The total kinetic energy of any system is equal to one-half the total mass times
the square of the speed of the CM.
T
√
F
[Plus K relative to the CM.]
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Physics 53
3.
a.
Summer 2010
A fireworks rocket is shot vertically into the air. At the top of its flight an
explosion takes place, breaking the rocket into pieces of mass m and 2m. The
lighter piece moves horizontally toward the north immediately after the
explosion, with speed v0 .
a.
How much energy did the internal forces of the explosion provide?
[Answer in terms of m and v0 .]
b.
Describe the motion of the CM of the system while the pieces are in the air.
[What external forces are acting?]
c.
If the lighter piece lands at distance R north of the original launch point,
where does the heavier one land? [Answer in terms of R.]
At the instant of explosion the system is at rest. By conservation of momentum the
heavier mass has speed v0 / 2 . The total kinetic energy is
1
mv02
2
+ 12 (2m)(v0 / 2)2 = 34 mv02 . This is the energy suppled by the explosion.
b.
The only external force is gravity, so the CM falls straight down.
c.
The heavier one lands at distance R / 2 to the south. The CM lands at the launch
point.
[It’s not that simple if they don’t land at the same time, because the ground
supplies another external force when they land.]
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