Question

A \(75.0 - {\rm{kg}}\) person climbs stairs, gaining \(2.50{\rm{ meters}}\) in height. Find the work done to accomplish this task.

Short answer

The work done is \(1837.5{\rm{ J}}\).

Step-by-step solution

Definition of Concept

Potential Energy: The work done against is stored in body as a form of potential energy.

The potential energy is expressed as follows:

\[\begin{aligned}W = {\rm{PE}}\\ = mgh\end{aligned}\]

Here, \(m\) is the mass, \(g\) is the acceleration due to gravity, and \(h\) is the height.

Calculating the work done

Putting\(75.0{\rm{ kg}}\)for\(m\),\(9.8{\rm{ m}}/{{\rm{s}}^2}\)for\(g\), and\(2.50{\rm{ m}}\)for\(h\)into equation (1.1),

\(\begin{aligned}{}W &= \left( {75.0{\rm{ kg}}} \right) \times \left( {9.8{\rm{ m}}/{{\rm{s}}^2}} \right) \times \left( {2.50{\rm{ m}}} \right)\\ &= 1837.5{\rm{ J}}\end{aligned}\)

Hence, the work done to accomplish this task is \(1837.5{\rm{ J}}\).