static friction

[tony873004]

To move a large crate across a rough floor, you push down on it at an angle of 21 degrees. Find the force necessary to start the crate moving, given that the mass of the crate is 32 kg and the coefficient of static friction between the crate and the floor is 0.57.

The back of the book gives 250 N as the answer, but that's not what I get.

maximum force of static friction = coefficient of static friction * force normal.
force = ma
force normal = -ma

force = 32 * -9.81 = -313.92
force normal = 313.92
maximum force of static friction = 0.57 * 313.92 = 178.9344

Taking this to be the force in the x direction to get the crate to start moving, F = 178.9344 /cos(21) = 191.6647

191.6647 does not equal 250. What did I do wrong :confused:

[Leong]

to get the normal force, you have to take the y component of the applied force into account.