Question

A marble block of mass $2kg$ lying on ice when given a velocity of $6m{s^{( - 1)}}$ is stopped by friction in $10s$. Then the coefficient of friction is? (Take$g = 10m{s^{( - 2)}}$)
A. $0.06$
B. $0.03$
C. $0.04$
D. $0.01$

Answer 1

First, use Newton's second law of motion to find the force acting on the object. Then use the relation of frictional force and normal force, and apply Newton’s third law of motion and balance out the equations to find the coefficient of friction. Normal force is the reaction force of the force due to gravity.

Complete step by step answer:
Here, let the mass of the block be m, thus m=2kg. The velocity of the block v is given as$6m{s^{( - 1)}}$. The time taken to stop the marble block from moving with the given velocity is 10 seconds. The block is stopped because of friction. Now, friction is the ability of a surface to resist motion between two bodies. As we know, the frictional force of a object moving on a surface is related to the normal force as follows:
$f = \mu N$

And the normal force of an object is given as$N = mg$. Here, f is the frictional force, N is the normal force,$\mu$is the coefficient of friction, m is the mass of the block and g is the acceleration due to the gravity. Now, from Newton’s second law of motion, we know that force is related to acceleration as follows:
$F = ma$
Where F is the force and a is the acceleration. But here in the question, we are given velocity.

So we need to present acceleration in the form of velocity, which can be written as:
$a = \dfrac{v}{t}$
Comparing all of these equations, we get that;

$$\mu N=f \\\ \Rightarrow ma=\mu N \\\ \Rightarrow m\dfrac{v}{t}=\mu mg \\\ \Rightarrow \mu =\dfrac{v}{gt} \\\ \Rightarrow \mu =\dfrac{6}{10\centerdot 10} \\\ \therefore \mu =0.06 \\\$$

Thus,the coefficient of friction is $\mu =0.06$.

Hence, option A is the correct answer.

Note: One can notice that even though the mass of block was given, it just cancelled out in the equation. Even if the mass of the block were more, the coefficient of friction would have been the same as it is obviously independent of the mass of the block.Coefficient of friction is solely dependent on the type of the material surface.