Question

A box of mass 20kg is pushed along a rough floor with a velocity 2m/s and then let go. The box moves 5m on the floor, before coming to rest. What must be the frictional force acting on the box? a) 4N b) 2N c) 2ON d) 8N​

Answer 1

Anѕwєr :

Option D [8N]

Exρlαnαtion :

As per the provided information in the given question, we have :

• Mass of the box, m = 20 kg
• Initial velocity of the box, u = 2 m/s
• Distance travelled by the box, s = 5 m
• Final velocity of the box, v = 0 m/s

We've been asked to calculate the frictional force acting on the box (F).

In order to calculate the frictional force acting on the box, firslty we need to calculate the acceleration.

$\underline{\Large{\pink{\sf{ Acceleration :}}}}$

• Acceleration is nothing but the rate of change in velocity.
• It is a vector quantity.
• Its SI unit is m/s².

We can calculate the acceleration here by using the third equation of motion.

$\bigstar \underline{\boxed{\bf { v^2 - u^2 = 2as}}}$

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• s denotes distance

$\implies\rm { (0)^2 - (2)^2 = 2 \times a \times 5}$

$\implies\rm { 0 - 4 = 10a}$

$\implies\rm { - 4 = 10a}$

$\implies\rm { \cancel{\dfrac{- 4}{10}} = a}$

$\implies\boxed{\rm { -0.4 \; ms^{-2}= a}}$

Now, as we know that,

$\bigstar \underline{\boxed{\bf { F = ma}}}$

• F denotes force
• m denotes mass
• a denotes acceleration

$\implies\rm { F = 20 \; kg \times (-0.4) \; ms^{-2} }$

$\implies\rm { F = - 8 \; kg.ms^{-2} }$

Or,

$\implies \underline{\boxed{\rm { F = - 8\; N}}}$

(Negative sign denotes that the force is acting in the opposite direction to that the direction in which the body is moving.)

∴ The frictional force acting on the box is 8 N.

$\rule{200}2$