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 M_1 is greater than that of M_2. Select the appropriate option for each statement. the kinetic energy of M_1 is ... 'the kinetic energy of M_2 once they both lose contact with the spring. the speed of M_1 is ... the speed of M_2 once they both lose contact with the spring. the momentum of M_2 is ... the momentum of M_1 once they both lose contact with the spring. the force exerted by the spring on M_2 is ... the force it exerts on M_1. the final height of the ramp reached by M_2 Is ... the height reached by M_1. the duration of the force exerted by the spring on M_2 is ... the time the force acts on M_1.

Explanation / Answer

1/2 kx^2 = 1/2 m1v^2 + 1/2 m2v2^2 ( conservation of energy)

where 1/2 m1v1^2 = 1/2 m2v2^2

m1v1 = m2v2 (conseervation of momentum)

m1 ( mass) > m2 (mass), therefore V1 < v2

therfore , m1v1 = m2 v2

a) KE of both the masses are equal once they lose control with spring

b)the speed of m1 is less than speed of m2

c)momentum of both masses are equal once they lose control with spring

d)Force exerted is equal

e)the final height of m2 is greater than final height of m1

f)duration of force is equal on both the masses

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