Question

Two balls of equal size are dropped from the same height from the roof of a building. the mass of ball a is twice that of ball b, m subscript a equals 2 m subscript

b. when the two balls reach the ground, how do their kinetic energies compare?

Answer 1

5.5 m/s

Step-by-step explanation:

Answer 2

The mass of ball a is twice the mass of ball b:

`m_a = 2 m_b`
This means that the initial potential energy of ball a (
`U_a = m_a gh=2 m_b gh`) is twice the potential energy of ball b (
`U_b = m_b g h`):

`U_a = 2 U_b`
When the two balls reach the ground, the potential energy of each ball has converted into kinetic energy (since now their altitude is h=0), because the total mechanical energy of each ball must be conserved. Therefore:

`K_a = U_a`

`K_b = U_b`
and so the kinetic energy of ball a must be twice the kinetic energy of ball b:

`K_a = 2 K_b`