Study of the spring lunching system of pinball

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SUMMARY

The discussion focuses on the mechanics of a pinball system where a 0.1 kg ball is launched by a spring with a spring constant of 40 N/m. The ball travels through a straight track of 60m and then follows a curved arc with a radius of 20m, inclined at 10 degrees to the horizontal. Key calculations involve determining the position and velocity of the ball when it loses contact with the spring and using the mechanical energy theorem to express the stopping position of the ball in relation to the spring's compression length.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with spring mechanics and Hooke's Law
  • Knowledge of mechanical energy conservation principles
  • Basic skills in plotting mathematical functions
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  • Calculate the potential and kinetic energy transformations in spring systems
  • Learn about projectile motion and its applications in curved paths
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Physics students, mechanical engineers, and hobbyists interested in the mechanics of pinball machines and spring dynamics.

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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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