# Calculating Net Force with Free Body Diagram

Question: Three forces are acting on a 4-kg block. The acceleration of the block is 5.0 $m/s^2$. Find the magnitude of the unknown force $F$.

The diagram I have shows the force F point left, a force of 4N point right and a force of 8N pointing straight up.

I found that Fnet would be 20 (F = ma – 5*4 = 20). Which leads me to my question... How do I calculate the Fnet from a free body diagram? I've done it where you are only dealing with one axis (x or y), but here it only gives me three forces, and i'm not sure how to find the unknown. Thanks for your help guys but I found the answer (22.3).

• Show the diagram. – DanielSank Feb 4 '15 at 4:02
• @DanielSank Heres a photo i.imgur.com/8RdUQcf.png – Smith Feb 4 '15 at 13:01
• Which direction is the acceleration along? – John Alexiou Feb 5 '15 at 13:40
• @ja72 That is not given. This is what made it a little confusing. – Smith Feb 5 '15 at 16:00

## 2 Answers

Here is what you need to know to solve all problems like this with point bodies.

For static bodies:

• Sum of force vector components is zero $$\sum{\vec{F}_i} = 0$$

For moving bodies:

• Sum of force vector components equals mass times acceleration of center of mass $$\sum{\vec{F}_i} = m \, \vec{a}_{cm}$$

If one of the force is unknown, but its direction is known then you must know the acceleration in that direction in order to solve the above for the force component.

Sometimes the above is treated as a static problem with $$\sum{\vec{F}_i} - m \, \vec{a}_{cm} =0$$ by including the inertial force in an opposite sense as a force in the free body diagram. So for acceleration along the +x axis, and force of $m a_x$ is applied along the -x axis.

Force and acceleration are vectors. Thus, $\overline F_1+\overline F_2+\overline F_3=m \overline{a}$ is a vector equation. Writing down this equation in components will give you the answer. In other words, you have to project above equation on x and y axes.

• So for the x it is something like F-4 and the y is just 8. From these two then how do I get to Fnet of 20? – Smith Feb 4 '15 at 13:05