# Homework Help: Calculating velocity in a slingshot

1. Apr 25, 2010

### skorned

1. The problem statement, all variables and given/known data
I launched a projectile from a slingshot to different distances by pulling the band back different distances. The projectile was launched horizontally, and the slingshot was a fixed height, 48 cm, above ground.
Known Data for the first run:
Height: 48 cm
Distance the band was pulled back: 4 cm
Force on the band at this stretched point: 1 N
Average distance the projectile traveled after launch: 17 cm
Mass of projectile: 100 gm

Now I need to know how to find the initial velocity of the projectile when it leaves the slingshot, so I can theoretically determine how far the projectile ought to have gone.

2. Relevant equations

s = ut + 1/2 at2
Potential Energy of Spring = 1/2 kx2

3. The attempt at a solution

Using the force and the extension, I determined k from Hooke's law. Then, using k and extension, I found the potential energy in the spring. Assuming all this energy got converted to kinetic energy, I equated this potential energy to 1/2 mv2. Using the known mass of the projectile, I was able to calculate the velocity of the projectile at launch.

However, using the height, gravitational acceleration, and the knowledge that the initial vertical velocity was 0, I was able to calculate the time the projectile was in motion for. Then, using the initial velocity of the projectile derived earlier, and the time, I calculated the horizontal distance it should have covered ignoring air resistance. However, the values didn't work out right.

Can you tell me where I'm going wrong, or suggest your own method for calculating the velocity of a projectile after it is launched from a slingshot.

2. Apr 25, 2010

### kuruman

If I were to do this, I would trust the projectile motion calculation for finding the initial horizontal velocity. I would also trust conservation of mechanical energy, i.e. that the potential energy stored in the rubber band is converted to kinetic energy of the projectile. I would not trust the validity of Hooke's Law which rubber bands do not generally obey. They also show "hysteresis", i.e. the force they exert depends on what was previously done to them and for how long. In short, I would not assume that the potential energy in the "spring" is (1/2) kx2.

There is a simple test. Hang different masses from your rubber band and measure how much it stretches for each mass. Plot mg vs. x and see if you get a straight line. If you do, Hook's Law is valid and the slope is the spring constant. Repeat your measurements a few times and see how reproducible the results are.

3. Apr 25, 2010

### skorned

Holy ****, as I begin writing this post, theres this strong feeling of deja vu hitting me.

Anyhow, yes, I am aware of the problems of inelasticity. However, it doesn't matter, since the elasticity was calculated after each experiment, and that was the value used. The consistency of the elasticity didn't matter so much. The spring constant did reduce a lot during the course of the experiment, indicating a decrease in elasticity, but that didn't affect my calculations in any way.

I have got my calculations in place now, I think it was just a calculation error due to SI units not being used. Its fixed now. Thanks for your suggestion though, kuruman.