You decide to launch a rockof mass m1 using a tube containing a spring of spring constant k. When the spring is at equilibrium, it fills the entire tube. To launch a rock, you push it into the tube, compressing the spring a distance d, at which point a locking mechanism holds the spring(and the rock) in place. When the lockis released, the spring pushes the rock to the end of the tube where it will be launched into the air. The coefficient of kinetic friction between the rock and the inside surface of the tube is given by μk. You setup the launcher at an angle q above the horizontal with the spring end buried such that when the spring is compressed and locked, the rock is at ground level. a)Find the work done on the rock by non-conservative forces as it moves from the point of release to the end of the tube. Express your answer in terms of μk, m1, q, d, and any necessaryconstants. b) Find the velocity of the rockvfas it exits the launch tube in terms of μk, k, m1, q, d, and any necessaryconstants. c) Unfortunately, just outside the end of the launch tube, there’s another rock m2 that is partially obstructing the hole. The launched rock collides with the blocking rock. After the collision, the launched rock moves horizontally and the blocking rock goes straight up. Find the magnitude of the velocity of the blocking rock in terms of m1, m2, vf, q, and any necessary constants.
You decide to launch a rockof mass m1 using a tube containing a spring of spring constant k. When the spring is at equilibrium, it fills the entire tube. To launch a rock, you push it into the tube, compressing the spring a distance d, at which point a locking mechanism holds the spring(and the rock) in place. When the lockis released, the spring pushes the rock to the end of the tube where it will be launched into the air. The coefficient of kinetic friction between the rock and the inside surface of the tube is given by μk. You setup the launcher at an angle q above the horizontal with the spring end buried such that when the spring is compressed and locked, the rock is at ground level.
a)Find the work done on the rock by non-conservative forces as it moves from the point of release to the end of the tube. Express your answer in terms of μk, m1, q, d, and any necessaryconstants.
b) Find the velocity of the rockvfas it exits the launch tube in terms of μk, k, m1, q, d, and any necessaryconstants.
c) Unfortunately, just outside the end of the launch tube, there’s another rock m2 that is partially obstructing the hole. The launched rock collides with the blocking rock. After the collision, the launched rock moves horizontally and the blocking rock goes straight up. Find the magnitude of the velocity of the blocking rock in terms of m1, m2, vf, q, and any necessary constants.
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