Question

A body of mass 2kg is being dragged with uniform velocity of $2m/s$ on a rough horizontal plane. The coefficient of friction between the body and the surface is $0.20$. The amount of heat generated in $5$ sec is
($J = 4.2$joule/cal and $g = 9.8m/{s^2}$)
(A) $9.33cal$
(B) $10.21cal$
(C) $12.67cal$
(D) $13.34cal$

Answer 1

Hint: When the body is dragged on the rough horizontal plane, the friction force causes it to lose energy and this dissipation of energy takes place in the form of heat production. Since the energy is equal to the work done, the heat can be determined by multiplying the force of friction to the distance covered by the body.
Formula used:
$W = F \times s$
Where, W is the work done by the object
F is the force applied to the object
s is the distance travelled by the object.

Complete step by step solution:
It is given that,
Mass of the body is, $m = 2kg$
The velocity with which the object is dragged, $v = 2m/s$
The coefficient of friction between the object and the plane surface, $\mu = 0.2$
We can write the distance travelled by the object $s$ in $5\sec $is-
$\Rightarrow$ $s = vt$
$\Rightarrow$$s = 2 \times 5 = 10m$
The force of friction on the object is given by,
$\Rightarrow$$F = \mu N$
Where N is the normal contact force, which is equal to-
$\Rightarrow$ $N = mg$
Taking the value of $g = 9.8m/{s^2}$
$\Rightarrow$ $N = 2 \times 9.8 = 19.6$
Therefore,
$\Rightarrow$$F = 0.2 \times 19.6$
$\Rightarrow$$F = 3.92N$
The work done is given by-
$\Rightarrow$$W = F \times s$
On putting the values of force and distance we get-
$\Rightarrow$$W = 3.92 \times 10$
$\Rightarrow$$W = 39.2J$
The work done by the friction force is equal to the heat energy that is produced. Therefore,
$H = 39.2J$
The units of Heat here are in Joules.
In the question it is given that $J = 4.2$joule/cal
To convert the given heat into calories, it needs to be divided by $4.2$.
$\Rightarrow$$H = \dfrac{{39.2}}{{4.2}}Cal$
$\Rightarrow$$H = 9.33Cal$
This is the amount of heat generated in 5 seconds.

Thus option (A) is correct.

Note: The work done is equal to the energy supplied/ possessed by the body, but they both have different definitions. Work is done in the body when a force causes it to move. While the energy is the quantity that determines how much work is/ can be done by an object.