Advertisements
Advertisements
Question
A body of mass m is moving with a velocity v. Write the expression for its kinetic energy.
Advertisements
Solution
Assume that a mass-m body is travelling at a velocity of v. An opposing force, F brings it to rest.
Let a represent the force's uniform retardation, and let it travel a distance of S before coming to rest at T. Then,
The kinetic energy of the body = the work done by the retarding force in stopping it.
Kinetic energy = Force × displacement
= F × S ...(i)
Retarding force F = ma ...(ii)
Initial velocity u = v, final velocity v = 0
From the relation v2 = u2 +2aS
0 = v2 - 2aS (since a is the retardation)
∴ Displacement S = `v^2/(2a)` ...(iii)
Substituting the values of F and S from equation (ii) and (iii) in equation (i), we get
kinetic energy `K = F × S = ma × v^2/(2a) = 1/2 mv^2`
Kinetic energy = `1/2 ` mass × (velocity)2
APPEARS IN
RELATED QUESTIONS
Name the type of energy (kinetic or potential) possessed by the following:
A bullet fired from a gun.
Give one relevant example for the following transformation of energy :
Chemical energy to light energy.
A boy of mass m climbs up a staircase of vertical height h.
(a) What is the work done by the boy against the force of gravity?
(b) What would have been the work done if he uses a lift in climbing the same vertical height?
What is meant by the renewable and non-renewable sources of energy? Distinguish between them giving two examples of weach.
What is a solar cell?
Show that the quantity 2K/v2 has the unit of mass, where K is the kinetic energy of the body.
State the energy changes which take place when:
In a heat engine.
A ball of mass 200 g falls from a height of 5 m. What will be its kinetic energy when it just reaches the ground? (g = 9.8 m s−2)
You do not have rangoli powder. What things can you use as an alternative?
The major problem in harnessing nuclear energy is how to
