Question

A ball of mass 10 g is moving with a velocity of 50 m/s. On applying a constant force for 2 seconds on the ball, it acquires a velocity of 70 m/s.
Calculate the initial and final momentum of the ball.

Answer 1

Provided that:

• Mass of the ball = 10 grams
• Initial velocity = 50 mps
• Final velocity = 70 mps
• Time taken = 2 seconds

To calculate:

• Initial momentum
• Final momentum

Solution:

• Initial momentum = 0.50 or 0.5 kg m/s

• Final momentum = 0.70 or 0.7 kg m/s

Knowledge required:

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

Using concepts:

• Formula to convert g into kg.
• Initial momentum formula.
• Final momentum formula.

Using formulas:

• Formula to convert grams into kilograms is mentioned:

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

• Formula to calculate initial momentum is mentioned below:

• ${\small{\underline{\boxed{\pmb{\sf{p \: = mu}}}}}}$

• Formula to calculate final momentum is mentioned below:

• ${\small{\underline{\boxed{\pmb{\sf{p' \: = mv}}}}}}$

Where, p denotes initial momentum, p′ denotes final momentum, m denotes mass, u denotes initial velocity and v denotes final velocity.

Required solution:

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

$:\implies \sf 1 \: g \: = \dfrac{1}{1000} \: kg \\ \\ :\implies \sf 10 \: g \: = \dfrac{10}{1000} \: kg \\ \\ :\implies \sf 10 \: g \: = \dfrac{1}{100} \: kg \\ \\ :\implies \sf 10 \: g \: = 0.01 \: kg \\ \\ {\pmb{\sf{Henceforth, \: converted!}}} \\ \\ \therefore \: \: \sf Mass \: = 0.01 \: kilograms$

~ Now let us find out the initial momentum by using suitable formula!

$:\implies \sf p \: = mu \\ \\ :\implies \sf p \: = 0.01(50) \\ \\ :\implies \sf p \: = 0.50 \: or \: 0.5 \: kg \: ms^{-1} \\ \\ {\pmb{\sf{Henceforth, \: solved!}}}$

~ Now let us find out the final momentum by using suitable formula!

$:\implies \sf p' \: = mv \\ \\ :\implies \sf p' \: = 0.01(70) \\ \\ :\implies \sf p' \: = 0.70 \: or \: 0.7 \: kg \: ms^{-1} \\ \\ {\pmb{\sf{Henceforth, \: solved!}}}$