Advertisements
Advertisements
Question
Prove that the kinetic energy of a freely falling object on reaching the ground is nothing but the transformation of its initial potential energy.
Solution
Let the object be at point A i.e. at height h above the surface of Earth as shown in the figure below.
At point A
The object is stationary i.e. its initial velocity, u = 0.
Kinetic energy, `K = 1/2mv^2 = 1/2m u^2 = 0`
Potential energy, U = mgh ...... (i)
At point B
Let the velocity of the object be vB and the object has fallen through distance x.
Using the third equation of motion, we have
`v_B^2 = 0 + 2gx`
⇒ `v_B^2 = 2gx`
Kinetic energy , `K = 1/2mv_B^2 = mgx`
Potential energy , U = mg(h-x) ....(ii)
At point C
Let the velocity of the object be vC and the object has fallen through a distance h.
Using the third equation of motion, we have
`v_C^2 = 0 + 2gh`
⇒ `v_B^2 = 2gh`
Kinetic energy, `K = 1/2 mv_C^2 = mgh` ....(iii)
Potential energy, U = 0
From (i) and (iii), we see that the Potential energy of the object at point A has transformed into its kinetic energy at point C. Thus, it can be concluded that the kinetic energy of a freely falling object reaching the ground is nothing but the transformation of its initial potential energy.
APPEARS IN
RELATED QUESTIONS
State two factors on which the potential energy of a body at a certain height above the ground depends.
A bucket full of water is on the first floor of your house and another identical bucket with the same quantity of water is kept on the second floor. Which of the two has greater potential energy?
A body of mass m is moved from ground to a height h. If the force of gravity on mass of 1 kg is g newton, find the force needed to lift the body.
A body at a height possesses ______.
A body falls freely under gravity from rest. Name the kind of energy it will possess at the point from where it falls.
Two bodies A and B of equal masses are kept at heights of h and 2h respectively. What will be the ratio of their potential energies?
What happens to the potential energy of a body when its height is doubled?
A boy weighing 50 kg climbs up a vertical height of 100 m. Calculate the amount of work done by him. How much potential energy does he gain? (g = 9.8 m/s2)
To what height should a box of mass 150 kg be lifted, so that its potential energy may become 7350 joules? (g = 9.8 m/s2)
Give one example each of a body possessing : (i) kinetic energy, and (ii) potential energy.
A body of mass 2 kg is thrown vertically upwards with an initial velocity of 20 m/s. What will be its potential energy at the end of 2 s? (Assume g = 10 m/s2).
Explain by an example what is meant by potential energy. Write down the expression for gravitational potential energy of a body of mass m placed at a height h above the surface of the earth.
If we increase the velocity of a car moving on a flat surface to four times its original speed, its potential energy ______.
The potential energy of your body is least when you are ______.
How much energy is gained by a box of mass 20 kg when a man, raises the box by 0.5 m in order to place it inside the bus? (g=10 m/s-2)
Potential energy and heat energy are the two forms of mechanical energy.
The energy, possessed by an object due to its position is called ______.
A body is falling from a height of h. After it has fallen a height `"h"/2`, it will possess
