Question

The breaking strength of the table used to pull a body is 40 N. A body of mass 8 kg is resting on a table of the coefficient of friction $\mu = 0.2$. What is the maximum acceleration which can be produced by the table? Assume $g = 10m/{s^2}$.
(A) $6m/{s^2}$
(B) $3m/{s^2}$
(C) $8m/{s^2}$
(D) $5m/{s^2}$

Answer 1

Hint: The breaking strength of a material is the maximum stress or force the material can withstand just before breaking. Friction is the opposition offered when an object tries to move across a surface.
$\Rightarrow F = \mu N$ where $F$is the frictional force exerted by a surface experiencing normal reaction $N$, with coefficient of friction$\mu $.

Complete step by step answer:
In the given question, we are provided with a table that has some significant breaking strength. This table also exhibits some friction, and we are asked to determine the acceleration that a mass resting on the table would undergo.
For solving this, we will try to find the net force that will be exerted on the body, and then use this to calculate the acceleration. The data provided to us:
Maximum force ${F_m} = 40$N
Mass of the body $m = 8$kg
Coefficient of friction of the table $\mu = 0.2$
We know that the frictional force can be calculated as:
$\Rightarrow F = \mu N$ [Eq. 1]
As N is the normal reaction, it will be equivalent to the weight of the object:
$\Rightarrow N = mg = 8 \times 10 = 80$N
Putting this value in Eq. 1 gives us:
$\Rightarrow F = 0.2 \times 80 = 16$N
The net force acting on the object kept on the table will be:
$\Rightarrow {F_{net}} = {F_m} - F$
$\Rightarrow {F_{net}} = 40 - 16 = 24$N
Now, this force is responsible for producing acceleration in the body. We know that
$\Rightarrow F = ma$
$\Rightarrow a = \dfrac{{{F_{net}}}}{m}$
Substituting the values in this equation will give us:
$\Rightarrow a = \dfrac{{24}}{8} = 3m/{s^2}$
Hence, the acceleration the body will experience is option (B).

Note:
As we saw, friction is responsible for reducing the net force acting on a body. One might think that it is bad for any system, but it has its own uses too. For example, if there were no friction, we would not be able to walk freely and would constantly slip. The breaks of a vehicle also work using friction.