Study of the spring lunching system of pinball

AI Thread Summary
The discussion focuses on the mechanics of a pinball launched by a spring, analyzing its motion along a straight track and a curved arc. Key questions include determining the ball's position and velocity when it loses contact with the spring, and using the mechanical energy theorem to express the stopping position in relation to the spring's compression. The spring constant is specified as 40 N/m, and the initial compression length is a critical factor in calculating the ball's trajectory. The participants are also interested in plotting a function to find the minimum compression needed for the ball to reach the end of the half-circle arc. The conversation emphasizes the application of physics principles to solve these problems.
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A ball of the pinball of mass 0.1kg assimilated to a point M is launched by a spring and move up without friction in a track straight 60m (the sprin is in the track) then move curvely to an arc of a half circle with radius 20m at the topof the track.
The plan contain the track and the arc is made a angle of 10 degree to the horizontal.
the initial length of the spring is 12cm. the end of the spring is fixed to the initial position of the track and the ball is put on the other end of the spring. It compressed until its length become x. It launched with initial velocity 0m/s. the spring constant is 40N/m
1) what is position of the ball during lunching lost contact with the spring? and it velocity.
2) using the mecanical energy theorem, express the position of the ball stop in the track in function of x.
3) plot the curve of X = f(x) how much the compess length minimum need so that the ball leach the end of the half circle arc of the track?
 
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1) i know that the legth compressed is L-(L-x), thus the length extend will be the same so if there is no frictional force inside the then i know that the ball lost contact with the spring is L+(L-x)...but how to prove??
 

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