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 less than that of M2. Select the appropriate option for each statement: greater than,less than, or equal to

A)The speed of M2 is ... the speed of M1 once they both lose contact with the spring.
B)Greater than Less than Equal to  The duration of the force exerted by the spring on M1 is ... the time the force acts on M2.
C)Greater than Less than Equal to  The force exerted by the spring on M1 is ... the force it exerts on M2.
D)Greater than Less than Equal to  The kinetic energy of M1 is ... 'the kinetic energy of M2 once they both lose contact with the spring.
E)Greater than Less than Equal to  The final height up the ramp reached by M2 is ... the height reached by M1.
F)Greater than Less than Equal to  The momentum of M2 is ... the momentum of M1 once they both lose contact with the spring.

Explanation / Answer

A) Momentum conservation: m1*v1 = m2*v2

KE1/KE2 = (1/2*m1*v1^2)/(1/2*m2*v2^2) = (m1v1)v1/[(m2v2)v2] = v1/v2 = m2/m1 > 1

Hence, v1> v2

B)

Duration of force on m1 is t1 = m1*v1/F

Duration of force on m2 is t2 = m2*v2/F

Since m1v1 = m2v2, we get t1 = t2.

C) F = kx

Hence, force is equal on both.

D) from point (a) , KE1> KE2

E)

KE1 = m1*g*h1

KE2 = m2*g*h2

KE1/KE2 = (m1/m2)(h1/h2)

h1/h2 = (KE1/KE2)(m2/m1) = (m2/m1)(m2/m1) = (m2/m1)^2 > 1

Hence, h1 > h2.

F)

Momentum consevation implies, momentum before and after shold be equal.

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