Wayne wants to play the game also, but it takes him twice as long to get up the stairs, or 6 seconds to go up.
The force of gravity acting on Wayne's body is 2000 Newtons and stairs are 3 meters high. How much power
does Wayne generate each time he goes up the stairs?

Hi ! Here, I will help you to calculate the power generated. Power is work done per unit time. If a person or machine can do a large amount of work in the shortest possible time, it will produce or require a large amount of power. The relationship between power, work, and time is expressed in the equation:

[tex] \boxed{\sf{\bold{P = \frac{W}{t}}}} [/tex]

With the following condition :

P = power that produce or require (Watt)
W = work that had done (J)
t = interval of the time (s)

Because the person is moving upwards, the work done will be equal to the change in potential energy. See this equation !

[tex] \boxed{\sf{\bold{P = \frac{F \times \Delta h}{t}}}} [/tex] ... (1)

[tex] \boxed{\sf{\bold{P = \frac{m \times g \times \Delta h}{t}}}} [/tex] ... (2)

With the following condition :

F = acting force (N)
[tex] \sf{\Delta h} [/tex] = change of altitude (m)
m = mass of the object (kg)
g = acceleration of the gravity (m/s²)

Note :

Use equation 1, if the action force is known.
Use equation 2, if the action force is unknown.

Problem Solving :

We know that :

F = acting force = 2,000 N
[tex] \sf{\Delta h} [/tex] = change of altitude = 3 m
t = interval of the time = 6 s

What was asked :

P = power that produce or require = ... Watt

Step by step :

[tex] \sf{P = \frac{F \times \Delta h}{t}} [/tex]

[tex] \sf{P = \frac{2,000 \times \cancel{3} \:_1}{\cancel{6} \:_2}} [/tex]

[tex] \sf{P = \frac{2,000}{2}} [/tex]

[tex] \boxed{\sf{P = 1,000 \: Watt}} [/tex]

Conclusion

So, the power does Wayne generate each time he goes up stairs is 1,000 Watt.

See More :

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