How does the power you generate, walking up the stairs, compare to a horse? How about when running up the stairs? (Hint: one hp=746 Watts) If one food Calorie equals 4184 (joules), how far up...

How does the power you generate, walking up the stairs, compare to a horse? How about when running up the stairs? (Hint: one hp=746 Watts)

If one food Calorie equals 4184 (joules), how far up could you climb on one cream-filled oreo cookie containing 50 calories? Give your answer in: Number of steps, Meters, Kilometers and Miles.

Expert Answers
gsenviro eNotes educator| Certified Educator

(A minor correction, actually power would be consumed and energy would be spent while climbing or running up the stairs).

Given the mass of a horse (in comparison to that of a person), a horse will consume much more power while walking or running or climbing the stairs. Power is the ratio of work done per unit time. Work done is the product of force times the displacement. Force is given as the product of mass and acceleration (due to gravity, for climbing). Thus, the power is given as the product of weight and displacement per unit time.

or, power = mgh/t

Assuming that an average adult human being has a mass of 70 kg and that one flight of stairs correspond to 20 steps, each of a displacement of 15 inches. Thus the total displacement in climbing a flight of stairs is 300 inches (= 20 steps x 15 inches per step).

Displacement = 300 inches = 25 feet = 7.62 m (1 foot = 0.3048 meters).

Let us assume it takes about 2 seconds per step while climbing the stairs at an easy pace. Total time to climb 20 steps is 40 seconds.

Thus, the power consumed in climbing the stairs = 70 x 10 x 7.62/40 W = 133.35 W 

Since 1 hp = 746 W, 

The power consumed = 133.35/746 = 0.18 hp (approximately).

Let us assume that we are about 3 times faster when running up a flight of stairs, then the time taken to climb the stairs will be one-third or, will be about 13.33 seconds.

The power consumed in running up the stairs = 3 x power consumed while walking up 

= 3 x 133.35 = 400 W = 0.54 hp (approximately).

In comparison, a horse has a mass about 10 times as much as an adult human being, thus the power consumed would be 10 times more. A horse will use 1.8 hp to climb a flight of stairs and will use 5.4 hp to run up the flight.

Now, 1 cream-filled oreo cookie has 50 calories, each of which has 4184 joules of energy. Total energy contained in one cream-filled oreo cookie = 50 x 4184 J = 209,200 J.

Energy is the power generation (or consumption) over a given time period. That is,

energy = power x time

Using the example calculations we just did, it takes 40 seconds to climb a flight of stairs and the power consumed is 133.35 W. Thus, the energy expense in climbing a flight of stairs is:

energy = 133.35 W x 40 sec = 5334 J

Thus, the number of flights of stairs one can climb on one oreo cookie is given as:

Number of flight of stairs = energy available/energy consumed in one flight 

= 209,200/5334 = 39.22 flights = 39.22 x 20 steps = 784.4 steps x 15 inches per step = 11,766 inches = 298.85 meter = 0.3 km = 0.186 miles. 

(you can convert between different length measures assuming, 1 mile = 1.609 km, 1 km = 1000 m, 1 m = 39.37 inches, etc.).

Thus, one can climb 11,766 steps or about 300 m or about 0.3 km or about 0.186 miles on one cream-filled oreo cookie. 

 

Hope this helps. 

t-nez eNotes educator| Certified Educator

A horse generates more power than a human going up stairs at the same speed as the human because the horse has more mass. Going faster increases power, but the human would have to go up the stairs a lot faster than the horse to generate the same power as the horse. 

Here's why:

Power is the rate of doing work: P = W/t

Work is force times displacement: W = Fd

Force = weight = mg

The average adult male wieighs about 70 kg and the average horse weighs about 500 kg.

Let's assume that the displacement, or distance from starting to ending positions, is 10 m and let's round acceleration due to gravity (g) to 10 m/s^s since precision isn't important here.

If the horse and the person both go up the stairs in 10 seconds;

Horse: weight = 500 kg x 10 m/s^s = 5000 N

Work = 5000N x 10 m = 50,000 N-m

Power = 50,000 N-m/10 sec = 5000 Watts = power of horse

Person: weight = 70 kg x 110 m/s^2 = 700 N

Work = 700 N x 10 m = 7000 N-m

Power = 7000 N-m/10 sec = 700 W = power of person

The horse generates about 7 times the power of the person at the same speed, so the person would have to run up the stairs at a rate more than seven times that of the horse to generate more power than the horse.

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