# Homework Help: Question w/ work and friction

1. Jan 7, 2004

Sally applies a horizontal force of 520 N with a rope to drag wooden crate across a floor with a constant speed. The rope tied to the crate is pulled at an angle of 84.5°

How much force is exerted by the rope on the crate and what work is done by the floor through force of friction between the floor and the crate?

how can i find the force on rope and force of friction w/o knowing the distance?

2. Jan 7, 2004

### HallsofIvy

Draw the force diagram. The force along the rope, horizontally, and vertically form a right triangle with angle 84.5°.

Since you are told that the horizontal force is 520 N, and "horizontal over hypotenuse" is cosine, we have 520/F= cos(84.5°) or F= 520/cos(84.5) where F is the force in the direction of the rope (hypotenuse). That is the force the rope applies to the crate and therefore, the force the crate applies to the rope (in the opposite direction).

If there were a net horizontal force on the crate, the crate would accelerate. Since it is moving at constant speed, the friction force must be exactly the same as the horizontal force, 520 N, but in the opposite direction.