Question

A bullet of mass 10g traveling horizontally with a velocity of 150$m{s}^{-1}$ strikes a stationary wooden block and comes to rest in 0.03s. 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.

Answer 1

Hint: Newton’s law gives a relation between a body which is motion and forces acting on that body. The three laws of Newton are used for the following questions. The four basic Newton’s equation of motion is used. According to the question and data provided we have to form an equation and substitute the given values in the equation.

Formula used:
Equation of motion
 \[v=u+at\]
 \[{{v}^{2}}={{u}^{2}}+2as\]
 \[F=ma\]

Complete step-by-step solution:
Let \[u\] be the initial velocity of bullet travelling with acceleration \[a\] in time \[t\] seconds. \[v\] be the final velocity of bullet
Given-
Initial velocity \[u=150m/s\]
Final velocity \[v=0\]
Mass \[m=10g=0.01kg\]
Time \[t=0.03s\]
Applying Newton's equation
 \[\begin{align}
  &\Rightarrow v=u+at \\
 &\Rightarrow 0=150+a(0.03) \\
\end{align}\]
Rearranging the terms \[a=-5000m/{{s}^{2}}\]
A negative sign indicates that the acceleration is negative which is called retardation.
For calculating the speed of the bullet apply Newton’s second law of motion
 \[\begin{align}
  &\Rightarrow {{v}^{2}}={{u}^{2}}+2as \\
 &\Rightarrow 0={{150}^{2}}+2\times (-5000)\times s \\
 &\Rightarrow s=2.25m \\
\end{align}\]
Applying Newton’s second law of motion
Force applied by the wooden block
Now, magnitude of force is given by
 \[\begin{align}
  &\Rightarrow |F|=m|a| \\
 &\Rightarrow |F|=0.01\times 5000 \\
\end{align}\]
 \[F=50N\]

Additional Information:
Newton’s first law: Object will continue to be in rest or in motion unless an external force is applied to it.
Newton's second law: The applied force on an object is equal to the product of acceleration and mass of the object.
Newton’s third law: When two objects interact with each other, then the force acting between them is equal in magnitude and opposite in direction.

Note: While calculating the magnitude of force always remember if there is retardation i.e. negative acceleration then the modulus makes that negative acceleration positive. The concept of Newton’s law should be crystal clear to solve the problems related to classical mechanics.