Question

The work done by the frictional force on a pencil in drawing a complete circle of

radius $r = \dfrac{1}{\pi }$ metre on the surface by a pencil of negligible mass with a normal

pressing force $N = 5N(\mu = 0.5)$

(A) $+ 4J$

(B) $- 3J$

(C) $- 2J$

(D) $- 5J$

Answer 1

In order to solve the problem we need to know about what is work done by frictional force and knowledge about normal force , direction of normal force , direction of frictional force.

Work done by frictional force is

$dw$

$$$$$dw = \overrightarrow {{F_k}} .dl$

Here $\overrightarrow {{F_k}}$ is the frictional force opposite to the applied force

Due to opposite in direction we can say that

$dw = - \overrightarrow {{F_k}} .dl$

Given:

a pencil in drawing a complete circle of radius $r = \dfrac{1}{\pi }$ metre on the surface by a pencil of negligible mass with a normal pressing force $N = 5N$

and ${\mu _k} = 0.5$(coefficient of kinetic friction)

To find the work done by the frictional force on a pencil

Complete step by step solution:

As per the given question first, we will draw the diagram as per the given situation,

Let the frictional force applied be $\overrightarrow {{F_k}}$​​

$\overrightarrow {{F_k}}$ acts tangentially opposite to the motion of the pencil.

For elementary displacement $dl$

The work done by $\overrightarrow {{F_k}}$is $dw$

$dw = \overrightarrow {{F_k}} .dl = - \overrightarrow {{F_K}} .dl$

Integrating on both side, we get

$\int_0^W {dw} = - \int_0^{2\pi r} {\overrightarrow {{F_K}} .dl}$

$\int_0^W {dw} = - {\mu _k}N\int_0^{2\pi r} {dl}$ as we know $(\overrightarrow {{F_K}} = {\mu _k}N)$

$W = - {\mu _k}N2\pi r$

Put value of ${\mu _k},r,N$

$W = -0.5 \times 5 \times 2 \times \pi \times \dfrac{1}{\pi }$

$W = - 5J$ is the work done by the frictional force on a pencil in drawing a complete circle.

So the correct answer is (d).

Note: We see friction in our day to day activities. Following are the ten examples of friction in daily life:

1. Walking

2. Writing

3. Scating

4. Lighting a matchstick

5. Driving of the vehicle on a surface

6. Applications of breaks in the vehicle to stop it

7. Flight of aeroplanes

8. Drilling a nail into the wall

9. The dusting of the carpet by beating it with a stick

10. Sliding on a garden slide