Section 4.6 Kinetic Energy
Definition 4.6.1. Kinetic Energy.
The translational kinetic energy of an object is:
\begin{equation*}
K_t = 1/2mv^2
\end{equation*}
When you make the Particle Model
Assumption 2.5.3 (that is, no rotational motion), all kinetic energy is translational, and it is often simply called
kinetic energy and written
\begin{equation*}
K = 1/2mv^2
\end{equation*}
Kinetic energy is the energy of motion. Most kinetic energy you will work with is translational. Objects that are rotating (which you will study later) have rotational kinetic energy, possibly in addition to translational kinetic energy.
Exercises Kinetic Energy Activities
1. Summarize What You Learned - Kinetic Energy.
Write a 1-2 sentence description of what the definition of kinetic energy says in words and why it makes sense given your everyday experience.
2. Sensemaking: Units.
Energy is measured in joules (J). Use the definition of kinetic energy to write a joule in terms of other units you are familiar with.
3. Extension: Systems with Multiple Objects.
Many systems include more than one object. In general, the different objects could have different masses and different speeds. How do you think you could find the kinetic energy for such a system? Write an equation for the total kinetic energy.
Answer.\(K_{\text{total}} = \Sigma K_i = K_1 + K_2 + K_3 + \dots = 1/2m_1v_1^2 + 1/2m_2v_2^2 + 1/2m_3v_3^2 + \dots\)
4. Sensemaking: Numbers for a Car.
Estimate the kinetic energy of a car traveling down a highway at the speed limit. Make sense of this number using
Sensemaking Strategy 2.3.7.
Answer.I estimated around \(576,000 \mathrm{~J}\text{.}\) (Many cars have a mass that is somewhere around \(1200 \mathrm{~kg}\text{,}\) and a typical highway speed limit is \(70 \mathrm{~mph}\text{,}\) which is about \(31 \mathrm{~m/s}\text{.}\))
5. Explanation: Numbers for Two Cars.
Estimate the kinetic energy (in J) of a system consisting of two identical cars traveling toward each other, both traveling at the same speed. Is your answer greater than, less than, or equal to the kinetic energy for a single car you found in the previous activity? Explain why this makes sense.
Answer.You simply add the kinetic energies for the two cars: \(576,000 \mathrm{~J} + 576,000 \mathrm{~J} = 1,152,000 \mathrm{~J}\text{.}\)
