7. Friction, Inclines, Systems

A pickup truck is carrying a toolbox, but the rear gate of the truck is missing. The toolbox will slide out if it is set moving. The coefficients of kinetic friction and static friction between the box and the level bed of the truck are $0.355$ and $0.650$, respectively. Starting from rest, what is the shortest time this truck could accelerate uniformly to $30.0$ m/s without causing the box to slide? Draw a free-body diagram of the toolbox.

A 36N force is needed to start a 7.0 kg box moving across the floor. If the 36.0 N force continues, the box accelerates at 0.70 m/s². What are the coefficients of static and kinetic friction?

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$, and the coefficient of kinetic friction is $0.20$. What minimum horizontal force must the monkey apply to start the box in motion?

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$, and the coefficient of kinetic friction is $0.20$. What is the magnitude of the friction force if a monkey applies a horizontal force of $6.0$ N to the box and the box is initially at rest?

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$, and the coefficient of kinetic friction is $0.20$. If no horizontal force is applied to the box and the box is at rest, how large is the friction force exerted on it?

Suppose you are standing on a train accelerating at 0.20 g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide?

The 70.0-kg climber in Fig. 5–53 is supported in the 'chimney' by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60, respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that the static friction forces are both at their maximum. Ignore his grip on the rope.

(II) Drag-race tires in contact with an asphalt surface have a very high coefficient of static friction. Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s, starting from rest.

A small mass m is set on the surface of a sphere, Fig. 5–54. If the coefficient of static friction is μ_s = 0.70, at what angle Ø would the mass start sliding?