Can Friction Actually Speed Up an Object?

[jchojnac]

Homework Statement

It is sometimes claimed that friction forces always slow an object down, but this is not true. If you place a box of mass M on a moving horizontal conveyor belt, the friction force of the belt acting on the bottom of the box speeds up the box. At first there is some slipping, until the speed of the box catches up to the speed v of the belt. The coefficient of friction between box and belt is . Do not worry about italics. For example, if a variable g is used in the question, just type g and for use mu.

(a) What is the distance d (relative to the floor) that the box moves before reaching the final speed v? (Use energy arguments to find this answer.)

(b) How much time does it take for the box to reach its final speed?

Homework Equations

W=-Fd/2
K=1/2mv^2
f=mu*N

The Attempt at a Solution

Can't figure it out.

 

[tiny-tim]

Welcome to PF!

Hi jchojnac! Welcome to PF!

(have a mu: µ )

If you place a box of mass M on a moving horizontal conveyor belt, the friction force of the belt acting on the bottom of the box speeds up the box. At first there is some slipping, until the speed of the box catches up to the speed v of the belt. The coefficient of friction between box and belt is … mu.

(a) What is the distance d (relative to the floor) that the box moves before reaching the final speed v? (Use energy arguments to find this answer.)

Hint: for (a), use the work-energy theorem:

work done by friction = energy gained