Question

1. Write detailed answers?
a. Explain the difference between
potential energy and kinetic energy.
b. Derive the formula for the kinetic
energy of an object of mass m,
moving with velocity v.
c. Prove that the kinetic energy of a
freely falling object on reaching
the ground is nothing but the
transformation of its initial potential
energy.
d. Determine the amount of work done when an object is displaced at an angle of 30 with respect to the direction of the applied force .
e. If an object has 0 momentum it have kinetic energy ? Explain your answer
f. Why is the work done on an object moving with uniform circular. motion. zero ?
​

Answer 1

A : KINETIC ENERGY

Kinetic energy is the kind of en inergy present in a body due to the property of its motion.

• It can be easily transferred from one body to another
• The determining factors for kinetic energy are Speed or velocity and mass.
• Flowing water is one of the examples for kinetic energy
• It is relative with respect to nature

POTENTIAL ENERGY

• Potential Energy is the type of energy present in a body due to the property of its state.
• It is not transferable
• Here, the determining factors are Height/ distance and mass
• Water present at the top of hill is an example of potential energy
• It is non-relative with respect to nature

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B : Kinetic Energy:

The energy possessed by an object due to its motion is called as kinetic Energy.

Derivation:

Let us consider an object of mass " m " which is at rest on smooth horizontal plane.

Let a Force , F acts on the object and let the object from rest moves from point A to point B and covers a displacement S.

The WORK Done by Force on the object is :

Workdone = Force x displacement.

W= FxS ____(1).

From third equation of motion;

V^2 -U^2 =2aS

S= V^2 -U^2/2a ______(2)

By Newtons second law of motion:

F= ma

From equation 1 and 2

W= m*a* (V^2- U^2)/2a

As we have assumed object is at rest, u=0

W=m*V^2/2

The WORK Done appears as kinetic energy of the body.

Therefore,

K.E = (1/2 )mv^2

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C : When a free falling object touches ground...its kinectic energy gets converted into heat (produced due to friction) and sound energy.

When a free falling object touches ground...its kinectic energy gets converted into heat (produced due to friction) and sound energy.Hence kinetic engery gets transformed into heat and sound energy. And energy remains conserved.

Explanation:

Total energy at initial position = K.E + P.E = 0 + mgh

Total energy when it reaches the ground = K.E + P.E = 0.5mv^2 + 0

Velocity when it reaches the ground = sqrt(2gh)

Substitute velocity in total energy equation

Total energy when it reaches the ground = 0.5mv^2 = 0.5m * 2gh = mgh

We found that total energy when it reaches the ground = Total energy at initial position.

We found that total energy when it reaches the ground = Total energy at initial position.In other words, kinetic energy with which it hits the ground is the transformation of its initial potential energy.

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D : Work done on a body when the body moves at an angle to the direction of force applied.W=Fx d cosθwhere F is forced is displace,and θ is the angle between F and d.

Given that θ is 30°

Workdone =W=Fxd Cos30°

=Fxd √3/2

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E : Yes. It have kinetic energy

Momentum = Mass × Change in velocity

Kinetic energy = 0.5 × mass × velocity²

Momentum is zero when change in velocity is zero, but kinetic can never be zero when body is motion.

Also,

Momentum is vector (it has both magnitude and direction) but kinetic energy scalar (it has only magnitude).

___________________

F : work done =force *displacement

in case of uniform circular motion, displacement is zero because the object returns to the same initial point repeatedly

hence work done is zero

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