- #1
Loupster
- 3
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1. A 2 kg mass slides along a horizontal surface with coefficient of friction U(K) = 0.30. The mass has a speed of 1.3 m/s when it strikes the horizontal spring with constant k=120 N/m. (a) By what distance does it compress the spring(take friction into account). The spring will recoil and push the mass back, losing contact with the mass at its natural length. (b) What is the speed of the mass when it loses contact from the spring? (c) how far will it travel?
2. Relevant Equations:
F(spring) = -kx
F(k) = U(k)mg
Kinetic Energy = (1/2) mv^2
Potential Energy = (1/2)kx^2
3. So far, I have come up with the equation that
F(net) = F(mass) - ((kx) + (U(K)mg))
However, I could not figure out how to get the force of the mass since I was only given the velocity, and not the acceleration of the mass. I also thought that once the spring is at the most compressed spot, it will have all potential energy, and no kinetic energy. This is how I would solve question (b) if there were no friction. Since there is friction, this is not a conservative force, so I cannot use the K + U = constant equation. I have no idea where to go with this problem :-/
2. Relevant Equations:
F(spring) = -kx
F(k) = U(k)mg
Kinetic Energy = (1/2) mv^2
Potential Energy = (1/2)kx^2
3. So far, I have come up with the equation that
F(net) = F(mass) - ((kx) + (U(K)mg))
However, I could not figure out how to get the force of the mass since I was only given the velocity, and not the acceleration of the mass. I also thought that once the spring is at the most compressed spot, it will have all potential energy, and no kinetic energy. This is how I would solve question (b) if there were no friction. Since there is friction, this is not a conservative force, so I cannot use the K + U = constant equation. I have no idea where to go with this problem :-/