Question

A student holds a book at rest on the palm of his hand. he lifts the book straight up, bringing it to rest again at a high point.

PART A:

1. Is the net work done on the book positive negative or zero? Explain.

For this, I think the net work is zero because as he speeds the book up the work being done is positive, but the work is negative when he begins to slow down to rest again at high point.

2. is the change in the gravitational potential energy postive, negative or zero? explain.

For this, I think this is positive because the displacement of the book is upward.

3. Is the ttotal mechanical energy conserved? Explain.

For this, I feel like its not conserved... but don't know why.

***** for part A, if you have better explanation, please do tell me. also, Part A #3, Could someone explain to me why mechanical energy is not conserved?

PART B:

Consider the following discussion about the situation described above:

Darius: "when the book was lifted up, it gained potential energy but not kinetic energy. That means the change in total mechanical energy is positive."

Katrina: "Also, the net work on the book is zero, because the work you did on the book is cancelled by the work the earth did on the book."

Volibear: "Does this mean the law of conservation of energy is violated? There was zero net work on the book but its energy increased."

Question: Which of these ideas are solid and which ideas need to be revised? How would you help Darius, Katrina, Volibear make sense of the situation?

Please answer with clarity.

Answer 1

Work is done upon an object whenever a force acts upon it to cause it to be displaced.

In this instance in which the book is lifted to the top, the student supplies the force in order to do the work.

The student doing the work possess chemical potential energy stored in food or fuel that is transformed into workIn the process of doing work, the student exchanges energy with the book upon which the work is done.

When the work is done upon the book,it gains energy known as mechanical energy.

Mechanical energy is the energy that is possessed by an object due to its motion or due to its position.

Mechanical energy can be either kinetic energy (energy of motion) or potential energy(stored energy of position).

PART A

1)Work is said to be positive if the direction of displacement of the object (or force) is in the same direction as the force. If the displacement is in the opposite direction of the force the work is negative and if the displacement is zero then the work is zero.

The displacment of the book and the force apllied by the student are in the same direction(upwards),hence net work done by the student is positive.

Note that the net work done by the gravity on the object is negative(As the gravitational force acts downwards)

2) Potential energy of book on palm=0

Potential energy of book at some height h=mgh

Change in potential energy=mgh-0=mgh(positive)

3) Whenever work is done upon an object by an external force (or nonconservative force), there will be a change in the total mechanical energy of the object. If only internal forces are doing work (no work done by external forces), then there is no change in the total amount of mechanical energy i.e.,the total mechanical energy is said to be conserved.

In this case,   KE_i + PE_i+ W_ext = KE_f + PE_f

PART B

1)Darius is correct

2)Net work done on the book by you is positive

  Net work done on the book by you is negative

That's the only difference,they dont cancel each other

3)Net work done is not zero.