Question

A ball of mass 100g moving with a velocity 0m/s is stopped by boy in 0.2s. Calculate the force applied by the boy to stop the ball.​

Answer 1

GiveN :

• Mass of the ball, m = 100 g = 0.1 kg

• Final velocity, v = 0m/s [As the ball is stopped by the boy]

• Initial velocity, u = 10 m/s [Correction in the question]

• Time taken to stop the ball, t = 2 sec

In order to calculate the force applied by the boy to stop the ball we've to find the required force. We can solve this question by 2 methods.

1st method :

We'll solve directly by the simple method by substituting the values.

we know that,

$\longrightarrow\sf F = ma$

$\longrightarrow\sf F = m\dfrac{(v - u) }{t}$

$\longrightarrow\sf F = 0.1 \times \dfrac{(0-10) }{0.2}$

$\longrightarrow\sf F = 0.1 \times \dfrac{-10}{0.2}$

$\longrightarrow\sf F = 0.1 \times -50$

$\longrightarrow\sf\large{ \boxed{ \sf{ F = -5 N}}}$

$\therefore$ Force applied by the boy to stop the ball is 5 N.

⠀⠀_______________________

2nd method :

We know that, total linear momentum of an object remains constant if no external unbalanced force acts on it.

So,

Applying this concept, we get :

$\longrightarrow\sf F = \dfrac{Change \: in \: momentum}{Time \:Taken}$

$\longrightarrow\sf F = \dfrac{mv - mu}{t}$

$\longrightarrow\sf F = \dfrac{0 - 0.1 \times 10}{0.2}$

$\longrightarrow\sf F = \dfrac{ - 0.1 \times 10}{0.2}$

$\longrightarrow \large{ \boxed{\sf F = -5 \:N}}$

$\therefore$ Force applied by the boy to stop the ball is 5 N.

Answer 2

Correct Question : A ball of mass 100g moving with a velocity 10m/s is stopped by boy in 0.2s. Calculate the force applied by the boy to stop the ball.

Given Parameters :

• Mass of the ball (m) = 100 g = 0.1 kg
• Initial Velocity (u) = 10m/s
• Final Velocity (v) = 0 m/s
• Time taken (t) = 2 seconds

Answer:

• According to newton's second law of motion "force on a body is the product of mass and acceleration". :]

Acceleration is the change in velocity of a body with time;

$:\implies \sf Acceleration = \dfrac{Final \: Velocity- Initial \: Velocity}{Time}$

$:\implies \sf Acceleration = \dfrac{v- u}{t}$

$\bullet \: \: \sf Since ,\: Force = mass \times Acceleration$

$:\implies \sf Force = mass \times \Bigg \lgroup\dfrac{Final \: Velocity- Initial \: Velocity}{Time} \Bigg \rgroup$

$:\implies \sf Force = mass \times \bigg \lgroup\dfrac{v-u}{t} \bigg \rgroup$

$:\implies \sf Force = 0.1 \times \bigg \lgroup\dfrac{0-10}{0.2} \bigg \rgroup$

$:\implies \sf Force = 0.1 \times \dfrac{-10}{0.2}$

$:\implies \sf Force = 0.1\times - 50$

$:\implies \underline{ \boxed{ \sf Force = - 5 \:Newton's }}$

Therefore, Force applied by the boy to stop the ball is 5 N.