Final answer:
Mechanical work is calculated by the product of force and displacement; specifically, W = Fd. It represents the energy required to move an object against a force over a certain distance. Gravity is often the opposing force in the case of vertical movement, such as climbing stairs.
Step-by-step explanation:
The formula for mechanical work (W) is the product of force (F) and displacement (d), typically along the direction of the force. This can be expressed by the equation W = Fd cos θ, where θ is the angle between the direction of force and displacement. Mechanical work is essentially the amount of energy transferred by a force to move an object through a distance. In the presence of a constant force acting parallel to the displacement, this relationship simplifies to W = Fd. If the force is caused by gravity (where the acceleration due to gravity g is approximately 9.8 m/s² on Earth), then the force can be calculated using the mass (m) of the object as F = mg.
When you climb stairs or an elevator rises to a higher floor, you are overcoming the force of gravity, hence performing mechanical work. According to the work-energy theorem, the work done by a force also relates to the change in kinetic energy, that is W = 0.5 mv² - 0.5 mv², assuming mass (m) remains constant and v represents the velocity.