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
Pa/Pb = (W/ta) / (W/tb)
or
Pa/Pb = tb / ta = 15/20
or
Pa/Pb = 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 106 J
(6)
W = mgh
or height/depth would be
h = W/mg
here,
W = 800J
m = 40kg
g = 9.81 m/s2
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/s2
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