3.1 Translational Kinetic Energy

Learning objectives

3.1A—Describe the translational kinetic energy of an object in terms of the object’s mass and velocityDescribe the translational kinetic energy of an object in terms of the object’s mass and velocity.• An object’s translational kinetic energy is given by the equation =Km v1 2 2• T ranslational kinetic energy is a scalar quantity.• Different observers may measure different values of the translational kinetic energy of an object, depending on the observer’s frame of reference. TOPIC 3.2 Work

Connect motion to energy

An object has translational kinetic energy because its center of mass is moving. For an object of mass $m$ moving with velocity $\vec v$ , use the speed $v=|\vec v|$ in the kinetic-energy equation.

$\begin{gathered}K=\frac{1}{2}mv^2\\ [K]=\text{J}=\text{kg}\,\text{m}^2/\text{s}^2\end{gathered}$

Read the squared-speed relationship

At fixed speed, doubling the mass doubles $K$ . At fixed mass, doubling the speed makes $K$ four times as large because velocity magnitude is squared. Reversing the direction of motion without changing speed leaves $K$ unchanged.

Calculate with units

Worked example: A $2.0\,\text{kg}$ cart moves at $3.0\,\text{m/s}$ relative to the laboratory.

$K=\dfrac12(2.0\,\text{kg})(3.0\,\text{m/s})^2=9.0\,\text{J}$ .

The cart therefore has $9.0\,\text{J}$ of translational kinetic energy in the laboratory frame.

State whose measurement it is

Kinetic energy is a scalar, so it has no direction, but its value depends on the observer's reference frame. An observer moving alongside the cart at $3.0\,\text{m/s}$ measures the cart's speed as zero and therefore measures $K=0$ , while the laboratory observer measures $9.0\,\text{J}$ . Both values are correct in their own frames.

Next Topic

—3.2 WorkRead