Question

Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has 1. as much kinetic energy as the lighter one. 2. twice as much kinetic energy as the lighter one. 3. half as much kinetic energy as the lighter one. 4. four times as much kinetic energy as the lighter one. 5. impossible to determine

Answer 1

Given that one marble is twice as heavy as the other, the correct statement is: the heavier marble has twice as much kinetic energy as the lighter one

How to determine the energy of the lighter marble

• Mass = m
• Acceleration due to gravity = g
• Height = h
• Kinetic energy of light marble (KE₁) =?

KE = PE = mgh

KE₁ = mgh

How to determine the energy of the heavier marble

• Mass = 2m
• Acceleration due to gravity = g
• Height = h
• Kinetic energy of heavier marble (KE₂) =?

KE = PE = mgh

KE₂ = 2mgh

How to campare both kinetic energies

• Kinetic energy of light marble (KE₁) = mgh
• Kinetic energy of heavier marble (KE₂) = 2mgh
• Comparison (KE₂ / KE₁) =?

KE₂ / KE₁ = 2mgh / mgh

KE₂ / KE₁ = 2

Cross multiply

KE₂ = 2 × KE₁ =

KE₂ = 2KE₁

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