Week 5 Homework Assignment

1. (P.173 Prob.6)An elevator cable winds on a drum of radius 90.0cm that is connected to a motor. (a) If the elevator is moving down at 0.50m/s, what is the angular speed of the drum? (b) If the elevator moves down 6.0m, how many revolutions has the drum made?
2. (P.174 Prob.12) The rotor (Fig.5.21) is an amusement park ride where people stand against the inside of a cylinder. Once the cylinder is spinning fast enough, the floor drops out. (a) What force keeps the people from falling out the bottom of the cylinder? (b) If the coefficient of friction is 0.40 and the cylinder has a radius of 2.5m, what is the minimum angular speed of the cylinder so that the people don't fall out? (Normally the operator runs it considerably faster as a safety measure.)
   
3. (P.174 Prob.18) A highway curve has a radius of 122m, at what angle should the road be banked so that a car traveling at 26.8m/s (60mph) has no tendency to skid sideways on the road? [Hint: No tendency to skid means the frictional force is zero.]
4. (P.175 Prob.30) A satellite travels around Earth in uniform circular motion at altitude 35,800km above Earth's surface. The satellite is in geosynchronous orbit (that is, the time for it to complete one orbit is exactly one day). In Fig.5.18, the satellite moves counterclockwise (ABCDA). State directions in terms of  the x- and y-axes.. (a) What is the satellite's instantaneous velocity at point C? (b) What is the satellite's average velocity for one quarter of an orbit, starting at A and ending at B? (c) What is the satellite's average acceleration for one quarter of an orbit, start at  A and ending at B? (d) What is the satellite's instantaneous acceleration at point D?
   
5. (P.175 Prob.38) During normal operation, a computer's hard disk spins at 7200rpm. If it takes the hard disk 4.0s to reach this angular velocity starting from rest, what is the average angular acceleration of the hard disk in rad/s²?
6. (P.208 Prob.2) A sled is dragged along a horizontal path at a constant speed pf 1.5m/s by a rope that in inclined at an angle of 30.0° with respect to the horizontal (Fig.6.24). The total weight of the sled is 470N. The tension in the rope is 240N. How much work is done by the rope on the sled in a time interval of 10.0s?