What is the acceleration of a block on a frictionless surface?

[dirtybirdhouse183]

Homework Statement

A block is on a frictionless horizontal surface. A force of 20 N is applied to the block at an angle of 30 degrees to the horizontal. If the mass of the block is 5 kg, what is the acceleration of the block?

The choices for acceleration are: a) 5.3 b) 6.2 c) 7.5 d) 4.7 e)3.2

Homework Equations

Do I need to compute the vertical forces acting on the block?

The Attempt at a Solution

So I am guessing that the horizontal component of the force is the force that causes the block to accelerate, or move. So then the horizontal force would be 20cos30 which is 17N. Then I divided that by the mass to get the acceleration but it's wrong.

 

[lizzyb]

I did what you did:
$$F_x = \cos 30 \cdot 20 = m a_x$$
$$F_y = \sin 30 \cdot 20 - n = 0$$
so $$a_x = \frac {\cos 30 \cdot 20}{5} = .62$$

 

[Doc Al]

So I am guessing that the horizontal component of the force is the force that causes the block to accelerate, or move. So then the horizontal force would be 20cos30 which is 17N. Then I divided that by the mass to get the acceleration but it's wrong.

Your method is correct; the answer is not among those given (although one of them is pretty close).

so $$a_x = \frac {\cos 30 \cdot 20}{5} = .62$$

Check your arithmetic.

 

[dirtybirdhouse183]

I tried

Yes, my acceleration was 3.46, but there acceleration is 3.2. Hopefully, the answer choices aren't incorrect lol. Thanks for the replies though, I really apperciate them.