Question

Calculate the thermal energy lost in a collision if a 0.150 kg bullet travelling with a speed of 30 m/s strikes and embeds in to a metal ball of mass 3 kg at rest.
(a) 15.3 J (b) 90.3 (c) 64.3 J (d) 38.6 J

Answer 1

The thermal energy lost in collision is 64.3 J.

(c) is correct option.

Explanation:

Given that,

Mass of bullet = 0.150 kg

Mass of metal ball = 3 kg

Speed of bullet = 30 m/s

We need to calculate the kinetic energy of bullet

Using formula of kinetic energy

$K.E_{bu}=\dfrac{1}{2}mv^2$

Put the value into the formula

$K.E_{bu}=\dfrac{1}{2}\times0.150\times(30)^2$

$K.E_{bu}=67.5\ J$

We need to calculate the final velocity

Using conservation of momentum

$m_{1}u_{1}+m_{2}u_{2}=(m_{1}+m_{2})v$

Put the value into the formula

$0.150\times30+0=(0.150+3)v$

$v=\dfrac{0.150\times30}{(0.150+3)}$

$v=1.42\ m/s$

We need to calculate the kinetic energy of metal ball after collision

Using formula of kinetic energy

$K.E_{ba}=\dfrac{1}{2}\times mv^2$

Put the value into the formula

$K.E_{ba}=\dfrac{1}{2}\times3\times(1.42)^2$

$K.E_{ba}=3.02\ J$

We need to calculate the thermal energy lost in collision

Using formula of change energy

$\Delta K.E=K.E_{bu}-K.E_{ba}$

Put the value into the formula

$\Delta K.E=67.5-3.02$

$\Delta K.E=64.5\approx 64.3\ J$

Hence, The thermal energy lost in collision is 64.3 J.

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Topic :kinetic energy

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