Question

A girl weighing 42 kg eats a banana whose energy is 980 calories. If this energy is used to go to height h, then find the value of h. ( 1 cal = 4.2 J)

Answer 1

Hint: The girl gets muscular energy by eating bananas. This muscular energy is converted into potential energy when the girl goes to the height h. So, 980 calories is used to gain the potential energy. This implies we have to equate 980 calories to the potential energy expression.

Complete step by step solution:
Mass of the girl, m = 42 kg
Energy gained by the girl on eating banana = 980 calories
While solving problems, we have to make sure that every quantity is in the same system of units as the energy is in calories, we have to convert it into joule before solving the equation.
980 cal = 980 × 4.2 J = 4116 J
The equation for potential energy is mgh
Where g is the acceleration due to gravity = 9.8 m/$s^2$
Equating the expression of potential energy to energy gained on eating banana
mgh = 4116J
42 × 9.8 × h = 4116 J
h = 10 m

The girl can climb 10 m on an eating banana. Here chemical energy gained by eating bananas is converted into muscular energy. While climbing the height h, the muscular energy is converted into potential energy.

Note: If the girl jumps from height h, then the potential energy will get converted into kinetic energy. She acquires velocity while coming down due to the gained kinetic energy. By observing the given situation carefully and by applying the law of conservation of energy, we can solve these kinds of problems very easily.