Chapter 10, Problem 5STP

To determine

To Choose: The correct option.

Answer to Problem 5STP

Option C

Explanation of Solution

Given:

Weight of the box, $w=mg=40\text{N}$

Length of the ramp, $s=2.00\text{m}$

Height of the platform, $h=1.00\text{m}$

Time taken by person 1, $t_1=2.00\text{s}$

Time taken by person 2, $t_2=4.00\text{s}$

Formula Used:

Power consumed can be obtained by:

  $P=\frac{W}{t}$

Where, W is the work done and t is the time elapsed.

Work done: $W=F\cdot s$

Here, $F=w$

Calculations:

For person 1:

  $\begin{array}{c}{P}_1=\frac{F\cdot s}{t_1}\\ =\frac{\text{40}\text{.0}\text{N}\cdot \text{2}\text{.00}\text{m}}{2.00\text{}\text{s}}\\ =40.0\text{W}\end{array}$

For person 2:

  $\begin{array}{c}{P}_1=\frac{F\cdot s}{t_1}\\ =\frac{\text{40}\text{.0}\text{N}\cdot \text{2}\text{.00}\text{m}}{4.00\text{}\text{s}}\\ =20.0\text{W}\end{array}$

Difference in the power:

  $\begin{array}{c}\Delta P=P_1-P_2\\ =40.0\text{W-20}\text{.0}\text{W}\\ \text{=20}\text{.0}\text{W}\end{array}$

Conclusion:

Thus, correct option is C.