Question

Given a ball at some height above the ground where its total mechanical energy is 5.00 J. If the ball falls down to a lower height in free fall where it’s gravitational potential energy is 2.00 J then what must its kinetic energy be at this lower height?A) 3.00 JB) 9.10X10^-1 JC) 12.9 JD)15.3 JE)6.40 J

Answer 1

A. 3.00 J

Step-by-step explanation

By the law of conservation of energy, total mechanical energy must be conserved. At both points, the kinds of mechanical energy the ball has are gravitational potential energy and kinetic energy,

`ME=PE+KE`

At some point, the total mechanical energy is 5 J. This energy must be conserved, so if at the lower height its gravitational potential energy is 2J, then its kinetic energy must be such that the sum gives 5J,

`\begin{gathered} 5J=2J+KE \\ KE=5J-2J=3J \end{gathered}`

Hence, the kinetic energy at the lower height is 3.00 J.