Physics Slingshot Help?

Question

My friend and I are going to do a physics project. We are making a big sling shot and using math to find out where it hits the ground. We have a scale in which will convert to how much force this sling shot will shoot with, but we dont know how to figure out the distance and all. How do you go about doing this?

Answer 1

If you know the force the slingshot puts on the projectile, the you can fgure out the speed of the projectile.

Assume the sling behaves like a stretched spring and obeys Hooke's law. Then the energy stored in the spring when you stretch it a distance s, is

PE = 1/2 ks^2

But you need to know k. YOu can get this from measuring the force needed to stretch the sling a distance s and using Hooke's law:

F = ks ----> k = F/s

So the energy in the sling is:

PE = 1/2 Fs and you can measure both F and s.

Now the projectile leave the sling at a speed v. This can be found from:

PE = KE = 1/2Fs = 1/2mv^2 ---> v = sqrt(Fs/m)

Again, you can measure the mass of the projectile so the speed it leave the sling can be calculated.

Assume your sling is at a height h above the ground and points at an angle q with respect to the ground. You can measure both of these quantities. The projectile will have some of the initial speed in the horizontal (x) direction and in the vertical (y) direction. These initial speeds are given by:

v0x = v*cos(q)

v0y = v*sin(q)

The time of flight of the projectile is set by how high it rises. You can compute that:

hmax = 1/2 v0y^2/g +h

The time it takes the projectile to get to hmax is equal to the time it takes to fall to h (remember it starts above ground).

hmax =1/2(-g)t^2 - h --> t = sqrt(2[hmax-h]/g)

But it still has to fall a distance h. The time required t1 is:

0= 1/2(-g)t1^2 -v0yt1 + h

This is a quadratic that you'll have to solve once you plug in your values. The total time of flight is:

T = t + t1

Now the projectile is in uniform motion in x. Therefore it travels:

xmax = v0x*T

That should do it. Just be careful to control all the variables when you do the experiment (hiehgt and angle of launch, stretch and force on sling).

Answer 2

Link below has all the formulas. If you haven't studied algebra yet, you'll need an older student or adult to explain it to you.

Keep in mind that a big rubber strap will not act like a spring. You don't get as much energy out as what you put in. To keep the math simple, it is better to use a long coil spring.