Chapter 8, Problem 1CQ

Is it possible for the kinetic energy of an object to be negative? Is it possible for the gravitational potential energy of an object to be negative? Explain.

To determine

Whether it is possible for the kinetic and potential energy to be negative.

Answer to Problem 1CQ

The kinetic energy cannot be negative but potential energy can be negative.

Explanation of Solution

Write the expression of kinetic energy of the body.

$K=\frac{1}{2}m{v}^2$

Here,

$m$ is the mass of the body.

$v$ is the velocity of the body.

Kinetic energy is the product of mass and square of the velocity and mass and the term $v^2$ cannot be negative.

Thus, the kinetic energy of an object cannot be negative.

Write the expression of potential energy of the object.

$U=mgh$

Here,

$g$ is the acceleration due to gravity.

$h$ is the height of the object form the datum.

The datum line can be selected anywhere. If the object is at height $H$ and the datum line is selected at height $2H$. Then the term $h$ will be the $-H$ measured in downward direction.

Thus, the potential energy of the object can be negative.

Conclusion:

Therefore, the kinetic energy cannot be negative but potential energy can be negative.