Question

Velocity versus time graph of a ball of mass $50\mathrm{g}$ rolling on a concrete floor is shown in figure .Calculate the acceleration and frictional force of the floor on the ball.

Answer 1

Step-1:Given data

Mass of ball =$\mathrm{M}=50\mathrm{gm}=0.050\mathrm{kg}$

The initial velocity of ball=$\mathrm{U}=80\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$

The final velocity of ball= $\mathrm{V}=0\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$

Time required=$\mathrm{t}=8\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$

Acceleration of the ball=$\mathrm{a}=?$

Frictional force=$\mathrm{F}=?$

Step-2: Formula

Acceleration=$\mathrm{a}=\frac{\mathrm{V}-\mathrm{U}}{\mathrm{t}}$

Frictional force = F = $\mathrm{m}\times \mathrm{a}$

Step-3: Calculation

1. Calculate the acceleration

Acceleration=$\mathrm{a}=\frac{\mathrm{V}-\mathrm{U}}{\mathrm{t}}=\frac{0-80}{8}=-10\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.$…………………………….($-ve$acceleration shows retardation)

2. Calculate Frictional Force

Frictional force = F = $\mathrm{m}\times \mathrm{a}=0.05\times (-10)=-0.5\mathrm{N}$…………………($-ve$ sign shows this force acts in the opposite direction of motion)

Hence, the Acceleration of the ball is $10\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$ and the frictional force that acts on the ball is $0.5\mathrm{N}$