Question

Interactive Exercises 6.03: Frictional force on Inclined Surface (Making Deliveries on the Streets of San Francisco.) A delivery truck with a flat bed drives around the city of San Francisco, which is famous for its steep hills. The truck carries a crate on its bed. Unwisely, the driver has not secured the crate to the bed, so the crate merely rests on the bed of the truck. See Fig. 6.3.1. rateretbad of truk Stoplight Stoplight a base of hll Interactive Figure 6.3.1: A crate rests on the flat bed of a delivery truck. The truck travels on streets that are hilly ▼ Question 1 Suppose the truck is at a red stoplight when the light changes to green, and the road is in a flat portion of the city. See point A in Fig. 6.3.1. The driver can speed up from rest at a maximum rate of 4.90 m/s without the crate slipping against the bed of the truck. What is the coefficient of static friction between the crate the bed of the truck? the tolerance is +/-2% By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor.

Answer 1

The following figure shows free body diagram of the track when the road is flat The net force acting on the truck when the road is flat is equal to its friction force F_fric = F_net mu_s (mg) = ma (Since F_fric = mu_s (mg) F_net = ma) Solve the above equation for mu_s mu_s = a/g = 4.90 m/s^2/9.80 m/s^2 = 0.5 \r\n Hence, the required coefficient of friction is mu_s = 0.5 Free body diagram When truck is moving downward hill, then the net force along hill is as follows: F_net = mu_s mg cos theta - mg sin theta ma_x = mu_s mg cos theta - mg sin theta (Since F_net = ma_x) a_x = g(mu_s cos theta - sin theta) = (9.8 m/s^2)((0.5) cos 20 degrees - sin 20 degrees) = 1.25 m/s^2 Hence, the maximum acceleration is a_x = 1.25 m/s^2 \r\n Free body diagram In this case, the net force acting on the truck is as follows: