Question

a person throws a ball of mass 100 gram with a speed of 20meter per second . It came to rest after 5 second . Find the average force applied by the person​

Answer 1

Answer:

• 0.4 Newton will be the required force.

Explanation:

According to the Question

• Mass of ball ,m = 100g = 0.1 kg
• Initial velocity ,u = 20m/s
• Final velocity ,v = 0m/s
• Time taken ,t = 5 s

we have to calculate the Average Force applied by the Person .

For calculating the force applied , we will apply here formula .

Force is calculated by the product of mass and acceleration .

And, also acceleration is defined as the rate of change in velocity at per unit time.

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

$\dashrightarrow\sf\; F_{avg} = m \frac{v-u}{t}$

by substituting the value we get

$\dashrightarrow\sf\; F_{avg} = 0.1 \times\frac{0-20}{5} \\\\\\\dashrightarrow\sf\; F_{avg} = 0.1\times\frac{-20}{5} \\\\\\\dashrightarrow\sf\; F_{avg} = 0.1\times (-4) \\\\\\\dashrightarrow\sf\; F_{avg} = -0.4N \\\\\sf\; Here\;, negative \; sign \; shows \; that \; the \; force \; is \; acting \; in \; opposite \; direction \; of \; motion .$

$\bullet\;\; \boxed{\bf{Hence, \; the \; Average\; Force \; applied\; by \; the \; person \; will \; be \; 0.4\; Newton. }}$

Answer 2

From the Question, we know that,

• Mass of the ball $(m)$ = $\sf{100\:g}$ = $\sf{0.1\:kg}$
• Initial velocity $(u)$ = $\sf{20\:m}$
• Time $(t)$ = $\sf{5\:seconds}$
• Final velocity $(v)$ = $\sf{0}$

Let's find Initial Momentum and Final Momentum,

$\boxed{Initial\:Momentum=mass\:\times\:Initial\:Velocity}$

Substituting known values in Formula, we get,

$\implies\sf{Initial\:Momentum=m\:\times\:u}$

$\implies\sf{Initial\:Momentum=0.1\:\times\:20}$

$\implies\sf{Initial\:Momentum=2}$

Then,

$\boxed{Final\:Momentum=mass\:\times\:Final\:Velocity}$

$\implies\sf{Final\:Momentum=m\:\times\:v}$

$\implies\sf{Final\:Momentum=0.1\:\times\:0}$

$\implies\sf{Final\:Momentum=0}$

And,

$\boxed{Change\:in\:Momentum=mv\:-\:mu}$

Substituting values in Formula, we get,

$\implies\sf{Change\:in\:Momentum=0\:-\:2}$

$\implies\sf{-2}$

Average force applied,

$\boxed{Average\:Force={\dfrac{Change\:in\:Momentum}{Time}}}$

Substituting values in Formula, we get,

$\implies\sf{Average\:Force={\dfrac{-2}{5}}}$

$\implies\sf{Average\:Force={\cancel{{\dfrac{-2}{5}}}}}$

$\implies\sf{Average\:Force=-0.4\:N}$

Note : Negative sign indicates that the force was applied in the opposite direction.

Hence, The average force applied by the person = 0.4 Newton.