# Homework Help: Spring-based Slingshot energy transfer

1. May 19, 2008

### MendicantBias

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

I am working on an AP physics project, and the assignment is to launch a golf ball accurately at close (10 - 15m) and long (50-60m) range. My group and I have decided on a spring based slingshot that will consist of a T shaped launcher with two springs (one on each side of the T) connected to a pouch. My question is about how to experimentally obtain a value e (efficiency).

2. Relevant equations

I know that Fs = -kx, so for two springs: Fs = -2kx

Integrate this to get the stored energy: Us = kx^2

I have researched some and found that an e is added to account for the efficiency at transferring this stored energy into kinetic energy, so: Us = ekx^2

And Kinetic energy: K = (1/2)mv^2

3. The attempt at a solution

Set k = Us
(1/2)mv^2 = ekx^2
mv^2 = 2ekx^2
v^2 = (2ekx^2)/m

v = ((2ekx^2)/m)^(1/2) meters per second

rearrange this to solve for e:

ekx^2 = (1/2)mv^2

e = (mv^2)/(2kx^2)

e is then the ratio of the actual kinetic energy of the golf ball to the stored energy in the spring for a given draw-length x.

My question is not so much about the math as it is how to find e accurately. I'm not sure what sensors can measure velocities upwards of 20m/s. Can e be accurately determined from one or two measurements at a low velocity?

Your input is greatly appreciated.

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