Principle 4.3.1. The Work-Energy Theorem.
The net work done by external forces on an object or system is equal to the change in total energy of that system:
\begin{equation*}
W_{net,external} = \Delta E
\end{equation*}
Section 4.3 The Work-Energy Theorem
The Work-Energy Theorem is one of the most fundamental laws in physics. In fact, it is used throughout essentially all of science. It says something simple but profound: if you want to change the energy of a system, something external has to interact with the system. In most of physics, the kind of interaction that can transfer energy to a system is work.
Assumption 4.3.2. No Heat Transfer.
The Work-Energy Theorem assumes that no heat is transferred into or out of the system of interest. 1
Exercises Activities
1.
How do you think you would find the net work if more than one thing is doing work on your system? Write an equation corresponding to your thinking.
Answer.
\begin{equation*}
W_{net,external} = \Sigma W_i = W_1 + W_2 + W_3 + \dots
\end{equation*}
2. Explanation: Changing Energies.
Suppose you have a system that initially includes some kinetic energy and some potential energy. You observe that the potential energy decreases by \(7000 \mathrm{~J}\) and the kinetic energy increases by \(4500 \mathrm{~J}\text{.}\) Is the net external work on this system positive, negative, or zero? Explain your reasoning.
Tip.
Draw an Energy System Diagram to help keep track of the changes. How is the Work-Energy Theorem represented in an Energy System Diagram?
3. Explanation: Conserved Energy.
Suppose you have a system with two objects, each with some initial kinetic energy. The net external work on the system is equal to zero. If the kinetic energy of the first object increases, what happens to the kinetic energy of the second object? Explain your reasoning.
Tip.
Draw an Energy System Diagram to help keep track of the changes. How is the Work-Energy Theorem represented in an Energy System Diagram?
If heat is transferred, you can use the First Law of Thermodynamics instead of the Work-Energy Theorem:
\begin{equation*}
W_{net,external} + Q_{net,external} = \Delta E
\end{equation*}
where \(Q_{net,external}\) is the net heat transferred to the system.
