A body weighing 10 kg is lifted to a height of 50 m in 20 seconds . What is his power? ( g = 9 . 8 m / s 2 )

Given, Mass, m = 10 k g , Height, h = 50 m , Acceleration due to gravity, g = 9.8 m / s 2 In lifting the body, the person is acting against the gravity. Therefore, wo r k d o n e = m × g × h = ( 10 kg ) × ( 50 m ) × ( 9 .8 m / s 2 ) = 4900 J Average power (or simply power) with which work was done, P o w e r = t o t a l w o r k d o n e t i m e t a k e n = 10 × 50 × 9.8 20 = 245 W

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What is the definition of 'returns to scale' in economics?

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Important Questions on Work, Energy and Power

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Physics>Mechanics>Work, Energy and Power>Work

The work done to raise a mass

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from the surface of the earth to a height

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Let

a_{1}, a_{2}, {\dots . . a}_{10}

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\frac{a_{3}}{a_{1}} = 25,

then

\frac{a_{9}}{a_{5}}

equals:

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Physics>Mechanics>Work, Energy and Power>Work

A block of mass

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\frac{g}{2}

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

t

is,

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A rectangle is inscribed in a circle with a diameter lying along the line

3 y = x + 7 .

If the two adjacent vertices of the rectangle are

(- 8, 5)

and

(6, 5),

then the area of the rectangle

(

in sq. units

)

is:

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Let

a, b

and

c

be the

7^{t h}, 11^{t h}

and

13^{t h}

terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then

\frac{a}{c}

is equal to:

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Physics>Mechanics>Work, Energy and Power>Work

A particle of mass

m

is moving in a circular path of constant radius

r

such that its centripetal acceleration

a_{c}

is varying with time

t

a_{c} = k^{2} r t^{2}

, where

k

is a constant. The power delivered to the particle by the force acting on it is -

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Physics>Mechanics>Work, Energy and Power>Work

A body weighing

10 kg

is lifted to a height of

50 m

20 seconds

. What is his power? (

g = 9.8 m / s^{2}

)

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Physics>Mechanics>Work, Energy and Power>Work

A box is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

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Determine the power of an engine required to lift $100000 kg$ of coal per hour from a mine which is $360 m$ deep. ( $g = 10 m / s^{2}$ )

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Physics>Mechanics>Work, Energy and Power>Work

An old man does

200 J

of work in

10 s

and a young man does

100 J

of work in

4 s

. (i) Who is delivering more power? (ii) Find the ratio of the power delivered by the old man to that delivered by the young man.

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Physics>Mechanics>Work, Energy and Power>Work

A family uses

8 kW

of power. Direct solar energy is incident on the horizontal surface at an average rate of

200 W

per square meter. If

20 %

of this energy can be converted to useful electrical energy, how large an area is needed to supply

8 kW

? Compare this area to that of the roof of a typical house.

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Physics>Mechanics>Work, Energy and Power>Work

A force

\vec{F} = 2 \hat{i} + 2 \hat{j} N

displaces a particle through

\vec{S} = 2 \hat{i} + 2 \hat{k}

m in 16 s. The power developed by

\vec{F}

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A car of mass

1000 kg

moves at a constant speed of

20 m s^{- 1}

up an incline. Assume that the frictional force is

200 N

and that where,

θ

is the angle of the incline to the horizontal.

\sin θ = \frac{1}{20}

g = 10 m s^{- 2}

. Find the power developed by the engine

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A boy of mass

40 kg

climbs up stairs of

50

steps, each of

10 cm

high, in

5 s

. Find the power developed by the boy. (

g = 10 m / s^{2}

)

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Physics>Mechanics>Work, Energy and Power>Work

An electric pump is used to fill an overhead tank of capacity 9

m^{3}

kept at a height of 10 m above the ground .If the pump takes 5 min to fill the tank by consuming 10 KW .power the efficiency of the pump should be (Take g=10

m s^{- 2}

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The engine of a train has to apply a force of

5000 N

to overcome friction to run at a uniform rate of

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Physics>Mechanics>Work, Energy and Power>Work

A car of mass $(m)$ accelerates, starting from rest, while the engine supplies constant power $P$ . Then velocity varies with time $(t)$ as

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Physics>Mechanics>Work, Energy and Power>Work

A machine gun fires six bullets per second into a target. The mass of each bullet is

3 g

and the speed

500 m s^{- 1}

. The power delivered to the bullets is

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A body is moving uni-directionally under the influence of a source of constant power. Its displacement in time t is proportional to

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The work done by the heart is

1 J

per beat. Find the power of the heart if it beats

72

times per minute.

What is the definition of 'returns to scale' in economics?

Important Questions on Work, Energy and Power

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