who develops more power,an 80kg man who walks up a height of 20 steps each 17.5cm high in 7second or one who pushes an 80kg box up a frictionless slope to a height of 5m in 10seconds? Give a reason for your answer
powerman=mgh/time=80g*20*.175/7
powerbox=80*g*5/10
which is greater?
To determine which scenario requires more power, we need to calculate the work done in each situation and divide it by the time taken.
1. Scenario 1: Man climbing stairs
To calculate the work done, we can use the formula: Work = Force x Distance
Distance: Each step is 17.5 cm high, and the man climbs 20 steps. So the total vertical distance covered is 17.5 cm x 20 = 350 cm or 3.5 m.
Force: The force required is equal to the man's weight, which is 80 kg x 9.8 m/s^2 (acceleration due to gravity) = 784 N.
Work: Work = Force x Distance = 784 N x 3.5 m = 2744 Joules
Power: Power = Work / Time = 2744 J / 7 s = 392 Watts
2. Scenario 2: Pushing a box up a slope
To determine the work done, we need to calculate the change in potential energy of the box.
Change in height: The box is pushed up a slope to a height of 5 meters.
Force: The force required to push the box up the frictionless slope is equal to the man's weight, which is again 784 N.
Work: Work = Force x Distance = 784 N x 5 m = 3920 Joules
Power: Power = Work / Time = 3920 J / 10 s = 392 Watts
Both scenarios require the same amount of power, 392 Watts. This is because the power is determined by the work done divided by the time taken. Although the distance covered and the time taken are different in each scenario, the work done is the same (as both involve moving an 80 kg object against gravity) and thus results in the same power output.
Therefore, the power developed in both scenarios is equal, regardless of the different distances and times involved.