Gerry, who weighs 500 newtons, is late for class. It takes her 7.5 seconds to run up two flights of stairs, a total height of 8.0 meters. How much power does Gerry expend in her run upstairs?
533.33333
Power = Work/Time
= W*H/T
W is her weight and H is the height climbed. T = 7.5 s.
The answer will be in watts.
To calculate the power expended by Gerry in her run upstairs, we can use the formula:
Power = Work / Time
First, we need to calculate the work done by Gerry when she runs up the stairs. The work done is equal to the force applied multiplied by the distance covered:
Work = Force x Distance
The force applied by Gerry is equal to her weight, which is given as 500 Newtons. The distance covered is the height of the stairs, which is 8.0 meters.
Let us calculate the work done by Gerry:
Work = 500 N x 8.0 m
Work = 4000 Joules
Now, we can substitute the values into the formula to calculate power:
Power = Work / Time
Power = 4000 J / 7.5 s
Power ≈ 533.33 Watts
Therefore, Gerry expends approximately 533.33 Watts of power in her run upstairs.
To calculate the power Gerry expends while running upstairs, we need to use the formula:
Power = Work / Time
First, we need to calculate the work done by Gerry to climb the stairs, which is equal to the change in potential energy. The potential energy is given by the formula:
Potential energy = mass * gravity * height
Given that Gerry weighs 500 newtons, the mass can be calculated using the formula:
Weight = mass * gravity
So, mass = Weight / gravity
Let's calculate the mass:
mass = 500 N / 9.8 m/s^2
mass ≈ 51.02 kg
Now, we can calculate the potential energy:
Potential energy = mass * gravity * height
Potential energy = 51.02 kg * 9.8 m/s^2 * 8.0 m
Potential energy ≈ 3981.12 J (Joules)
Next, we divide the potential energy by the time taken to climb the stairs to find the power:
Power = Work / Time
Power = 3981.12 J / 7.5 s
Power ≈ 531.48 W (Watts)
Therefore, Gerry expends approximately 531.48 Watts of power while running upstairs.