Calculate the kinetic energy of a particle of mass M moving with a velocity v . Show that P = F → . v → where P is the power, F → is the force and v → is the velocity along an inclined plane.

a) To Calculate the kinetic energy of a particle of mass M moving with a velocity v . b) To show that P = F → . v → where P is the power, F → is the force and v → is the velocity along an inclined plane. The energy possessed by the virtue of motion is called kinetic energy. When work is done without allowing it changes the potential energy, in that case, work done is equal to a change in the kinetic energy. We know that according to work-energy theorem, work done=difference of kinetic energy W = ∫ u v f d x = ∫ u v m d v d t d x = ∫ u v m v d v = m 2 v 2 u v = m 2 ( v 2 - u 2 ) If the initial velocity u = 0 , then difference of kinetic energy is numerically equal to kinetic energy. So, the kinetic energy K . E . = 1 2 m v 2 The work done by a variable force whose both magnitude and direction are variable is given by the relation. W = ∫ F → . dx → = ∫ Fdx cos θ Power can be written can be written as: P = dW dt = d dt ( Fdx cos θ ) ⇒ P = F ( d dt dx ) cos θ = F v cosθ where F is the applied force, dx is the displacement and cos θ is the angle between them.

E M B I B E

A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 2

HARD

11th West Bengal Board

IMPORTANT

Earn 100

What do you mean by 'work done by a couple'? If a body makes $n$ complete rotations, show that work done $= 2 πnτ$ where $τ$ is the torque applied.

Important Questions on Work, Energy and Power

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 3

What do you mean by 'horse-power'? Obtain a relation between horse-power and kilowatt.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 4

How would you find out the work done by a variable force, varying both in magnitude and direction?

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 5

Describe the difference between kinetic energy and potential energy, mentioning the ways in which they are measured.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 6

Explain what you understand by 'kinetic energy'. Show that the work done by a force is equal to the change of kinetic energy.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 7

Prove that if a piston moves in a cylinder due to a constant pressure, the work done in each stroke is equal to the product of the pressure and the volume swept out by the piston.

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 8

Calculate the kinetic energy of a particle of mass