Question

A 28-g rifle bullet traveling at 300 m/s embeds itself in a3.1-kg pendulum hanging on a 2.8-m-long string, whichmakes the pendulum swing upward in an arc. Determinethe vertical components of the pendulum’smaximum displacement.

Answer 1

Given:

The mass of the bullet, m=28 g=0.028 kg

The speed of the bullet, v=300 m/s

The mass of the pendulum, M=3.1 kg

The length of the string, l=2.8 m

To find:

The vertical component of the pendulum's maximum displacement.

Step-by-step explanation:

The law of conservation of energy states that energy can neither be created nor be destroyed. Thus the kinetic energy of the bullet will be transferred into the kinetic energy of the bullet and the pendulum. Which will be converted into its potential energy when it reaches the maximum height, i.e, the vertical component of its maximum displacement.

Thus,

`(1)/(2)mv^2=(m+M)gh`

Where g is the acceleration due to gravity and h is the vertical component of the pendulum's maximum displacement.

On rearranging the above equation,

`h=(mv^2)/(2(m+M)g)`

On substituting the known values,

`\begin{gathered} h=(0.028*300^2)/(2(0.028+3.1)*9.8) \\ =41.1\text{ m} \end{gathered}`

Final answer:

Thus the vertical component of the maximum displacement of the pendulum is 41.1 m