HW#18 Ch 6: Force and Motion — II
Instructions: Show all work using Newton’s 2nd law and free body diagrams.
1. A 20 kg box is pushed along a frictionless surface with a force F, such that it has a constant acceleration of a1 = 3 m/s2, as shown in the accompanying figure. On top of the 20 kg box is a 5 kg box that slides backward relative to the 20 kg box along a rough surface. It has an acceleration a2 = 2 m/s2 in the forward direction. a) What is the frictional force exerted by the 20 kg box on the 5 kg box, including direction? b) What is the coefficient of kinetic friction µk between the two boxes? c) What is the applied force F? d) After the 5 kg box falls off, what is the acceleration of the 20 kg box, assuming the force F doesn’t change?
2. A typical velodrome features steeply banked oval tracks where cyclists can race at high speeds. If the curved portion of the track features a radius of 31.5 m and the banking angle is 43°, at what speed must the cyclist achieve so that the only force between the track and the bicycle tires is the normal force? Give your answer in miles per hour.
3. A miniature car negotiates a curve of radius 150 m that is banked at an angle of 10°. Assuming that its mass is 800 kg and that it is traveling at 23.6 m/s without skidding, find (a) the normal force on the tires exerted by the track, (b) the frictional force on the tires exerted by the track, and (c) the minimum coefficient of static friction between the track and tires.