The models you built for forces in the previous chapters can be used to explain many different physical systems. For some systems, it is useful to define the work done by a force.
Every force that acts on an object has the capacity to do work. Since objects frequently have many forces acting on them, it can be useful to keep track in a table like the one introduced below.
A Work Table is a representation for keeping track of the work done on a system. In a work table, each row represents a different force acting on the system, while the columns represent the displacement, force, and work for that force. A work table can be qualitative, where you only represent the direction of the displacement and the force and the sign of the work, or quantitative, where you include the full value for each quantity.
At the end of a work table, you can often easily add up the last column to get the net work on the system! Sometimes, if you only have a qualitative work table, you may not have enough information to determine the net work.
In the last part of The Bag of Groceries, you lifted a bag of groceries so that it moves upward at constant speed. Find the work done on the bag of groceries by each force.
The bag is an obvious choice for a system, along with a Cartesian reference frame stationary with respect to the ground. Since the bag is moving upward at constant speed, there are two forces acting on the bag, as shown in the figure below.
Below are examples of qualitative and quantitative Work Tables summarizing the work done by each force, and the net work at the end, supposing the mass of the bag is \(m\) and the vertical displacement of the bag is \(h\text{.}\)
You are pulling a box across the floor using a horizontal rope with a constant tension force of \(250 \mathrm{~N}\text{.}\) How much work have you done after the box has slid \(3 \mathrm{~m}\) along the floor?
Suppose you were to angle your rope so that it makes an angle of \(20^o\) with the horizontal (the magnitude of the tension is unchanged). How much work have you done after the box has slid \(3 \mathrm{~m}\) along the floor?
Suppose you were to angle your rope so that it is oriented vertically (the magnitude of the tension is unchanged). How much work have you done after the box has slid \(3 \mathrm{~m}\) along the floor?
Suppose you have a system with two objects, \(A\) and \(B\text{.}\) Different constant external forces, \(\vec{F}_A\) and \(\vec{F}_B\text{,}\) act on the two objects, which undergo different displacements \(\Delta \vec{r}_A\) and \(\Delta\vec{r}_B\text{.}\) Which of the following expressions do you think correctly describes the net work on this system? Why?
