# How do I find the angle given the mass, the acceleration and the force acted on a body?

## My Issue

I have the mass, the horizontal acceleration and a force that acts on a body. The force forms an angle $\alpha$ of unknown degrees with the x-axis. I would like to know how I can find the angle $\alpha$ formed by the force and in which way the angle is connected with the horizontal acceleration.

## What I tried

This formula calculates the horizontal acceleration given the force $F$, the mass $m$ and angle formed by the force $\alpha$:

$$a_x = \frac{F}{m} \cos(\alpha)$$

By inverting it, I can easily calculate the cosine of the angle $\alpha$:

$$cos(\alpha) = a_x\frac{m}{F}$$

However, I'm not sure about how can I revert the cosine of the angle to find its degrees.

## Questions

What am I missing? In which way is the angle $\alpha$ connected with the horizontal acceleration?

• The reverse operation of $\cos$ is $\arccos$. Apply that to both sides and you get $\alpha$. Commented Mar 5, 2015 at 15:57
• This question is confusing. If the force acts completely in the x direction it makes no sense to talk about an angle other than 0
– Sean
Commented Mar 5, 2015 at 16:27
• European and American punctuation on units. Commented Mar 5, 2015 at 16:29
• The question is not properly stated. Is the TOTAL force 10N? Commented Mar 5, 2015 at 16:31
• Yes, it is. Sorry for that. Commented Mar 5, 2015 at 16:45

Assuming the total force is $10~\text{N}$, the $7~\text{kg}$ mass is accelerated by $1.0~\text{m/s^2}$, so it is experiencing $7~\text{N}$ force in x-direction. Therefore, $F_x = .7F$. The angle is roughly $45^\circ$.