Chapter 9, Problem 11A

What will be the kinetic energy of an arrow having a potential energy of 50 J after it is shot from a bow?

To determine

The kinetic energy of an arrow having potential energy of 50 J.

Answer to Problem 11A

50 J

Explanation of Solution

Introduction:

For every day’s work, energy is necessary. Basically, energy is the capacity of doing work in a different form. This energy can be stored in different forms. The energy associated with the motion of the particle is kinetic energy.

Mathematically kinetic energy can be written as,

  $\therefore K=\frac{1}{2}m{v}^2$ -------------- (1)

Where,

m - Mass of the particle.

v - Velocity of the particle.

The energy associated with the position of the particle is the potential energy. For example, the energy stored in the dam is in the form of potential energy. Mathematically, it can be written as

  $\therefore P=mgh$ ------------------ (2)

Where,

m -Mass of the particle.

h - Height from the ground.

From equation (1) and (2), the total mechanical energy of the system is,

  $\therefore E=K+P$ ----------------- (3)

The potential energy of an arrow when it is in the bow is,

  $P=50\text{ J}$

Initial kinetic energy, $K=0\text{ J}$

When an arrow is shot from the bow, it acquires the kinetic energy. In this case, the potential energy of an arrow gets converted into kinetic energy. Since the total energy of the mechanical system is constant, the kinetic energy of the arrow when it is shot can be calculated as follows:

According to equation (3), energy, before the arrow is shot, is,

  $\begin{array}{l}{E}_{initial}=K+P=50\text{J}\\ \Rightarrow E_{initial}=0+P=50\text{J}\\ E_{final}=E_{initial}\\ E_{final}=K\text{'}+P\text{'}=50\text{J}\\ P\text{'}=0\Rightarrow K\text{'}=50\text{J}\end{array}$

Conclusion:

Since energy before and after the shot is the same, the kinetic energy of an arrow after it is shot from the bow is 50 J.