Kinetic energy..

The mass of Munem and Shahriar is 40 kg and 30 kg respectively. Both of them are running in a race.

Assume that the momentum of Shahriar and Munem is equal. Who have the greater kinetic energy among them?

Munem Their kinetic energy is equal. Shahriar

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1 solution

Munem Shahriar
Jul 26, 2018
  • The mass and velocity of Munem is m 1 = 40 m_1 = 40 kg and v 1 v_1 .
  • The mass and velocity of Shahriar is m 2 = 30 m_2 = 30 kg and v 2 v_2 .

According to the condition, m 1 v 1 = m 2 v 2 m_1 v_1 = m_2 v_2 .

So,

The kinetic energy of Munem, E k = 1 2 m 1 ( v 1 ) 2 = ( m 1 v 1 ) 2 2 m 1 E_{k'} = \dfrac 12 m_1 (v_1)^2 = \dfrac{(m_1 v_1)^2}{2m_1} .

The kinetic energy of Shahriar, E k = 1 2 m 2 ( v 2 ) 2 = ( m 2 v 2 ) 2 2 m 2 E_{k''} = \dfrac12 m_2 (v_2)^2 = \dfrac{(m_2 v_2)^2}{2m_2} .

Now,

E k E k = ( m 1 v 1 ) 2 2 m 1 ( m 2 v 2 ) 2 2 m 2 = ( m 1 v 1 ) 2 2 m 1 × 2 m 2 ( m 2 v 2 ) 2 = m 2 m 1 = 30 40 = 3 4 \large \dfrac{E_{k'}}{E_{k''}} = \dfrac{\frac{(m_1v_1)^2}{2m_1}}{\frac{(m_2 v_2)^2}{2m_2}} = \dfrac{(m_1 v_1)^2}{2m_1} \times \dfrac{2m_2}{(m_2 v_2)^2} = \dfrac{m_2}{m_1} = \dfrac{30}{40} = \dfrac 34

Since E k > E k , E_ {k''} > E_{k'}, the kinetic energy of Shahariar is greater.

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