Question

A student with a mass of 80.0 kg runs up three flights of stairs in 12.0 sec. The student has gone a vertical distance of 8.0 m. Determine the amount of work done by the student to elevate his body to this height. Determine the power consumed by the student. Assume that his speed is constant.

Answer 1

The amount of work done by the student to elevate his body to this height is 6278.4 J

Power is 523.2 Watts

Explanation:

Work = Force x Displacement

Force = Weight of student

Weight = Mass x Acceleration due to gravity

Mass, m = 80 kg

Acceleration due to gravity, g = 9.81 m/s²

Weight = 80 x 9.81 = 784.8 N

Displacement = 8 m

Work = 784.8 x 8 = 6278.4 J

The amount of work done by the student to elevate his body to this height is 6278.4 J

Power is the ratio of work to time taken

         $P=\frac{W}{t}\\\\P=\frac{6278.4}{12}\\\\P=523.2W$

Power is 523.2 Watts

Answer 2

The power consumed by the student is 523.2 watts.

• The calculation is as follows:

$Work = Force \times Displacement$

Force = Weight of student  

$Weight = Mass \times Acceleration\ due\ to\ gravity$

Mass, m = 80 kg

Acceleration due to gravity, g = 9.81 m/s²

$Weight = 80 \times 9.81 = 784.8 N$  

Displacement = 8 m

$Work = 784.8 \times 8 = 6278.4 J$

So,

Power consumed should be

$= 6278.4 \div 12$

= 523.2

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