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 M₂ is ... the time the force acts on M₁.
     B) The force exerted by the spring on M₁ is ... the force 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 M₂ is ... the height reached by M₁.
     E) The kinetic energy of M₁ is ... the kinetic energy of M₂ once they both lose contact with the spring.
     F) The momentum of M₁ is ... the momentum of M₂ once they both lose contact with the spring.

Thank you for your help.

Answer 1

Hello, Here I am going to add my answer regarding the given problem I hope it would be better to understand the students.

Answer:

According to the conservation of energy and momentum we observed this situation as the force exerted by the spring because of two masses is an internal force so that the total momentum immediately after the masses separate is equal to the total momentum (conservation of momentum) when the spring is compressed (and the blocks are at rest). Once the masses have separated, there are no non-conservative forces and mechanical energy is conserved (conservation of energy).

After understanding the problem, we analyzed and made judgments as follows;

For

Option A: The duration of the force exerted by the spring on M2 is Greater the time the force acts on M1. Because the duration of force would be longer for M1 since it has a greater mass and more force is required to move it.

Option B: The force exerted by the spring on M1 is Greater the force it exerts on M2. Because according to Newton's second law Force is the product of mass and acceleration means directly depends on mass since M₁ has a greater mass a greater force is exerted on it by the spring.

Option C: The speed of M₂ is Greater than the speed of M₁ once they both lose contact with the spring. Because, as stated before, since both have the same momentum and M1 has greater mass, then M2 must have a greater velocity.

Option D: The final height up the ramp reached by M2 is Less the height reached by M1. Because, from above discussion M₁ has a lesser speed than M₂, it would travel a shorter distance up the slope than M₂.

Option E: The kinetic energy of M1 is Greater the kinetic energy of M₂ once they both lose contact with the spring. Because, we all know less massive particle moves faster than high mass particle so M₂ has a higher velocity since it has less mass and the same momentum, therefore the KE derived from 0.5mv^2 would be greater than that of M₁.

Option F: The momentum of M1 is Equal to the momentum of M2 once they both lose contact with the spring. Because momentum is conserved therefore both are equal.

The final tabulated answer will be GGGLGE.