A particle of mass m moves on a straight line with its velocity varying with the distance travelled, according to the equation ν = a x , where a is a constant. Find the total work done by all the forces during a displacement from x = 0 to x = d .

Given, particle moves from x = 0 to x = d . Displacement of particle s = d - 0 = d . . . ( 1 ) The relation between velocity and position given by, v = a x Differentiating with respect to time(using chain rule), d v d t = a 2 x · d x d t = a 2 x · v , ∵ v = a x ⇒ d v d t = a 2 x × a x = a 2 2 Force acting on the particle, F = m d v d t = m a 2 2 . . . 2 As the force is constant, the work done by the force is W = F s cos θ ⇒ W = F s , as θ = 0 ° From equation 1 and 2 W = m a 2 d 2

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JEE Main

IMPORTANT

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Find the average frictional force needed to stop a car weighing $500 kg$ at a distance of $25 m$ if the initial speed is $72 km h^{- 1}$ .

Important Questions on Work and Energy

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 8 - Work and Energy>EXERCISES>Q 14

Find the average force needed to accelerate a car weighing

500 kg

from rest to

72 km h^{- 1}

through a distance of

25 m

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 8 - Work and Energy>EXERCISES>Q 15

A particle of mass

m

moves on a straight line with its velocity varying with the distance travelled, according to the equation

ν = a \sqrt{x}

, where

a

is a constant. Find the total work done by all the forces during a displacement from

x = 0

x = d

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 8 - Work and Energy>EXERCISES>Q 16

A block of

2.0 kg

mass kept at rest on an inclined plane of inclination

37 °

is pulled up the plane by applying a constant force of

20 N

parallel to the incline. The force acts for one second.

(a)

Show that the work done by the applied force does not exceed

40 J

(b)

Find the work done by the force of gravity in that one second if the work done by the applied force is

40 J

(c)

Find the kinetic energy of the block at the instant the force ceases to act. Take

g = 10 m s^{- 2}

MEDIUM

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 8 - Work and Energy>EXERCISES>Q 16

A block of mass of

2.0 kg

kept at rest on an inclined plane of inclination

37 °

is pulled up the plane by applying a constant force of

20 N

parallel to the incline. The force acts for one second. Find the work done by the force of gravity in that one second if the work done by the applied force is

40 J

MEDIUM

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 8 - Work and Energy>EXERCISES>Q 16

A block of mass

2 kg

kept at rest on an inclined plane of inclination

37 °

is pulled up the plane by applying a constant force of

20 N

parallel to the incline. The force acts for one second. Find the kinetic energy of the block at the instant the force ceases to act. Take

g = 10 m s^{- 2}

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 8 - Work and Energy>EXERCISES>Q 17

A block of mass of

2.0 kg

is pushed down an inclined plane of inclination

37 °

with a force of

20 N

acting parallel to the incline. It is found that the block moves on the incline with an acceleration of

10 m s^{- 2}

. If the block started from rest, find the work done

(a)

by the applied force in the first second,

(b)

by the weight of the block in the first second and

(c)

by the frictional force acting on the block in the first second. Take

g = 10 m s^{- 2}

MEDIUM

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 8 - Work and Energy>EXERCISES>Q 18

250 g

block slides on a rough horizontal table. Find the work done by the frictional force in bringing the block to rest if it is initially moving at a speed of

40 cm s^{- 1}

. If the friction coefficient between the table and the block is

0 \cdot 1

, how far does the block move before coming to rest?

EASY

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 8 - Work and Energy>EXERCISES>Q 19

Water falling from a

50 m

high fall is to be used for generating electric energy. If

1.8 \times 10^{5} kg

of water falls per hour and half the gravitational potential energy can be converted into electrical energy, how many

100 W

lamps can be lit with the generated energy?

Find the average frictional force needed to stop a car weighing 500 kg at a distance of 25 m if the initial speed is 72 km h-1.

Important Questions on Work and Energy

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Find the average frictional force needed to stop a car weighing $500 kg$ at a distance of $25 m$ if the initial speed is $72 km h^{- 1}$ .