# Work and Energy Problem

1. Jan 22, 2008

### rabar789

This is an annoying problem for which I have a close answer to, not sure where I went wrong.

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

Cannonball Man (mass = 75kg) is stuff into his circus cannon, compressing a giant spring by 1.5 meters. He is launched vertically upward at 5 m/s reaching a maximum height above the circus floor of 10 meters. What is the spring constant of the spring?

2. Relevant equations

Conservation of Energy "Master Equation," as I like to call it:
(1/2mv^2 + mgh + 1/2kx^2)initial = (1/2mv^2 + mgh + 1/2kx^2)final
Where k = the spring constant
x = compression/extention of spring
h = the change in height

3. The attempt at a solution

I think I went wrong with the final and initial velocities, but I'm not sure specifically where my error was. First I cancelled stuff:

(0 + mgh + 0)initial = (1/2mv^2 + 0 + 1/2kx^2)final

Then I plugged in my variables

(75)(9.8)(10) = (0.5)(75)(5^2) + (0.5)k(1.5^2)

And solved for k: 5700 N/m

All I know for sure is that I'm relatively close to what my answer should be; I recieved 17/20 for my entire submission (this was an old written assignment; I have no way of checking for the actual complete answer).

Can someone help me out please?

2. Jan 22, 2008

### Staff: Mentor

I guess I don't understand the problem setup. Is the speed of man 5 m/s immediately after leaving the spring? (Or after leaving the barrel?) If so, how does it rise 10 m? What's the height of the cannon?

Is this the exact statement of the problem?

3. Jan 22, 2008

### rabar789

This is the exact statement. This was the problem, no one in the class knew whether or not the 5 m/s occurred immediately and where. And yes, 10 meters does sound a bit short; unless it's one of those goofy circus cannons that just shoot the guy out a little bit...