AP Physics 1- 3.1 Translational Kinetic Energy- Study Notes- New Syllabus
AP Physics 1-3.1 Translational Kinetic Energy – Study Notes
AP Physics 1-3.1 Translational Kinetic Energy – Study Notes -AP Physics 1 – per latest Syllabus.
Key Concepts:
- Translational Kinetic Energy
- Frame Dependence of Translational Kinetic Energy
Translational Kinetic Energy
An object in motion has the capacity to do work because of its motion → this energy is called kinetic energy (KE).
For translational motion (straight-line motion of the center of mass), the kinetic energy is given by:
\( KE = \tfrac{1}{2} m v^2 \)
Where:
\( m \) = mass of the object (kg)
\( v \) = speed of the object (m/s)
Kinetic energy is a scalar quantity → it depends only on the magnitude of velocity, not its direction.
Work–Energy Theorem: The net work done on an object is equal to its change in kinetic energy.
\( W_{net} = \Delta KE = KE_f – KE_i \)
Example:
A car of mass \( 1200 \, \text{kg} \) is moving at a speed of \( 20 \, \text{m/s} \). Find its kinetic energy.
▶️Answer/Explanation
Step (1): Apply the formula \( KE = \tfrac{1}{2} m v^2 \).
Step (2): Substitute values → \( KE = \tfrac{1}{2} (1200)(20^2) \).
\( KE = 600 \times 400 = 240,000 \, \text{J} \).
Final Answer: The car’s kinetic energy is \( 2.4 \times 10^5 \, \text{J} \).
Frame Dependence of Translational Kinetic Energy
Translational kinetic energy is not absolute → it depends on the reference frame of the observer.
- Different observers moving relative to each other may measure different values of an object’s kinetic energy, even though the object’s mass is the same.
- This is because kinetic energy depends on velocity, and velocity is relative to the observer’s frame.
- Important: While kinetic energy is frame-dependent, the work–energy theorem still holds true in every inertial frame.
Example:
A car of mass \( 1000 \, \text{kg} \) is moving at \( 20 \, \text{m/s} \) relative to the ground. Find its kinetic energy as measured by:
- (i) An observer standing on the ground.
- (ii) An observer moving alongside the car at \( 20 \, \text{m/s} \) in the same direction.
▶️Answer/Explanation
Case (i): Ground observer
Velocity of car relative to ground = \( v = 20 \, \text{m/s} \).
\( KE = \tfrac{1}{2} m v^2 = \tfrac{1}{2} (1000)(20^2) = 200,000 \, \text{J} \).
Case (ii): Observer moving with the car
Velocity of car relative to observer = \( v’ = 20 – 20 = 0 \, \text{m/s} \).
\( KE = \tfrac{1}{2} m v’^2 = \tfrac{1}{2} (1000)(0^2) = 0 \, \text{J} \).
Final Answer:
- Ground observer measures \( 2.0 \times 10^5 \, \text{J} \).
- Moving observer measures \( 0 \, \text{J} \).
Thus, the value of kinetic energy depends on the chosen reference frame.