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Review Chapter 7 & 8
1. A rocket, which has a mass of 87,000 kg is to be launched from the surface of Triton [mTriton = 1.34 x
1023 kg, rTriton = 1.90 x 106 m, G = 6.67 x 10-11 Nm2/kg2]
a. What will be the total gravitational energy of this rocket while sitting on the surface of Triton?
b. With what velocity must this rocket be launched from the surface of Triton in order for it to escape
the gravitational effect of Triton?
c. Suppose that this rocket is launched from the surface of Triton with a velocity of 5.5 x 103 m/sec.,
what will be the velocity of this rocket when it is very far from Triton?
Suppose that this rocket is orbiting Triton at an altitude of 1.2 x 106 meters.
d. What velocity is required to orbit Triton at this altitude?
e. What will be the total energy content of the rocket as it orbits Triton at this altitude?
f. How much energy must be added to this rocket if it is to escape the gravitational force of Triton
from this orbit?
2. A wheel with a radius of 25 cm rotates from rest to an angular speed of 75 rpm on a time of 35
seconds.
a. what is the angular acceleration of the wheel?
b. What is the tangential velocity of the wheel at 35 seconds?
c. What is the centripetal acceleration of the wheel at this time?
d. What is the total acceleration of the wheel at this time?
e. At t = 15 seconds how many times has the wheel rotated?
3. Three weights are hung from a meterstick, which has a mass of 145 grams, as shown in the diagram to the
right. The system is at equilibrium.
a. What is the torque supplied by the 220 gram mass about the 25.0 cm mark on the meterstick?
b. What is the total clockwise torque about the 25.0 cm mark of the meterstick?
c. What is the total counterclockwise torque about the 25.0 cm mark of the meterstick?
d. What is the mass m1 required to produce equilibrium about the 25.0 cm mark of the meterstick?
e. How much upward force must be applied to this meterstick at the 25.0 cm mark in order to generate
equilibrium?
4. A ball of mass M attached to a string of length L moves in a circle in a vertical plane as shown above.
At the top of the circular path, the tension in the string is twice the weight of the ball. At the bottom, the
ball just clears the ground. Air resistance is negligible. Express all answers in terms of M, L, and g.
a. Determine the magnitude and direction of the net force on the ball when it is at the top.
b. Determine the speed vo of the ball at the top.
The string is then cut when the ball is at the top.
c. Determine the time it takes the ball to reach the ground.
d. Determine the horizontal distance the ball travels before hitting the ground.
5. A box of mass M, held in place by friction, rides on the flatbed of a truck which is traveling with
constant speed v. The truck is on an unbanked circular roadway having radius of curvature R.
a. On the diagram provided above, indicate and clearly label all the force vectors acting on the box.
b. Find what condition must be satisfied by the coefficient of static friction  between the box and
the truck bed. Express your answer in terms of v, R, and g.
If the roadway is properly banked, the box will still remain in place on the truck for the same speed v even
when the truck bed is frictionless.
c. On the diagram below indicate and clearly label the two forces acting on the box under these
conditions
d. Which, if either, of the two forces acting on the box is greater in magnitude?