# Compressed Springs and Conservation of Momentum

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"A spring of negligible mass is compressed between two masses on a frictionless table with upward sloping ramps at each end. The masses are released simultaneously. The mass of M1 is less than the mass of M2.

A) Is the force exerted by the spring on M1 greater than, equal to, or less than the force it exerts on M2?

B) Is the final height up the ramp reached by M1 greater than, equal to, or less than the height reached by M2?

C) Is the speed of M2 greater than, equal to, or less than the speed of M1 once they both lose contact with the spring?

D) Is the momentum of M2 greater than, equal to, or less than the momentum of M1 once they both lose contact with the spring?

E) Is the kinetic energy of M1 greater than, equal to, or less than the kinetic energy of M2 once they both lose contact with the spring?

F) Is the duration of the force exerted by the spring on M1 greater than, equal to, or less than the time the force acts on M2?"

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The solution gives all steps along with proper explanations so that you can solve similar problems yourself. The compressed spring and conservation of momentum is analyzed.

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a)The force exerted by the spring is given by, F = k dx

where k is the spring constant and dx is the distance through which the spring moves from the equilibrium position.

The spring generates a force of this magnitude at each end of the spring, so if we take a spring of equilibrium length x,the force acting on each mass is +kdx and -kdx (so that there is no net force and the system is in equilibrium)

b)The energy stored in the compressed spring is ...

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