Question

3.
Velocity versus time graph of a ball of mass 20 g rolling on a concrete floor is shown in the
figure given below. What will be the frictional force of the floor on the ball?
20
velocity (ms
5
02
4
12
6 8 10
Time (s)
(a) 0.04 N
(b) - 40 N
O (c) - 4 N
(d) - 0.04 N

Answer 1

Provided that:

• Mass = 20 g
• Time taken = 10 seconds
• Final velocity = 0 mps
• Initial velocity = 20 m/s

To calculate:

• The force

Solution:

• The force = -0.04 N

Knowledge required:

• SI unit of force = Newton
• SI unit of velocity = m/s
• SI unit of time = sec
• SI unit of mass = kg

Using concepts:

• Formula to convert g into kg
• Formula to calculate the force

Using formulas:

• Formula to convert grams into kilograms is mentioned below:

• ${\small{\underline{\boxed{\sf{1 \: g \: = \dfrac{1}{1000} \: kg}}}}}$

• Formula to calculate force is mentioned below:

• ${\small{\underline{\boxed{\sf{F \: = m\bigg(\dfrac{v-u}{t}\bigg)}}}}}$

Where, F denotes force, m denotes mass, v denotes final velocity, u denotes initial velocity and t denotes time taken.

Required solution:

~ Firstly let us convert grams into kilograms by using suitable formula!

$\begin{gathered}:\implies \sf 1 \: g \: = \dfrac{1}{1000} \: kg \\ \\ :\implies \sf 20 \: g \: = \dfrac{20}{1000} \: kg \\ \\ :\implies \sf 20 \: g \: = \dfrac{2}{100} \: kg \\ \\ :\implies \sf 20 \: g \: = 0.02 \: kg \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}\end{gathered}$

~ Now let's calculate force!

$:\implies \sf F \: = m\bigg(\dfrac{v-u}{t}\bigg) \\ \\ :\implies \sf F \: = 0.02 \bigg(\dfrac{0-20}{10}\bigg) \\ \\ :\implies \sf F \: = 0.02 \bigg(\dfrac{-20}{10}\bigg) \\ \\ :\implies \sf F \: = 0.02 \bigg(\dfrac{-2}{1}\bigg) \\ \\ :\implies \sf F \: = 0.02 \times -2 \\ \\ :\implies \sf F \: = -0.04 \: N \\ \\ :\implies \sf Force \: = -0.04 \: Newton$

• Henceforth, force = -0.04 Newton. Therefore, option (d) is correct!