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A boy whose mass is 45.0 kg runs up 35 steps, each step .350m high in 50.0 seconds. Find the power in watts expended by the boy.​

Sagot :

The power in watts is 66.15 Watts

Explanation:

In this problem, we will use the concept of the work-energy theorem to relate the potential energy of the boy and compute his power in running over the stairs.

Formula to use

a. PE = mgh

b. P = W/t

where

PE     is the potential energy, the unit is in Joules (J)

m      is the mass, the unit is in kg

g       is the pull of the Earth's gravity, 9.8 m/s²

h       is the height, the unit is in meter (m)

P       is the power, the unit is in J/s or Watts

W      is the work, the unit is in Joules (J)

t        is the time, the unit is in seconds

Given information

m = 45 kg

h = 25 x 30 cm = 750 cm = 7.5 m

t = 5.0 s

P = ?

Solving the problem

Let us solve the potential energy of the boy

PE = mgh

PE = (45 kg)(9.8 m/s²)(7.5 m)

PE = 3307.5 J

Now, this energy is also equivalent to work according to the concept of energy-work theorem, therefore, PE = Work, so Work = 3307.5 JJ.

Now, let us solve the power exerted by the boy by running over the stairs using

P = W/t

Substitute the given data

P = 3307.5 J / 50 s

P = 66.15 Watts

Therefore, the power exerted by the boy is 66.15 Watts.

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Definition of power

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