P1112 Fall 2008
Solution to Homework #7
1.
A small remotecontrol car with mass 1.60 kg
moves at a
constant speed of v= 12.0 m/s in a vertical
circle
inside a hollow metal cylinder that has a radius
of 5.00 m. What is the magnitude of the normal force
exerted on the car by the walls of the cylinder at
a) the bottom of the vertical circle and
b) at the top of the vertical circle?
At the bottom, the free body diagram has W=mg
going down, and normal force N from the track going
up.
NW=Nmg=ma=mv
2
/r
or
N=m(v
2
/r+g)=1.60 kg (12.0
2
/5+9.8) m/s
2
=61.8 N
At the top, both the weight and the normal force are
pointing downward, so
N+mg= mv
2
/r
N=m(v
2
/rg)=30.4 N
2.
The International Space Station (ISS) orbits the
Earth in an approximately circular orbit at a height of
about 240 miles (384 km) above the Earth's surface.
(a)
What is the speed of the space station in its orbit
(in km/s)?
Newton’s law of gravitation combined with the
formula for centripetal acceleration gives
GMm/r
2
=mv
2
/r
so
v=
√
(GM/r)=7.7 km/s
where r is the radius of the earth plus 384 km.
(b)
What is the space station's orbital period (in
hours)?
Period is circumference divided by velocity
T=2
π
r/v=1.5 hours
3.
A neutral buoyancy torpedo of mass M=100kg is
fired horizontally from one submarine to another.
[Neutral buoyancy means that the buoyancy force
exactly cancels the force of gravity.] The propellers
on the torpedo provide a constant force of F=500N.
Before reaching its target the torpedo reaches its
terminal speed v
t
=30m/s.
(a)
When the torpedo reaches its terminal speed,
what is the magnitude of the drag force?
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 Fall '07
 LECLAIR,A
 Force, Mass, Work, terminal speed

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