Question

A block of mass 10 kg is placed on a rough horizontal surface whose coefficient of friction is 0.5. If a horizontal force of 100 N is applied on it, then acceleration of the block will be
[Take g=10 ms$^{-2}$]
A. 10 ms$^{-2}$
B. 5 ms$^{-2}$
C. 15 ms$^{-2}$
D. 0.5 ms$^{-2}$

Answer 1

Hint: - This question is based on the friction force concept, a resisting force that resists or opposes the motion and acts in the opposite direction of motion for a moving body and the body’s acceleration depends on the net force acting on the body.

Complete step by step answer:
Given:
The mass of the block is m=10 kg.
The acceleration due to gravity is g=10 ms-2.
The applied force is F=100 N.
The coefficient of friction is $\mu = 0.5$.
We will now calculate the friction force f.
$\begin{array}{l} f = \mu mg\\\ = 0.5 \times 10kg \times 10m{s^{ - 2}}\\\ = 50N \end{array}$
We will now calculate the force ${F_1}$ that produces acceleration $a$.
We know that $a = \dfrac{{{F_1}}}{m}$
We can now calculate ${F_1}$ as:
$\begin{array}{l} {F_1} = F - f\\\ = 100N - 50N\\\ = 50N \end{array}$
We will now calculate the acceleration as:
$\begin{array}{l} a = \dfrac{{{F_1}}}{m}\\\ = \dfrac{{50N}}{{10kg}}\\\ = 5m{s^{ - 2}} \end{array}$
Therefore the acceleration of the block is $5m{s^{ - 2}}$

the correct option is (B)

Additional Information: Static friction force- This type of friction force acts on a body kept at rest in the opposite direction of some other force acting on the object.

Kinetic force - When the body starts moving then this force opposes the motion of the object. its value is a little bit less than the static friction force

Note: Generally, friction force acts as a barrier or opposing in motion of anything like machines, vehicles etc. and causes a lot of losses and tear and fear of friction but it is also very important in some cases like it is the force which enables us to walk on the road. The angle of repose lies between 0 and 90 degrees.