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. The masses are released simultaneously. The masses have the same volume, but the density of M1 is greater than that of M2. Select the appropriate symbol for each statement: G (Greater than), L (Less than), or E (Equal to). (If the first two are 'greater than,' and the last four 'less than,' then enter GGLLLL).



A) The duration of the force exerted by the spring on M1 is ... the time the force acts on M2.
B) The magnitude of the force exerted by the spring on M1 is ... that it exerts on M2.
C) The speed of M1 is ... the speed of M2 once they both lose contact with the spring.
D) The final height up the ramp reached by M1 is ... the height reached by M2.
E) The kinetic energy of M2 is ... the kinetic energy of M1 once they both lose contact with the spring.
F) The magnitude of M1's momentum is ... that of M2 before and just after loss of contact with the spring.

Explanation / Answer

1) The force exerted by the spring is kx where x is the deflection. Hence first is equal. 2) 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. 3)Density of M1 is more hence its mass is more. As momentum is same, speed of the lighter object would be more. 4) As both were acted upon by the same force initially the heavier mass would reach less height than the lighter one as its weight (mass*g) is more. So under gravity it is acted upon by a greater downward force. Hence once released, the heavier mass experiences less upward force than the lighter one and would reach to a lesser height. 5) Both masses would loose contact with the spring simultaneously but heavier one would move away more slowly. 6) The energy stored in the spring is converted into kinetic energy of masses and hence both will have the same amount of kinetic energy.

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