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A 16 kg block moving on a frictionless horizontal surface with a velocity of 4 m/s compresses an ideal spring and comes to rest. If the force constant of the spring be 100 N/m, then the spring is compressed by

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Important Questions on Work, Energy and Power

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

The work done to raise a mass

m

from the surface of the earth to a height

h

, which is equal to the radius of the earth is:

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

The work done on a particle of mass

m

by a force

K [\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} \hat{i} + \frac{y}{{(x^{2} + y^{2})}^{3 / 2}} \hat{j}]

(

K

being a constant of appropriate dimensions, when the particle is taken from the point

(a, 0)

to the point

(0, a)

along a circular path of radius

a

about the origin in the x-y plane is

EASY

Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

A force

F = 20 + 10 y

acts on a particle in

y

-direction where

F

is in Newton and

y

is in meter. Work done by this force to move the particle from

y = 0

y = 1 m

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

Consider a force

\vec{F} = - x \hat{i} + y \hat{j}

. The work done by this force in moving a particle from point

A (1,0)

B (0,1)

along the line segment is : (all quantities are in SI units)

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EASY

Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

A particle moves from a point

(- 2 \hat{i} + 5 \hat{j})

(4 \hat{j} + 3 \hat{k})

when a force of

(4 \hat{i} + 3 \hat{j}) N

is applied. How much work has been done by the force?

HARD

Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

A force

(F) = - 5 \hat{i} - 7 \hat{j} + 3 \hat{k}

acting on a particle causes a displacement

(s) = 3 \hat{i} + 2 \hat{j} + a \hat{k}

in its own direction. If the work done is

14 J

, then the value of

a

is:

HARD

Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals

μ

. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR.
The values of the coefficient of friction

μ

and the distance

x = (Q R)

, are respectively close to:

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

When a rubber string is stretched through a distance

x

, the restoring force developed has a magnitude

(p x + q x^{2} + r x^{3})

where

p, q

and

r

are constants. Work done in stretching the unstretched rubber string by a distance

l

, is

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

A time dependent force

F = 6 t

acts on a particle of mass

1 kg

. If the particle starts from the rest, the work done by the force during the first

1 \sec

will be:

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

A block of mass $m$ slides from rest at a height $H$ on a frictionless inclined plane as shown in the figure. It travels a distance $d$ across a rough horizontal surface with coefficient of kinetic friction $μ$ and compresses a spring of spring constant $k$ by a distance $x$ before coming to rest momentarily. Then the spring extends and the block travels back attaining a final height of $h$ .

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Then

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

If a force

\vec{F} = \hat{i} - 2 \hat{j} - 4 \hat{k}

acting on a particle displaces it from

(1, 1, 1)

(2, - 1, 0),

then the work done by the force (in units of work) is

MEDIUM

Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

A block of mass

m

is kept on a platform which starts from rest with a constant acceleration

\frac{g}{2}

upwards, as shown in the figure. Work done by normal reaction on block in time

t

is,

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

A person pushes a box on a rough horizontal platform surface. He applies a force of

200 N

over a distance of

15 m

. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to

100 N

. The total distance through which the box has been moved is

30 m

. What is the work done by the person during the total movement of the box?

HARD

Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

A particle is moved along a path

A B - B C - C D - D E - E F - F A,

as shown in figure, in presence of a force

\vec{F} = (α y \hat{i} + 2 α x \hat{j}) N,

where

x

and

y

are in meter and

α = - 1 N m^{- 1} .

The work done on the particle by this force

\vec{F}

will be ____ Joule.
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EASY

Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

Two springs of spring constants

K

and

2 K

are stretched by same force. If

W_{1}

and

W_{2}

are the energies stored in them respectively then

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

The work done by a force

\vec{F} = - 5 x^{4} \hat{i} N

in displacing a body from

x = 2 m

x = - 2 m

EASY

Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

A particle of mass

10 g

is thrown vertically upwards with a speed of

20 m s^{- 1}

. The work done by the gravitational force during the time the particle moves upward is

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

Consider a drop of rain water having mass

1 g

falling from a height of

1 km

. It hits the ground with a speed of

50 m s^{- 1}

. Take

g

constant with a value

10 m s^{- 2}

. The work done by the (i) gravitational force and the (ii) resistive force of air is

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

Two similar springs

P

and

Q

have spring constants

K_{P}

and

K_{Q}

, such that

K_{P} > K_{Q}

. They are stretched, first by the same amount (case a), then by the same force (case b). the work done by the springs

W_{P}

and

W_{Q}

are related as respectively, in case

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Physics>Mechanics>Work, Energy and Power>Potential Energy of a Spring

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude
F = ax + bx² where a and b are constants. The work done in stretching the unstretched rubber-band by L is :

A 16 kg block moving on a frictionless horizontal surface with a velocity of 4 m/s compresses an ideal spring and comes to rest. If the force constant of the spring be 100 N/m, then the spring is compressed by

Important Questions on Work, Energy and Power

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