Calculate the Force of a Certain Push

[Darkstr958]

Homework Statement

A person exerts a force 25 degrees to the horizontal on a 5kg book resting against a vertical wall. If the coefficient of static friction is .76, what is the minimum force that the person must exert to keep the book from sliding down the wall.

Homework Equations

force of friction= coeffecient of static friction * normal force
fg=mg

The Attempt at a Solution

I know the net force must be zero for the book to be at rest, so all the forces have to cancel each other out. Also, the force of gravity is 49N. I also know you need to resolve the force of the push into its x and y components since its at a 25 degree angle. normal force should be opposite the force of the push along the x-axis, and the force of gravity should be opposite the force of friction plus the force of the push in the y direction, but I don't seem to have enough information to find out many of these values.

 

[tiny-tim]

Welcome to PF!

Hi Darkstr958! Welcome to PF!

(have a mu: µ and a degree: º )

I know the net force must be zero for the book to be at rest, so all the forces have to cancel each other out … but I don't seem to have enough information to find out many of these values.

Call the force F.

You have two equations, one with F cos25º, and one with F sin25º. You also have friction = µ_sN, so you have two unknowns (F and N) and two equations.