Physics 201 Homework 4
Jan 30, 2013
1. There is a clever kitchen gadget for drying lettuce leaves after you wash them.
It consists of a cylindrical container mounted so that it can be rotated about its
axis by turning a hand crank. The outer wall of the cylinder is perforated with
small holes. You put the wet leaves in the container and turn the crank to spin
off the water. The radius of the container is 0.12 meters. When the cylinder is
rotating at 2.0 revolutions per second, what is the magnitude of the centripetal
acceleration at the outer wall?
19 m/s2
2. A jet flying at 123 m/s banks to make a horizontal circular turn. The radius of
the turn is 3810 meters, and the mass of the jet is 2.00 × 105 kilograms. Calculate
the magnitude of the necessary lifting force.
2.11 × 106 meters
3. Mars has a mass of 6.46 × 1023 kilograms and a radius of 3.39 × 106 meters.
(a) What is the acceleration due to gravity on Mars? (b) How much would a
65-kilogram person weigh on this planet?
(a) 3.75 m/s2 ; (b) 244 newtons
4. A car travels at a constant speed around a circular track whose radius is
2600 meters. The car goes once around the track in 360 seconds. What is the
magnitude of the centripetal acceleration of the car?
0.79 m/s2
5. In a skating stunt known as crack-the-whip, a number of skaters hold hands
and form a straight line. They try to skate so that the line rotates about the
skater at one end, who acts as the pivot. The skater farthest out has a mass of
80.0 kilograms and is 6.10 meters from the pivot. He is skating at a speed of 6.80
m/s. Determine the magnitude of the centripetal force that acts on him.
606 newtons
6. The moon orbits the earth at a distance of 3.85×108 meters. Assume that this
distance is between the centers of the earth and the moon and that the mass of
the earth is 5.98 × 1024 kilograms. Find the period for the moon’s motion around
the earth. Express the answer in days and compare it to the length of a month.
27.5 days
7. The National Aeronautics and Space Administration (NASA) studies the
physiological effects of large accelerations on astronauts. Some of these studies
use a machine known as a centrifuge. This machine consists of a long arm, to one
end of which is attached a chamber in which the astronaut sits. The other end of
the arm is connected to an axis about which the arm and chamber can be rotated.
The astronaut moves on a circular path, much like a model airplane flying in a
circle on a guideline. The chamber is located 15 meters from the center of the
circle. At what speed must the chamber move so that an astronaut is subjected
to 7.5 times the acceleration due to gravity?
33 m/s
8. The hammer throw is a track-and-field event in which a 7.3-kilogram ball (the
“hammer”) is whirled around in a circle several times and released. It then moves
upward on the familiar curving path of projectile motion and eventually returns
to earth some distance away. The world record for this distance is 86.75 meters,
achieved in 1986 by Yuriy Sedykh. Ignore air resistance and the fact that the ball
is released above the ground rather than at ground level. Furthermore, assume
that the ball is whirled on a circle that has a radius of 1.8 meters and that its
velocity at the instant of release is directed 41◦ above the horizontal. Find the
magnitude of the centripetal force acting on the ball just prior to the moment of
release.
3500 newtons
9. A car moving at 5.0 m/s tries to round a corner in a circular arc of 8.0 meters
radius. The roadway is flat. How large must the coefficient of fricton be between
the wheels and roadway if the car is not to skid?
0.32
10. A satellite orbits the Earth at a height of 200 kilometers. Find (a) the speed
of the satellite and (b) the time taken (in minutes) to complete one revolution.
(a) 7.8 km/s; (b) 88 minutes
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