# How to get height from potential energy? [closed]

I am making a spring launcher for an RC car. but i am trying to understand elastic potential energy of a spring and hooks law. this is what i have.

The car will weigh 200 grams. The spring has a spring constant $k$ of 8.81 N/mm = 8810 N/m compressed by 36.2 mm = 0.0361 m

So using Hooke's Law for Potential Energy I got:

E $=\frac{1}{2}kx^2 = 0.5*8810*0.0361 = 159.0205$J

So how do I get height from that? I found one formula $z(height) = \frac{E}{mg}$ but to get g, $g = \frac{E}{mz}$I now need the height. So now I'm confused on what to do.

I'm hoping to at less achieve 60 cm or more. What else do I need to consider to achieve this? Thank you for your time.

• Assuming this is on Earth, $g$ is about 9.8 $m/s^2$. Things to consider: how lossy is the system? How much margin do you want to design in? – JEB Nov 24 '17 at 3:12
• Welcome to Physics! Please note that homework-like questions and check-my-work questions are generally considered off-topic here. We intend our questions to be potentially useful to a broader set of users than just the one asking, and prefer conceptual questions over those just asking for a specific computation. – ACuriousMind Nov 24 '17 at 11:35

Yes, this equation is what you need! $$U=mgh$$ Where U is potential energy, m is mass in kilograms, g is the acceleration due to gravity $g=(9.81m/s^2)$, and h is height is meters. Your equation $h=E/mg$ is simply this formula rearranged to solve for height. All you need to do is plug in your values and solve for height. I tried this and it seems that you need to look again at Hooke's Law and find what you forgot. As for the construction, it looks like you will achieve your desired height and them some. If you want more height, compress the spring further, get a stronger spring, or both. I hope this was helpful!
What you missed here is the value of g=9.8 m/s2. But to get your values precisely, you should also consider friction in all practical jobs. You will loose energy because of some friction. If your surface is smooth enough you will get approximate value. Loss due to friction can be calculated as, Uf = $\mu Nd$. where $\mu$ = coefficient of friction, N=normal force, d=distance moved on the surface.