Question

calculate the kinetic energy of a body of mass 0.1 kg and momentum 20 kgm/s​

Answer 1

Provided that:

• Mass of a body = 0.1 kg
• Momentum = 20 kg m/s

To calculate:

• The kinetic energy

Solution:

• The kinetic energy = 2000 J

Using concepts:

• Momentum formula
• Kinetic energy formula

Using formulas:

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

• ${\small{\underline{\boxed{\sf{E_k \: = \dfrac{1}{2} \: mv^2}}}}}$

Where, p denotes momentum, m denotes mass of the body, v denotes velocity and E_k denotes kinetic energy.

Required solution:

~ Firstly let us find the velocity by using the formula of momentum!

$:\implies \sf Momentum \: = mas\times velocity \\ \\ :\implies \sf p \: = m \times v \\ \\ :\implies \sf p \: = mv \\ \\ :\implies \sf 20 = 0.1(v) \\ \\ :\implies \sf 20 \: = 0.1 \times v \\ \\ :\implies \sf \dfrac{20}{0.1} \: = v \\ \\ :\implies \sf \dfrac{200}{1} \: = v \\ \\ :\implies \sf 200 \: = v \\ \\ :\implies \sf v \: = 200 \: ms^{-1} \\ \\ :\implies \sf Velocity \: = 200 \: ms^{-1}$

~ Now let's calculate kinetic energy!

$:\implies \sf E_k \: = \dfrac{1}{2} \: mv^2 \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 0.1 \times (200)^{2} \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 0.1 \times 200 \times 200 \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 0.1 \times 40000 \\ \\ :\implies \sf E_k \: = \dfrac{1}{2} \times 4000 \\ \\ :\implies \sf E_k \: = \dfrac{1}{\cancel{{2}}} \times \cancel{4000} \\ \\ :\implies \sf E_k \: = 2000 \: J \\ \\ :\implies \sf Kinetic \: energy \: = 2000 \: Joules$