a labourer lifts 100 stone to a height of 6m in two minute.if mass of each stone be one kilogram, calculate the average power
g=10m/s2
=>total mass=1×100
=>100kg
=>Height=6m
=>work done=mgh
100×10×6=6000J
Time=2 minutes=2×60=120 sec
=>Average power=work done/time taken
=6000/120
=50W.Ans
total mass = 1 kg x 100 = 100 kg
height = 6 m
time taken = 2 x 60 sec = 120 s
work done = mass x g (acceleration due to gravity ) x height
work done = 100 x 9.8 x 6
= 5880 J
average power = work done / time taken
= 5880 / 120
= 49 W
To calculate the average power, we need to know the work done by the labourer. The work done can be calculated using the formula:
Work = Force x Distance
In this case, the force applied by the labourer is equal to the weight of the stones being lifted. The weight can be calculated using the formula:
Weight = Mass x Gravity
Where the mass is given as 1 kilogram and the acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 1 kg x 9.8 m/s^2 = 9.8 N
Next, we can calculate the work done by multiplying the force by the distance:
Work = Force x Distance
Work = 9.8 N x 6 m = 58.8 Joules
The time taken to do this work is given as 2 minutes, which can be converted to seconds:
Time = 2 minutes x 60 seconds/minute = 120 seconds
Now we can calculate the average power using the formula:
Average Power = Work / Time
Average Power = 58.8 Joules / 120 seconds
Calculating this, we find that the average power is approximately 0.49 Watts.
To calculate average power, we first need to determine the work performed by the laborer. The work done can be calculated using the formula:
Work = Force x Distance
The force can be determined by multiplying the mass of each stone by the acceleration due to gravity (9.8 m/s²). In this case, the mass of each stone is 1 kilogram. Therefore, the force exerted on each stone is:
Force = Mass x Acceleration due to gravity
= 1 kg x 9.8 m/s²
= 9.8 N
The distance the stones are lifted is given as 6 meters. Now we can calculate the total work done:
Work = Force x Distance
= 9.8 N x 6 m
= 58.8 Joules (J)
Next, we need to determine the time it took to complete the work. The question states that it took 2 minutes (120 seconds) to lift the 100 stones.
Average power is defined as the work done per unit of time. So, the average power can be calculated as:
Power = Work / Time
Power = 58.8 J / 120 s
= 0.49 Watts (W)
Therefore, the average power exerted by the laborer is 0.49 Watts.