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The situation is as follows:

http://img2.freeimagehosting.net/uploads/a87ac3e9ef.jpg [Broken]

http://img2.freeimagehosting.net/uploads/a87ac3e9ef.jpg [Broken]

There is friction, but no friction while in the barrel of the spring gun.

I am suppose to derive an equation to solve for L, using x(c), m, g, theta, mu, and k.

What I did so far:

I did a FBD, I see the following forces:

1. Force of the spring from the spring gun, 2. force of the weight parallel to the plane, 3. force of kinetic friction

U(spring) = 1/2 k*x(c)^2

F(weight) = m*g*sin(theta)

F(friction) = kinetic friction constant* normal force

= mu(k) * m*g*cos(theta)

W=F*s = 1/2 * m*v^2 - 0

F(net) = U - F(w) - F(f)

s = F/W

= [U - F(w) - F(f)] / [(1/2) * m * v^2]

= [(1/2)k*x(c)^2 - (mgsin(theta)) - mu*mgcos(theta))]/ [(1/2)/m*v^2]

Since I can't use v in the equation;

U(spring) = KE = (1/2)k*x^2 = (1/2)m*v^2

v = Sqrt((k*x^2)/m)

L = s

L = [(1/2)k*x(c)^2 - (mgsin(theta)) - mu*mgcos(theta))]/ [(1/2)/m*((k*x^2)/m)]

What did I do wrong here? I think it's more than one thing wrong.

http://img2.freeimagehosting.net/uploads/a87ac3e9ef.jpg [Broken]

http://img2.freeimagehosting.net/uploads/a87ac3e9ef.jpg [Broken]

There is friction, but no friction while in the barrel of the spring gun.

I am suppose to derive an equation to solve for L, using x(c), m, g, theta, mu, and k.

What I did so far:

I did a FBD, I see the following forces:

1. Force of the spring from the spring gun, 2. force of the weight parallel to the plane, 3. force of kinetic friction

U(spring) = 1/2 k*x(c)^2

F(weight) = m*g*sin(theta)

F(friction) = kinetic friction constant* normal force

= mu(k) * m*g*cos(theta)

W=F*s = 1/2 * m*v^2 - 0

F(net) = U - F(w) - F(f)

s = F/W

= [U - F(w) - F(f)] / [(1/2) * m * v^2]

= [(1/2)k*x(c)^2 - (mgsin(theta)) - mu*mgcos(theta))]/ [(1/2)/m*v^2]

Since I can't use v in the equation;

U(spring) = KE = (1/2)k*x^2 = (1/2)m*v^2

v = Sqrt((k*x^2)/m)

L = s

L = [(1/2)k*x(c)^2 - (mgsin(theta)) - mu*mgcos(theta))]/ [(1/2)/m*((k*x^2)/m)]

What did I do wrong here? I think it's more than one thing wrong.

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