Problem 86
You are called as an expert witness in a trial for a traffic violation. The facts are these: A driver slammed on his brakes and came to a stop with constant acceleration. Measurements of his tires and the skid marks on the pavement indicate that he locked his car's wheels, the car traveled 192 ft before stopping, and the coefficient of kinetic friction between the road and his tires was 0.750. He was charged with speeding in a 45-mi/h zone but pleads innocent. What is your conclusion: guilty or innocent? How fast was he going when he hit his brakes?
Problem 88
A 12.0-kg box rests on the level bed of a truck. The coefficients of friction between the box and bed are \(\mu_s = 0.19\) and \(\mu_k = 0.15\). The truck stops at a stop sign and then starts to move with an acceleration of 2.20 m/s\(^2\). If the box is 1.80 m from the rear of the truck when the truck starts, how much time elapses before the box falls off the truck? How far does the truck travel in this time?
Problem 92
Block \(B\), with mass 5.00 kg, rests on block \(A\), with mass 8.00 kg, which in turn is on a horizontal tabletop \(\textbf{(Fig. P5.92).}\) There is no friction between block \(A\) and the tabletop, but the coefficient of static friction between blocks \(A\) and \(B\) is 0.750. A light string attached to block \(A\) passes over a frictionless, massless pulley, and block \(C\) is suspended from the other end of the string. What is the largest mass that block \(C\) can have so that blocks \(A\) and \(B\) still slide together when the system is released from rest?
Problem 93
Two objects, with masses 5.00 kg and 2.00 kg, hang 0.600 m above the floor from the ends of a cord that is 6.00 m long and passes over a frictionless pulley. Both objects start from rest. Find the maximum height reached by the 2.00-kg object.
Problem 94
You are riding in an elevator on the way to the 18th floor of your dormitory. The elevator is accelerating upward with \(a =\) 1.90 m/s\(^2\). Beside you is the box containing your new computer; the box and its contents have a total mass of 36.0 kg. While the elevator is accelerating upward, you push horizontally on the box to slide it at constant speed toward the elevator door. If the coefficient of kinetic friction between the box and the elevator floor is \(\mu_k =\) 0.32, what magnitude of force must you apply?
Problem 97
Block \(A\), with weight \(3w\), slides down an inclined plane \(S\) of slope angle 36.9\(^{\circ}\) at a constant speed while plank \(B\), with weight \(w\), rests on top of A. The plank is attached by a cord to the wall \(\textbf{(Fig. P5.97).}\) (a) Draw a diagram of all the forces acting on block \(A\). (b) If the coefficient of kinetic friction is the same between \(A\) and \(B\) and between \(S\) and \(A\), determine its value.
Problem 98
Jack sits in the chair of a Ferris wheel that is rotating at a constant 0.100 rev/s. As Jack passes through the highest point of his circular path, the upward force that the chair exerts on him is equal to one-fourth of his weight. What is the radius of the circle in which Jack travels? Treat him as a point mass.
Problem 99
A curve with a 120-m radius on a level road is banked at the correct angle for a speed of 20 m/s. If an automobile rounds this curve at 30 m/s, what is the minimum coefficient of static friction needed between tires and road to prevent skidding?
Problem 102
You are riding in a school bus. As the bus rounds a flat curve at constant speed, a lunch box with mass 0.500 kg, suspended from the ceiling of the bus by a string 1.80 m long, is found to hang at rest relative to the bus when the string makes an angle of 30.0\(^{\circ}\) with the vertical. In this position the lunch box is 50.0 m from the curve's center of curvature. What is the speed \(\upsilon \) of the bus?
Problem 105
On the ride "Spindletop" at the amusement park Six Flags Over Texas, people stood against the inner wall of a hollow vertical cylinder with radius 2.5 m. The cylinder started to rotate, and when it reached a constant rotation rate of 0.60 rev/s, the floor dropped about 0.5 m. The people remained pinned against the wall without touching the floor. (a) Draw a force diagram for a person on this ride after the floor has dropped. (b) What minimum coefficient of static friction was required for the person not to slide downward to the new position of the floor? (c) Does your answer in part (b) depend on the person's mass? (\(Note\): When such a ride is over, the cylinder is slowly brought to rest. As it slows down, people slide down the walls to the floor.)
