Question

(a) An arrow moves forward when released from a stretched bow. State the type of energy possessed by the bow? What is the type of energy gained by the arrow?
(b) A boy of mass $50{\text{ }}kg$ climbs up a vertical height of $100{\text{ }}m$. Calculate the amount of potential energy he gains.

Answer 1

Hint: When a wire or string is stretched, potential energy is gained. This potential energy is known as elastic potential energy. When the stored energy releases it converts into kinetic energy which is associated with moving mass. In the question next to it we will use mass and height and from the formula of potential energy we will find the answer.

Complete step by step answer:
(a) As stated in the question, the arrow moves forward when released from a stretched bow. The stretched bow gains potential energy due to its change in deformation or shape. Such type of energy is known as elastic potential energy. So, it is clear that the energy possessed by the bow is elastic potential energy. When the elastic potential energy is released it converts into another energy. The arrow thus gains kinetic energy. Kinetic energy is associated with moving mass. And as the arrow is moving it gains kinetic energy. The type of energy gained by the arrow is kinetic energy.

(b) A boy of mass $50{\text{ }}kg$ climbs up a vertical height of $100{\text{ }}m$ is given here. We have to find the potential energy he gained.
Thus from the formula of potential energy we get,
$P = mgh - - - - \left( 1 \right)$
$P = $ potential energy, $m = $mass of the body $ = 50{\text{ }}kg$ and $g = 9.8{\text{ }}\dfrac{m}{{{s^2}}} = $ acceleration due to gravity.
$h = 100{\text{ }}m = $ height
Substituting the given values in equation $\left( 1 \right)$ we get,
$\therefore P = 50 \times 9.8 \times 100 = 4900{\text{ }}J = 4.9\,kJ$

So, the potential energy gained is $4.9\,kJ$.

Note: Energy is never gained or never lost. It always transforms from one energy to another energy. Here the stored potential energy of the bow is converted into the kinetic energy with the moving arrow. Another vital formula is their Kinetic Energy + Potential Energy= Total Energy.