Chapter 10, Problem 46A

a.

To determine

The work done on the $145\text{kg}$ mass if a horizontal force of $300.0\text{N}$ is used to push it by a distance of $30.0\text{m}$ horizontally in $3.00\text{s}$ .

Answer to Problem 46A

  $9000\text{J}$

Explanation of Solution

Given:

The considered mass, $m=145\text{kg}$

The horizontal force used to push the mass, $F=300.0\text{N}$

The distance by which the mass is moved horizontally, $d=30.0\text{m}$

Time taken, $t=3.00\text{s}$

Formula used:

Work done is given by,

  $W=Fd\cos \theta$

Where $F$ is the force done, $d$ is the distance, and $\theta$ is the angle between the distance and force.

Calculation:

Since the applied force and the displacement are in same direction, thus the direction between force and the displacement is $\theta =0°$

Thus, the work done is given by,

  $\begin{array}{c}W=Fd\cos \theta \\ =\left(300\right)\left(30\right)\cos 0°\\ =9000\text{J}\end{array}$

Conclusion:

Thus, work done on the $145\text{kg}$ mass is $9000\text{J}$ .

b.

To determine

The power developed when a horizontal force of $300.0\text{N}$ is used to push it by a distance of $30.0\text{m}$ horizontally in $3.00\text{s}$ .

Answer to Problem 46A

  $3000\text{W}$

Explanation of Solution

Given:

The considered mass, $m=145\text{kg}$

The horizontal force used to push the mass, $F=300.0\text{N}$

The distance by which the mass is moved horizontally, $d=30.0\text{m}$

Time taken, $t=3.00\text{s}$

From part (a), work done on the $145\text{kg}$ mass, $W=9000\text{J}$ .

Formula used:

Power is given by the work done divided by the time taken to do the work,

  $P=\frac{W}{t}$

Where $W$ is the work done, and $t$ is the time taken

Calculation:

Using the given and calculated values in above, the power developed will be

  $\begin{array}{c}P=\frac{W}{t}\\ =\frac{9000}{3}\\ =3000\text{W}\end{array}$

Conclusion:

Thus, the power developed is $3000\text{W}$ .