# Work and kinetic friction problem

1. Oct 29, 2004

### kmotoao

i have two questions that needs help on. thx in advance

1. You pull a box across the floor with a force of 425 N. The coefficient of kinetic friction is 0.305. The mass of the crate is 125 kg. Angle q = 35.0°. Find: (a) the acceleration of the box and (b) the amount of work done in moving the crate a distance of 3.50 m.

2. A 2.5 kg box slides across the flat surface of a table. The coefficient of kinetic friction for the table/box is 0.295. The box is attached to a light string that passes over a low friction pulley and is connected to a 3.0 kg mass that is hanging vertically. (a) find the acceleration of the system (b) find the velocity of the 2.5 kg box after it has been dragged 0.25 m if its initial velocity was 0.25 m/s, and (c) find the kinetic energy of the box at this point.

2. Oct 29, 2004

### ek

It's late, and I'm going to bed, but I did the first one. The most important thing is to realize that the Fn in Ff = uFn is not just mg but mg-Fsinx, because there is a component of that force pulling in the y direction, effectively lessening the normal force that friction acts on. So:

Ff = uFn

where Fn = mg - Fsinx

Ff = u(mg-Fsinx)

and

F' = Fcosx - Ff

then

F' = Fcosx - u(mg-Fsinx)

and

a = Fcosx - u(mg-Fsinx)/m

And for the work it's just Fcosx*d.