1)a boy weighing 350 N runs up a hight of 30 steps . each 0.2m high .calculate the work done

2)it takes 20s for A to climb up a stair while B does the same in 15 s. Compare the work done and power developed by aand b.

3) A WEIGHT LIFTER LIFTED A WEIGHT OF 200 kgf to a height of 2.5 m in 5 s. Calculate 1)the work done 2) the power developed by him (take g = 10ms ^{ 2 } )

4) a car of mass 2000 kg is lifted up a distance of 30m by a crane in 60 s. A second crane does the same job in 120s . do the cranes consume the same or different amounts of fuel.

5) how much work can a 2 horse power motor do in one hour

6)a man does 800 j of work in lifting a 40 kg bucket from a well .calculate the depth of the well. (g= 10m/s ^{ 2 } )

7) a Sherpa of mass 80 kg is instructed to carry a package of 20 kg from t he base camp to summit of a mountain 1200 m high . 1) how much work the Sherpa has to do againdt the gravity 2) also find the change in the potential energy at the base of the mountain is taken as zero.(g=10m/s ^{ 2 } )

8)in how much time can a water pump of 500w ,lift 1000kg of water to an overhead tank at a height of 7m.

We shall use an important concept of potential energy which equals to the work done.

**(1)**

potential energy = mgh

weight = mg = 350N

h = total height = height of one step x number of steps = 0.2m x 30 = 6m

so,

work done = potential energy = (mg).h

or

W = 350 x 6

or

W = 2100 J

**(2)**

the magnitude of work done does not depend upon time taken but the distance (or height moved)

so, work done by both A and B will be same.

the power is given as

P = work done / time taken

so, it does depend upon time. As B (t = 15s) takes less time than A (t = 20s) it will generate more power.

so, we can also compare

P_{a}/P_{b} = (W/t_{a}) / (W/t_{b})

or

P_{a}/P_{b} = t_{b }/ t_{a} = 15/20

or

P_{a}/P_{b} = 3/4

**(3)**

we know, work done

W = PE = mgh

w = mg = 200kgf = 200/9.81 = 20.38 N

h = 2.5m

so,

W = 20.38 x 2.5

or W = 50.95 J

and

power = W/t = 50.95 / 5

or

P = 10.19 W

**(5)**

1 horse power = 746 Watts

so,

P = 2hp = 1492 W

now,

P = work done / time taken

so,

W = P x t

here t = 1hr = 3600s

so,

W = 1492 x 3600

or

W = 5.37 x 10^{6 }J

(6)

W = mgh

or height/depth would be

h = W/mg

here,

W = 800J

m = 40kg

g = 9.81 m/s^{2}

so,

h = 800 / (40 x 10)

or

h = 2 m

(8)

we know that power is given as

P = work done / time

so

t = W / P = mgh / P

here

P = 500W

m = 1000kg

g = 9.81 m/s^{2}

h = 7m

so, we get

t = (1000 x 9.81 x 7) / 500 = 68670 /500

thus, the time taken will be

t = 137.34 s

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