Question

Consider the energy we use everyday in routine tasks, where that energy comes from, and where it goes. When you climb stairs you overcome the force of gravity to raise yourself to some height. It does not matter what the slope of the stairs are; the work done is against gravity which is always vertical so only the height counts. Take a typical human mass of 65 kg (roughly 143 lb of gravitational pull or weight) and a stairway up 2 stories which is about 6 meters.

How much energy in joules is needed to climb the stairs?

What is your potential energy at the top of the stairs?

How many "food calories" or kilocalories (1 calorie is 4.18 j) did you use to make the climb?

If you drop a coin from the top of the stairs down to the bottom of the stairwell, what is the velocity of the coin when it reaches the floor?

After you walk back down the stairs to retrieve your coin, how much work did you do to descend?

Explain Answers

Answer 1

As we move up the stairs, our body is gaining potential energy which is given by

P.E = m*g*h

P.E = 65*9.8*6

P.E = 3822 joules. This will be our potential energy at the top.

Now to calculate the number of calories = 3822 / 4.18 = 914 calories (approx)

Now, when we drop a coin, it falls under the action of gravity. The coin starts from rest. Therefore, initial velocity is zero. Using kinematics equation

h = u*t + 1/2*a*t²

6 = 1/2*9.8*t²

t = 1.1065 seconds to reach the floor.

Velocity can be calculated as

v = u+at

v = 9.8*1.1065

v = 10.844 m/s