A bullet of mass 10 g traveling horizontally with a velocity of 150 m s–1 strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also, calculate the magnitude of the force exerted by the wooden block on the bullet.
Solution and Explanation
Mass of bullet, m = 10g = \(\frac{10}{1000}\)kg = 0.001kg
Initial velocity, u = 150 ms-1
Final velocity, v = 0 (since the bullet finally comes to rest)
Time, t = 0.03s
From the equation of motion, v = u + at
0 = 150 + a × 0.03
a =\(-\frac{150}{0.03}\) = - 5000 ms-2
The magnitude of the force applied by the bullet on the block, F = ma = 0.01 × - 5000 = 50N
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Concepts Used:
Laws of Motion
The laws of motion, which are the keystone of classical mechanics, are three statements that defined the relationships between the forces acting on a body and its motion. They were first disclosed by English physicist and mathematician Isaac Newton.
Newton’s First Law of Motion
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion
Newton's 2nd law of motion deals with the relation between force and acceleration. According to the second law of motion, the acceleration of an object as built by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Newton’s Third Law of Motion
Newton's 3rd law of motion states when a body applies a force on another body that there is an equal and opposite reaction for every action.
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