Question

A bullet of mass 0.015kg strikes a metal plate of thickness 10 cm with a velocity of 400 m/s and emerges from it with a velocity of 260 m/s find the average resistance offered by the plate to the motion of bullet

Answer 1

Answer:

• Resistance Offered (F) is 6930 N.

Given:

1. Mass of the body (M) = 0.015 Kg.
2. Thickness (s) = 10 cm
3. Initial velocity (u) = 400 m/s
4. Final Velocity (v) = 260 m/s

Explanation:

$\rule{300}{1.5}$

From Third Kinematic Equation,

$\large \bigstar \; {\boxed{\tt v^2 - u^2 = 2as}} \\\\\\ \bold{Here}\begin{cases}\text{v Denotes final Velocity} \\ \text{u Denotes Initial Velocity} \\ \text{a Denotes acceleration} \\ \text{s Denotes distance}\end{cases}$

Now,

$\large{\boxed{\tt v^2 - u^2 = 2as}}$

Substituting the Values,

$\tt \longmapsto (260)^2 - (400)^2 = 2 \times a \times 10 \; cm \\\\\\ \dagger \; 1 cm = 10^{-2} \; m \implies 10 \; cm = 10 \times 10^{-2} \; m \\\\\\ \longmapsto (260)^2 - (400)^2 = 2 \times a \times 10 \times 10^{-2} \; m \\\\\\ \longmapsto (260)^2 - (400)^2 = 2 \times a \times 10 \times 10^{-2} \\\\\\ \longmapsto 67600 - 160000 = 2 \times 10^{-1} \times a \\\\\\ \longmapsto - 92400 = 0.2 \times a \\\\\\ \longmapsto a = \dfrac{- 92400 \times 10}{2} \\\\\\ \longmapsto a = \dfrac{- 924000}{2}$

$\\\\\\ \tt \longmapsto a = \cancel{\dfrac{- 924000}{2}} \\\\\\ \longmapsto{\underline{\boxed{\tt a = - 462000 \; m/s^2}}}$

$\rule{300}{1.5} \\\\ \rule{300}{1.5}$

From Newton's Second law of Motion

$\large \bigstar \; {\boxed{\tt F = ma}} \\\\\\ \bold{Here}\begin{cases}\text{M Denotes Force} \\ \text{a Denotes Acceleration} \\ \text{F denotes Force Acting}\end{cases} \\\\\\ \text{Now,} \\\\ \large{\boxed{\tt F = ma}}$

Substituting the Values,

$\tt \longmapsto F = 0.015 \times - 462000 \\\\\\ \longmapsto F = \dfrac{15}{1000} \times - 462000 \\\\\\ \longmapsto F = \dfrac{6930000}{1000} \\\\\\ \longmapsto F = \cancel{\dfrac{6930000}{1000}} \\\\\\ \longmapsto{\underline{\boxed{\red{\tt F = 6930 \; N}}}}$

∴ Resistance Offered (F) is 6930 Newtons.

$\rule{300}{1.5}$

Answer 2

Average resistance offered by the plate to motion of bullet is 6930 N

Explanation:

• Resistance force is the opposite force offered by the material to the movement of bullet. This can be calculated as the product of mass of bullet and acceleration of the bullet, it is similar to the frictional force

Given mass of bullet = 0.015 kg

thickness of plate = distance moved by the bullet = 10 cm = 0.1 m

initial velocity of the bullet = 400 m/s

final velocity of the bullet = 260 m/s

Acceleration of the bullet can be calculated by following equation

=> v² -u² =2 as

=> 260² -400² =2 a(0.1)

=> 67600 - 160000 = 0.2 a

=> a = - 92400/ 0.2

=> a = -92400 * 5

=> a = - 462000 m/s²

force exerted by the bullet can be calculated by F= ma

=> F = 0.015 * (-462000)

=> F = - 15*462

=> F = -6930 N

So, Resisting force is 6930 N

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