Question

when we climb stairs do we do any work?what energy change is taking place here?

Answer 1

When we climb stairs do we do any work? What energy change is taking place here?

**Answer:**

The first law of thermodynamics states that when work is done to a system its energy state changes by the same amount. This equates work and energy.

At the start position ( h=0 ) potential energy is:

$$E _ {p} (s t a r t) = 0;$$

At the end of the stairs:

$$E _ {p} (e n d) = m g h$$

Where g is

h is height of the stairs.

assume that the speed in the start and finish is the same and neglecting friction:

$$W = E _ {p} (e n d) - E _ {p} (s t a r t) = m g h$$ $$\boxed {W = m g h}$$

From other point of view

work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force.

If we climb stairs with the constant speed $v = \text{const}$ , thus: $a = 0$ ;

So neglecting friction:

$$\vec {F} _ {w o r k} = - m * \vec {g}$$

In projection on vertical axis:

$$F _ {w o r k} = m * g * \sin \alpha$$

Thus:

Work is:

$$W = F _ {w o r k} * d$$

Where $d$ is distance

$$d = \frac {l}{\sin \alpha}$$

So:

$$\boxed {W = m * g * h}$$