Chapter 11, Problem 42A

a.

To determine

Kinetic energy of T.

Answer to Problem 42A

  $2.25\times {10}^3\text{J}$

Explanation of Solution

Given:

Mass of T is $m=45\text{kg}$ .

Velocity of T is $v_1=10\text{m/s}$ .

Formula Used:

Kinetic energy, $\text{KE}=\frac{1}{2}m{v}^2$

Here, m is the mass and vis the velocity.

Calculation:

On putting the given values:

  $\begin{array}{l}\text{KE}=\frac{1}{2}\times 45\times {\left(10\right)}^2\\ =2.25\times {10}^3\text{J}\end{array}$

b.

To determine

Kinetic energy of T.

Answer to Problem 42A

Kinetic energy of T is $562.5\text{J}$

Explanation of Solution

Given:

Mass of T is $m=45\text{kg}$

Velocity of T is $v_2=5\text{m/s}$

Formula Used:

Kinetic energy $\text{KE}=\frac{1}{2}m{v}^2$

Where, m is the mass and vis the velocity.

Calculation:

On putting the given values,

  $\begin{array}{l}\text{KE}=\frac{1}{2}\times 45\times {\left(5\right)}^2\\ =562.5\text{J}\end{array}$

c.

To determine

Ratio of KE in parts a and b.

Answer to Problem 42A

Ratio of Kinetic energy a and b is $4:1$

Explanation of Solution

Given:

Kinetic energy for part a is ${\text{KE}}_1=\frac{1}{2}m{v}_1{}^2=2.25\times {10}^3\text{J}$

Kinetic energy for part a is ${\text{KE}}_2=\frac{1}{2}m{v}_2{}^2=562.5\text{J}$

Calculation:

The ratio of kinetic energy is

  $\frac{\frac{1}{2}m{v}_1{}^2}{\frac{1}{2}m{v}_2{}^2}=\frac{v_1{}^2}{v_2{}^2}=\frac{\left({10}^2\right)}{5^2}=\frac{100}{25}=\frac{4}{1}$