Chapter 7, Problem 10Q

To determine

To identify: Whether heavier or lighter object will have greater momentum for the same kinetic energy.

Explanation of Solution

Introduction:

Momentum is the mass times the change of velocity of an object. Momentum is a vector quantity.

The kinetic energy of an object of mass m moving with velocity v is

  $\begin{array}{c}KE=\frac{1}{2}m{v}^2\\ =\frac{1}{2}\times m{v}^2\times \frac{m}{m}\\ =\frac{1}{2}\times \frac{{\left(mv\right)}^2}{m}\\ =\frac{1}{2}\times \frac{p^2}{m}\end{array}$

Where,

p is the momentum

Rearranging the equation in terms of mass and kinetic energy for momentum

  $\begin{array}{l}{p}^2=2mKE\\ p=\sqrt{2mKE}\end{array}$

It is observed that momentum is directly proportional to mass.

Now, for two masses, lighter and heavier, the momentum of heavier objects is large since its mass is larger than the lighter object for the same kinetic energy.

Conclusion:

Heavier objects momentum is larger than the momentum of a lighter object.