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.
Advertisements
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
The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
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?
Find the gravitational potential energy of 2.5 kg mass kept at a height of 15 m above the ground. The force of gravity on mass 1 kg is 10 n.
The potential energy of a body is the energy by virtue of its ______.
A body at a height possesses ______.
A spring is kept compressed by a small trolley of mass 0.5 kg lying on a smooth horizontal surface as shown in the adjacent fig. When the trolley is released, it is found to move at a speed v = 2 m s-1. What potential energy did the spring possess when compressed?
A ball of mass m is thrown vertically up with an initial velocity so as to reach a height h. The correct statement is:
State whether the following statement is true or false :
The potential energy of a body of mass 1 kg kept at a height of 1 m is 1 J.
A weightlifter is lifting weights of mass 200 kg up to a height of 2 metres. If g = 9.8 m s−2, calculate :
work done by the weightlifter
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)
On what factors does the gravitational potential energy of a body depend?
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 ______.
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
