Finding acceleration of pushed crate

[missashley]

Homework Statement

A 900 N crate is being pushed across a level floor by a force of 313 N at an angle of 25 degree above the horizontal. The coefficient of kinetic friction between the crate and the floor is 0.17. Acceleration of gravity is 9.81 m/s^2

http://img233.imageshack.us/img233/3717/31nk3.jpg

What is the acceleration of the box in m/s^2?

Homework Equations

F = ma

The Attempt at a Solution

Fg = 900 N
mass of crate = 91.743 kg
U = 0.17
g = 9.81 m/s^2
theta = 25
Fn = 900 + 132.2795
Ff = 0.17 * Fn = 175.4875

313cos 25 = 283.674 N
313sin 25 = 132.2795 N

Fx = ma
283.67 = 987.743a
a = 3.201 m/s^2

I didn't know whether or not to incorporate the y direction forces

 

[Doc Al]

Looks like you forgot to include friction.

 

[Gannon]

Is the box moving up or down? What would this infer about acceleration?

 

[missashley]

Is the box moving up or down? What would this infer about acceleration?

The box is moving left not up or down. Since the force is applied at an angle, the acceleration is not as great if applied directly horizontal

 

[missashley]

Looks like you forgot to include friction.

F = UFN
Friction = 0.17* (900 + 132.2795)
Friction = 175.4875 N

 

[Doc Al]

F = UFN
Friction = 0.17* (900 + 132.2795)
Friction = 175.4875 N

Good. Now recalculate the total force in the x-direction. (Which way does friction act?)

 

[missashley]

Good. Now recalculate the total force in the x-direction. (Which way does friction act?)

Friction act against the block, therefore, total force in x direction:

283.67 - 175.4875 = ma
111.1825 = 91.7431a
111.1825 / 91.7431 = a
a = 1.211889 m/s^2

did I do that right?

 

[Doc Al]

Looks good. (Round off your answer to a reasonable number of significant figures.)

 

[missashley]

I plugged it into the site where we're suppose to turn in our answers and it says it wrong. Hmmm

 

[Doc Al]

arithmetic error!

283.67 - 175.4875 = ma
111.1825 = 91.7431a

Oops... double check that subtration. (Sorry for not catching that earlier.)

 

[missashley]

yay it worked thanks so much! The answer is 1.179 m/s^2