- #1
PascalPanther
- 23
- 0
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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