Question

A 2.0 kg book is lying on a 0.75-m-high table. You pick it up and place it on a bookshelf 2.25 m above the floor.
a. How much work does gravity do on the book?
b. How much work does your hand do on the book?

Short answer

a) Work done by gravity = -29.43 J

b) Work done by hand = 29.43 J

Step-by-step solution

Part(a)  Step 1: Given Information

A 2.0 kg book is lying on a 0.75-m-high table.
You pick it up and place it on a bookshelf 2.25 m above the floor.

Part(a) Step 2 Explanation

Work done = Force x displacement in the direction of force

So

Work done by gravity = gravitational force x vertical displacement
Vertical displacement = 2.25-0.75=1.5 m
Word done by gravity =2 x 9.81 x 1.5=29.43 J

Gravitational force acts downward and the book is lifted upward, That means the work is negative which is -29.43 J

Part(b) Step 1 : Given information

A 2.0 kg book is lying on a 0.75-m-high table.
You pick it up and place it on a bookshelf 2.25 m above the floor.

Part(b) Step2: Explanation

Work done = Force x displacement in the direction of force

We find that the hand lifts the book against the gravitational force.

In this case the direction of force applied by hand and the direction in which the book lifted is upward.

So the work done by hand = m x g x h = 2 x 9.81 x 1.5 = 29.43 J