Chapter 6, Problem 30P

To determine

a) Potential energy of the book relative to the ground.

b)The potential energy of book relative to person’s head.

c) The relation between the work done by the person to above question.

Answer to Problem 30P

Solution:a) Potential energy of the book relative to the ground is 35.57 J.

b)The potential energy of book relative to person’s head is 9.7 J.

c) Work done by the person is equal to 35.57 J, which is given in part (a).

Explanation of Solution

Given:Mass of book, $m=1.65\text{ kg}$

The final height of book is $h_{book}=2.20\text{ m}$

The initial height of book, $h_{ground}=0\text{ m}$

The height of person, $h_{head}=1.6\text{ m}$

Formula Used:

Potential energy is given by

  $\begin{array}{l}PE=P{E}_{book}-P{E}_{ground}\\ PE=mg{h}_{book}-mg{h}_{ground}\\ PE=mg(h_{book}-h_{ground})\end{array}$

Where m is mass of the book, g is the acceleration due to gravity

h_book is final height of the book

h_groundis the initial height of the book

Calculations:

a) Relative to the ground, the PE is given by

Substitute these values in above equation and solve for potential energy

  $\begin{array}{l}PE=mg(2.2-0)\\ PE=1.65\times 9.8(2.2)\\ PE=35.57\text{ J}\end{array}$

The potential energy of the book relative to the ground is $35.57\text{ J}\text{.}$

b) Relative to the top of the person’s head, the P.E. is given by:

  $PE=mg(h_{book}-h_{head})$ where the height of a person is 1.6 m

  $\begin{array}{l}PE=1.65\times 9.8(2.2-1.6)\\ PE=9.7\text{ J}\end{array}$

The potential energy of the book relative to the person’s head is 9.7 J

c) The work done by the person lifting the book from the ground to the final height is the same as the answer to part (a), 35.57 J. In part (a), the potential energy is calculated relative to the starting location of the application of the force on the book. The work done by the person is not related to the answer to part (b).

Conclusion:a) Potential energy of the book relative to the ground is $35.57\text{ J}\text{.}$ .

b)The potential energy of book relative to person’s head is $9.7\text{ J}.$

c) Work done by the person is equal to 35.57 J, which is given in part (a).