Question

A ball of mass 500 g is moving with a velocity of 50 m s-1. The ball is brought to rest by applying a constant force for 0.2 s. Calculate the force applied.

Answer 1

mass = 500 g = 0.5 kg

initial velocity = 50 m/s

final velocity = 0 m/s

time = 0.2 s

Force = mass × acceleration

Force = 0.5 × (v-u)/t

$force = 0.5 \times \frac{0 - 50}{0.2}$

Force = 0.5 × 250

Force = 125

therefore, the force exerted to stop the object was 125 N

Answer 2

AnswEr :

›»› The force applied by a ball is -125 N

Given :

• Mass of a ball (m) = 500 g
• Initial velocity of a ball (u) = 50 m/s
• Time taken (t) = 0.2 sec

To Calculate :

• Force applied by a ball (F) = ?

How to Calculate?

❒ To Calculate the force applied by a ball firstly we need to convert the unit of mass from gram to kg, after that we will find the Acceleration of a ball, then we will find the force applied by a ball on the basis of conditions given above.

Since, we are provided with the initial velocity and the time taken, we can use the first equation of motion to find the Acceleration produced or Acceleration of the ball.

But according to the given information, ball is moving with velocity 50 m/s After that ball came to the rest, i.e, the final velocity of the ball will be 0, although the Initial velocity will have some value.

Here, we concluded that :

→ Final velocity of the ball is 0 m/s.

After that, we are provided with the Mass and the Acceleration produced or Acceleration of the ball, we cab use Second law of Newton to find the Force applied by the ball.

Calculation :

→ Mass = 500 g

→ Mass = 500/1000

→ Mass = 0.5 kg

From first equation of motion

$\tt{: \implies v = u + at}$

⠀

$\tt{: \implies 0 = 50 + a \times 0.2}$

⠀

$\tt{: \implies 0 - 50 = 0.2a}$

⠀

$\tt{: \implies - 50 = 0.2a}$

⠀

$\tt{: \implies a = \dfrac{ - 50}{0.2} }$

⠀

$\frak{: \implies \underline{ \boxed{ \blue{ \frak{a = - 250 \: m/s^2}}}}}$

Now, we have two elements that used in formula, Mass and Acceleration of the ball,

• Mass of the ball (m) = 0.5 kg
• Acceleration of the ball (a) = -250 m/s²

And we need to calculate the Force applied by the ball.

We can find force applied by the ball by using the second law of Newton which says F = ma

So, let's calculate Force applied by ball.

From second law of Newton

$\tt{:\implies F = ma}$

⠀

$\tt{:\implies F = 0.5 \times - 250}$

⠀

$\frak{:\implies \underline{ \boxed{ \pink{ \mathscr{F = \frak{- 125} \: N}}}}}$

【NOTE : -ve sign indicates opposite direction.】

║Hence, the force applied by the ball is -124 N.║