Calculating Trebuchet Velocity: A Homework Help Guide

[steve092]

Trebuchet help: Calculating velocity

Homework Statement

I'm new to this site, so bear with me!
OK, so I'm doing a trebuchet for my physics project. I have done three trials with counterweights of different masses. I have all of the distances that a golf ball of mass=0.045kg has traveled. I also have the masses of the counterweights.
Just as a starting point for the first trial:
mass of the counterweight=10.937
h=0.631m

The average distance for this trial was 34.33m.

Homework Equations

PE_g=mgh
KE=(1/2)mv²

The Attempt at a Solution

I've done the calculations; however, my answers were nowhere near what the velocity should be. For one trial, the mass of the counterweight was 10.937kg. I did the calculations and the velocity came out to be 3.53m/s which seemed a little slow.

Obviously, I'm doing something wrong. I wonder if it is because the mass of the golf ball needs to be taken into account somehow? Anyways, thanks in advance!

I've used the example from https://www.physicsforums.com/showthread.php?t=250335&highlight=trebuchet and I still can't get it. I don't even understand how the answer was calculated in that example.

 

[steve092]

Well, I think I might have it! I used that example in the post I linked to in the previous post, and I just changed the values to fit my case. I did the other example to get the right answer that was provided. So, I'm assuming that my answer is correct

Here are the givens:
m₁=10.937
m₂=.045
h₁=.076
h₂=.838

I used:
m₁gh₁-m₂gh₂=(1/2)m₁v₁²+(1/2)m₂v₂²

And I used the proportion:
v₁ .076
-- = --
v₂ .838

And just solved for v₂.

My final answer was 10.742 m/s which sounds correct, but I'd like to see if I made any mistakes.

 

[steve092]

That proportion I used, v₁/v₂= 0.076/0.838, what exactly is that?

 

[steve092]

OK, I think that solved for velocity correctly. Using the calculated velocity and the average distance traveled of the golf balls in a trial, I calculated a time of about 3.3 seconds. When I launched golf balls and manually timed it, the results were close enough.