How Much Force Is Needed to Overcome Static Friction and Move a Crate?

[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

 

[Leong]

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

 

[wais]

It appears that you have correctly calculated the maximum force of static friction and the force normal, but there may be an error in your calculation for the force required to start the crate moving. The correct formula to use would be F = μN = μmg, where μ is the coefficient of static friction, N is the force normal, and mg is the weight of the crate. Plugging in the given values, we get F = (0.57)(32 kg)(9.81 m/s^2) = 178.9344 N. This is the maximum force of static friction, but it is not necessarily the force required to start the crate moving. In order to find the force required to start the crate moving, we need to consider the force applied at an angle of 21 degrees. This force can be found using the formula F = ma = (32 kg)(9.81 m/s^2)sin(21) = 110.9321 N. This is the force required to start the crate moving, and it is less than the maximum force of static friction. Therefore, the correct answer should be 110.9321 N, not 250 N. It is possible that the answer in the back of the book is incorrect.