Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Two bodies A and B of masses 10 kg and 20 kg respectively are at the same height above the ground. Which of the two has greater potential energy?
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 of mass m is moved from ground to a height h. If force of gravity on mass of 1 kg is g newton, find the potential energy stored in the body.
Two bodies of same masses are placed at heights h and 2h. Compare their gravitational potential energy.
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?
Is potential energy a vector or a scalar quantity?
A weightlifter is lifting weights of mass 200 kg up to a height of 2 metres. If g = 9.8 m s−2, calculate :
potential energy acquired by the weights.
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
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)
On what factors does the gravitational potential energy of a body depend?
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 784 J of work was done in lifting a 20 kg mass, calculate the height through which it was lifted. (g = 9.8 m/s2)
A man is instructed to carry a package from the base camp at B to summit A of a hill at a height of 1200 metres. The man weighs 800 N and the package weighs 200 N. If g = 10 m/s2,
- how much work does man do against gravity?
- what is the potential energy of the package at A if its is assumed to be zero at B?
A car is accelerated on a levelled road and acquires a velocity 4 times of its initial velocity. During this process, the potential energy of the car :
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)
A body is falling from a height of h. After it has fallen a height `"h"/2`, it will possess
