1. Consider the following 3 scenarios. The masses are as shown, all masses start

Question

1. Consider the following 3 scenarios. The masses are as shown, all masses start from the same height above the horizontal surface, and they all start at rest. There is no air resistance, and all surfaces are frictionless. 2m (falls straight down) 450 30° aj (5 pts)?which one will have the greatest speed just before reaching the bottom ill they all have the same speed just before reaching the bottom)? Explain the reasoning behind your answer b) (5 pts) Which one will have the greatest kinetic energy just before reaching the bottom (or will they all have the same kinetic energy just before reaching the bottom)? Explain the reasoning behind your answer.

Explanation / Answer

a)
Acceleration for mass m, a1 = g = 9.81 m/s2
Acceleration for mass 2m, a2 = g sin(45) = 6.94 m/s2
Acceleration for mass 3m, a3 = g sin(30) = 4.905 m/s2

Using the formula, v2 - u2 = 2ah
Initial velocity of all the masses, u = 0
Final velocity, v = SQRT[2ah]
Since h is same for all the masses, final velocity depends only on the acceleration. Since the acceleration of mass m is highest, its final velocity is greater than other masses.

b)
For the mass m, KE = 1/2 mv2
= 0.5 x m x 2a1h
= 0.5 x 2 x 9.81 x mh
= 9.81 mh

For the mass 2m,
KE = 0.5 x 2m x 2a2 h
= 0.5 x 4 x 6.94 x mh
= 13.87 mh

For the mass 3m,
KE = 0.5 x 3m x 2 a3 h
= 0.5 x 6 x 4.905 mh
= 14.72 mh

So kinetic energy of 3m mass is greatest.

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