scenario: A mass m starts at the top of the ramp on the left with an initial spe

Question

scenario: A mass m starts at the top of the ramp on the left with an initial speed v_o = 3.5 m/s downward. It descends the frictionless ramp on the left, moves across the frictionless plane and then moves up the ramp on the right. You may neglect the size of the mass.

problem: If the mass of the block were doubled, h_f would: increase, decrease, or stay
the same

And suppose that u_k of flat surface between the ramps is 0.30. If the initial height is H_i, what is the final height h_f on the right ramp? (g = 9.8 m/s^2)

Explanation / Answer

For the first part, hf would not change.

As the acceleration due to gravity doesn't depend on the value of the mass.

Or if you want to prove it mathematically, just conserve energy

0.5 m v2 + mghi = mghf

As you can see m gets cancelled in both sides, implying that hf doesn't depend on m.

For the second part, just use the work energy equation.

0.5 m v2 + mghi - kmgx = mghf (Where x = distance between both the ramps)

0.5 v2 + ghi - kgx = ghf substitute the values and get the answer.

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