Chapter 11, Problem 68A

To determine

The amount of the mechanical energy that transforms to other forms due to friction.

Answer to Problem 68A

  $1173.76\text{J}$

Explanation of Solution

Given:

The mass of the Lorena, $m=28\text{kg}$

The height climbed by her, $h=4.8\text{m}$

The velocity of Lorena at the bottom of the slide, $v_f=3.2\text{m/s}$

Formula used:

The kinetic energy of an object of mass $m$ travelling at a speed of $v$ is given by,

  $KE=\frac{1}{2}m{v}^2$

And, the PE of an object of mass, m , due to its height, h , and gravity is given by,

  $PE=mgh$

Conservation of Mechanical Energy is given as,

  $M{E}_{before}=M{E}_{after}$

Where $ME$ is the mechanical energy.

Calculation:

The initial total energy of Lorena at the top of climb is,

  $\begin{array}{c}M{E}_{before}=P{E}_{before}+K{E}_{before}\\ =mgh+0\\ =\left(28\right)\left(9.8\right)\left(4.8\right)\\ =1317.12\text{J}\end{array}$

Let the mechanical energy lost due to friction be $E_{lost}$ , then using conservation of mechanical energy,

  $\begin{array}{c}M{E}_{before}=E_{after}+E_{lost}\\ 1317.12=P{E}_{after}+K{E}_{after}+E_{lost}\\ 1317.12=0+\frac{1}{2}m{v}_f^2+E_{lost}\\ 1317.12=0+\frac{1}{2}\left(28\right){\left(3.2\right)}^2+E_{lost}\\ E_{lost}=1173.76\text{J}\end{array}$

Conclusion:

Thus, the mechanical energy loss due to friction is $1173.76\text{J}$ .