A spring of negligible mass is compressed between two masses on a frictionless t

Question

A spring of negligible mass is compressed between two masses on a frictionless table with sloping ramps at each end. m_1 is more massive than m_2. The masses are released simultaneously. Select the appropriate symbol to complete each statement G (greater than). L (less than), or E (equal to). E.g.. if the first two are greater than' and the others less than', enter GGLLLL. The final height up the ramp reached by m_1 is the height reached by m_2. The kinetic energy of m_2 the kinetic energy of M once they both lose contact with the spring The force exerted by the spring on m_1 is the force it exerts on m_2. The magnitude of the momentum of m_2 is the magnitude of the momentum of m_1 once they both lose contact with the spring. The duration of the force exerted by the spring on m_1 is the tune the force acts on m_2. The speed of m_1 is the speed of m_2 once they both lose contact with the spring.

Explanation / Answer

1) Once it is released, the heavier mass experiences less upward force than the lighter one and would reach to a lesser height.

2) The energy stored in the spring is converted into kinetic energy of masses and hence both will have equal momentum and kinetic energy = (momentum)2/2m then the Lighter mass will have greater amount of kinetic energy.

3) The force exerted by the spring is kx where x is the deflection. Hence it must be equal. There can't be net force on spring of negligible mass otherwise the acceleration would be to infinite.

4) As we know that the Force is rate of change of momentum. So momentum is also equal though accelerations would be different due to difference in masses. Heavier mass would accelerate less.

5) Both masses would loose contact with the spring simultaneously but heavier one would move away more slowly.

6) Density of M1 is more hence its mass is more. As momentum is same, speed of the lighter object would be more.

So the answer will be LGEELL.

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