Question 44: Work, Energy and Power & Circular Motion

Question

A bullet of mass $$50 \mathrm{~g}$$ is fired with a speed $$100 \mathrm{~m} / \mathrm{s}$$ on a plywood and emerges with $$40 \mathrm{~m} / \mathrm{s}$$. The percentage loss of kinetic energy is :

Accepted Answer

To find the percentage loss of kinetic energy of the bullet, we first calculate the initial kinetic energy before the bullet hits the plywood and the final kinetic energy after it emerges. The formula for kinetic energy (KE) is given by:
$$KE = \frac{1}{2} mv^2$$
where $m$ is the mass of the object and $v$ is its velocity.
Let's calculate the initial and final kinetic energies.
Initial Kinetic Energy:
$$KE_{	ext{initial}} = \frac{1}{2} 	imes 50 	imes (100)^2 = \frac{1}{2} 	imes 50 	imes 10000 = 25 	imes 10000 = 250000 \, 	ext{g.m}^2/	ext{s}^2$$
Note: To keep units consistent, we used grams and meters per second. We can also convert the mass to kilograms (by dividing by 1000) which would result in the energy being calculated in Joules, but for the purpose of finding the percentage change, the form of units does not matter as long as they are consistent, since it will be a ratio.
Final Kinetic Energy:
$$KE_{	ext{final}} = \frac{1}{2} 	imes 50 	imes (40)^2 = \frac{1}{2} 	imes 50 	imes 1600 = 25 	imes 1600 = 40000 \, 	ext{g.m}^2/	ext{s}^2$$
The loss of kinetic energy is then:
$$\Delta KE = KE_{	ext{initial}} - KE_{	ext{final}} = 250000 - 40000 = 210000 \, 	ext{g.m}^2/	ext{s}^2$$
Finally, the percentage loss of kinetic energy can be calculated using the formula:
$$	ext{Percentage loss of KE} = \left( \frac{\Delta KE}{KE_{	ext{initial}}} ight) 	imes 100\%$$
$$	ext{Percentage loss of KE} = \left( \frac{210000}{250000} ight) 	imes 100\% = 0.84 	imes 100\% = 84\%$$
Thus, the percentage loss of kinetic energy is
84%
, which corresponds to
Option C
.

Answer

$$44 \%$$

Answer

$$16 \%$$

Answer

$$84 \%$$

Answer

$$32 \%$$

Work, Energy and Power & Circular Motion

A bullet of mass $50 \mathrm{~g} is fired with a speed 100 \mathrm{~m} / \mathrm{s} on a plywood and emerges with 40 \mathrm{~m} / \mathrm{s}$. The percentage loss of kinetic energy is :

Choose the correct answer: