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Ball Launched from spring gun (max height)

by jti3066
Tags: ball, height, launched, spring
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jti3066
#1
Apr24-10, 05:54 PM
P: 46
1. The problem statement, all variables and given/known data

A ball of mass m is launched at an angle theta from a spring gun of length D. The lower end of the gun, where the spring is attatched, is at ground level. The spring has spring constant k and an unstretched length D. Before launch, the spring is compressed to a length d.

Determine the maximum height h above the ground the ball reaches.

2. Relevant equations

(k(x^2)/2)=mgh

?? x = mgcos(theta)

3. The attempt at a solution

Plugging in "x" I get: h=(k(mgcos(theta))^2)/2mg

Is this correct? If not please explain in detail and provide the steps and solution. TIA.
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Doc Al
#2
Apr24-10, 06:08 PM
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Quote Quote by jti3066 View Post
(k(x^2)/2)=mgh
Here x is a velocity. You can use conservation of energy to find the additional height reached after the ball leaves the gun, if x is the vertical component of the speed at that point. Note that h will not be the height above the ground.

?? x = mgcos(theta)
You can't set a velocity (x) equal to a force.

3. The attempt at a solution

Plugging in "x" I get: h=(k(mgcos(theta))^2)/2mg

Is this correct?
No. Note that you haven't even used the spring constant or the amount the spring was compressed.

Try to solve it in two steps: Find the speed of the ball as it leaves the gun. Then find the height that it reaches after it becomes a projectile.
jti3066
#3
Apr24-10, 06:38 PM
P: 46
Well then I guess I have no idea what i'm doing then...A little more help please

K_i + U_i + S_i = K_f + U_f + S_f

K = .5mv^2

U = mgh

S = .5kx^2

What is the muzzle velocity?

How to find the height that it reaches?

Doc Al
#4
Apr25-10, 09:36 AM
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Ball Launched from spring gun (max height)

Quote Quote by jti3066 View Post

K_i + U_i + S_i = K_f + U_f + S_f

K = .5mv^2

U = mgh

S = .5kx^2

What is the muzzle velocity?
To find the muzzle velocity, use conservation of energy as you outlined above. Hint: What's the change in height of the ball as it travels through the gun?

How to find the height that it reaches?
Once the ball leaves the gun it's a projectile. Solve that part like any other projectile motion problem.
jti3066
#5
Apr25-10, 02:42 PM
P: 46
Could someone please solve the problem for me.....BTW this is NOT a homework problem....It is a final test review problem....I learn differently than most.....By looking at the steps involved in solving the problem along with the answer I can use deductive reasoning as to why those methods were used....TIA


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