Question

A 2.0 kg book is lying on a 0.78 m -high table. You pick it up and place it on a bookshelf 2.1 m above the floor.Part ADuring this process, how much work does gravity do on the book?Part BDuring this process, how much work does your hand do on the book?

Answer 1

Given data:

* The mass of the book is 2 kg.

* The initial height of the book is 0.78 m.

* The final height of the book is 2.1 m.

Solution:

(A). The work done by the gravity on the book is,

$W=mg(h_f-h_i)$

where m is the mass, g is the acceleration due to gravity, h_i is the initial height and h_f is the final height,

The work is done in moving the object in upward direction where as the gravitational force is acting in the down ward direction. Thus, the value g (acceleration due to gravity) is taken as negative in this case.

Substituting the known values,

$\begin{gathered} W=2\times(-9.8)\times(2.1-0.78) \\ W=-19.6\times1.32 \\ W=-25.9\text{ J} \end{gathered}$

Thus, the work done by the gravitational force is -25.9 J.

(B). The work done by the hand on the moving the book is,

$\begin{gathered} W_1=-W \\ =25.9\text{ J} \end{gathered}$

Thus, the work done by the hand on the book is 25.9 J.