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Waiting for his new game to come in the mail, Billy races up the stairs in 3 seconds from the basement when
ever he hears the doorbell. The force of gravity acting on Billy is 500 Newtons and the stairs are 3 meters
high. How much power does Billy generate each time he goes up stairs?

Sagot :

MDKPfromIDN

So, the power does Billy generate each time he goes up stairs is 500 Watt.

Introduction

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 = 500 N
  • [tex] \sf{\Delta h} [/tex] = change of altitude = 3 m
  • t = interval of the time = 3 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{500 \times \cancel 3}{\cancel 3}} [/tex]

[tex] \boxed{\sf{P = 500 \: Watt}} [/tex]

Conclusion :

So, the power does Billy generate each time he goes up stairs is 500 Watt.

See More :

  • How much power is used by a washing machine if it does 7,200 joules of work in 3 minutes? https://brainly.com/question/26529363

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