Question

A 60-kg jogger runs up a long flight of

stairs in 4.0 s. The vertical height of the
stairs is 4.5 m.
a. Estimate the jogger's power
output in watts and horsepower.
b. How much energy did this
require?

Answer 1

The power output of the jogger is approximately 661.5 watts or 0.886 horsepower, calculated from the work done against gravity over time. The energy required for the task is 2646 joules, equivalent to the gravitational potential energy gained.

Step-by-step explanation:

The student is asking about the power output and the energy required for a 60-kg jogger to run up a flight of stairs with a vertical height of 4.5 meters in 4.0 seconds. To calculate the jogger's power output in watts, we use the formula for power (P), which is the work done (W) over time (t). Work done is equivalent to the gravitational potential energy (GPE) since the jogger is lifting their body against gravity, and GPE is calculated by the formula GPE = mgh, where m is mass in kilograms, g is the acceleration due to gravity (9.8 m/s²), and h is the height in meters.

First, we calculate the GPE:

GPE = m × g × h = 60 kg × 9.8 m/s² × 4.5 m = 2646 Joules

Now, we calculate the power output:

Power (P) = Work done / Time = GPE / t = 2646 J / 4.0 s = 661.5 Watts

To convert this to horsepower (hp), we use the conversion factor 1 hp = 746 watts:

Power in hp = 661.5 W ÷ 746 = approximately 0.886 hp

Finally, the energy required is the same as the GPE, which is 2646 Joules.

Answer 2

Step-by-step explanation:

Given parameters:

Mass of Jogger = 60kg

Time = 4s

Vertical height = 4.5m

Unknown:

Jogger's power output = ?

Energy required = ?

Solution:

The power output of the jogger is defined as the rate at which work is done.

Power =
`(force x distance)/(time)`

Now insert the parameters and solve;

Work done = Force x distance = mgh

m is the mass

g is the acceleration due to gravity = 9.8m/s²

h is the height

Work done = 60 x 9.8 x 4.5 = 2646J

Power =
`(2646)/(4)` = 661.5W

Energy required;

The work done here is also the energy required;

Energy required = 2646J