# Calculate acceleration of object with applied force and friction

1. Jun 13, 2009

1. The problem statement, all variables and given/known data

A worker drags a crate across a factoryt floor by pulling on a rope tied to the crate. The worker exerts a force of 450 N on the rope, which is inclined 38 degrees to the horizontal, and the floor exerts a horizontal frictional force on 125 N that opposes the motion. You can assume the crate doesn't leave the ground.

Calculate the acceleration of the crate (mass = 310 kg).

2. Relevant equations

F = ma

3. The attempt at a solution

Broke the force of the pull into x and y components:

Fx = 450 cos 38 = 354 N
Fy = 450 sin 38 = 227 N

Then the friction opposes motion, so subtract that from the x component

Fx = 354 - 125 = 229 N

so the net force is $$\sqrt{229^2 + 227^2}$$ = 322 N

then, $$a = \frac{F}{m} = \frac{322}{310} = 1.0 ms^{-2}$$ to 2 s.f.

However the answer given is 0.74 ms

2. Jun 13, 2009

### Cyosis

You're doing well until

The crate does not leave the ground so the only acceleration will be in the x-direction.

3. Jun 13, 2009

$$a = \frac{F_x}{m} = \frac{229}{310} = 0.74$$