Chapter 7.4, Problem 63PPS

a.

To determine

To simplify the formula when mass of the ball is 3 kilograms.

Answer to Problem 63PPS

  $v=\sqrt{\frac{2k}{3}}$

Explanation of Solution

Given:

  $v=\sqrt{\frac{2k}{m}}$

k is the kinetic energy in Joules

m is the mass of the ball in kilograms.

v is the speed of the ball.

Calculation:

Mass of the ball ( m ) = 3 kilograms, which means m = 3.

Now, $v=\sqrt{\frac{2k}{m}}=\sqrt{\frac{2k}{3}}$

Conclusion:

Hence, the simplified form according to the given situation will be: $v=\sqrt{\frac{2k}{3}}$

b.

To determine

To find the kinetic energy of the ball.

Answer to Problem 63PPS

73.5 Joules

Explanation of Solution

Given:

  $v=\sqrt{\frac{2k}{3}}$

k is the kinetic energy in Joules

v is the speed of the ball

Calculation:

Let, $v=\sqrt{\frac{2k}{3}}\mathrm{..............................}(i)$

Given that, the ball moves at the speed of $7m/s$ , which means, $v=7$ .

Now substituting the value of v in equation ( i ),

  $\Rightarrow 7=\sqrt{\frac{2k}{3}}$

  $\Rightarrow {\left(\sqrt{\frac{2k}{3}}\right)}^2=7^2[\because \text{Squaring on both sides}]$

  $\begin{array}{l}\Rightarrow \frac{2k}{3}=49\\ \Rightarrow 2k=147\\ \Rightarrow k=\frac{147}{2}\\ \Rightarrow k=73.5\end{array}$

Conclusion:

Hence, the required kinetic energy of the ball is 73.5 Joules.