Physics 5054/12 — October/November 2011

Walkthrough

Terminal velocity is defined as the maximum constant speed attained by an object falling through a fluid (like air). It occurs when the upward resistive force (drag or air resistance) becomes equal in magnitude to the downward driving force (weight).

1. Analyze the forces: As a parachutist falls, gravity pulls them down (weight, $W$). Air resistance pushes up (drag, $R$). Initially, speed is low, so drag is small, and $W > R$. There is a resultant downward force, so the parachutist accelerates.
2. Effect of the parachute: When the parachute opens (Position C), the surface area increases dramatically, causing drag to increase rapidly. Eventually, $R$ increases enough to equal $W$.
3. Newton's First Law: When $W = R$, the resultant force is zero. According to Newton's first law, an object with zero resultant force moves at a constant velocity. Since the parachutist is still falling, this constant velocity is the terminal velocity. The label 'not accelerating' confirms this state.
4. Evaluate other positions:
   • A (not yet moving): Speed is zero. Terminal velocity is a non-zero constant falling speed.
   • B (accelerating): Resultant force is downwards ($W > R$). Speed is increasing, not constant.
   • D (not moving): The parachutist has landed. Speed is zero.

Key Takeaways

• Terminal velocity is a state of constant velocity, meaning acceleration is zero.
• It occurs when the resistive force (drag) equals the driving force (weight).
• 'Not accelerating' during a fall is the key indicator of terminal velocity.

Common Mistakes

• Confusing terminal velocity with zero speed: Students might choose A or D because they are 'not moving', but terminal velocity refers to the constant high speed of the fall, not being stationary.
• Choosing the moment the parachute opens: Students might think the moment the parachute opens is terminal velocity. Actually, opening the parachute causes a new, lower terminal velocity to be reached after a period of deceleration. Position C shows the steady state of 'not accelerating'.
• Ignoring Newton's First Law: Failing to link 'not accelerating' to 'resultant force is zero' and 'constant speed'.

Things to Be Careful About

• Context of 'not accelerating': While an object at rest (A and D) is also not accelerating, 'terminal velocity' specifically describes the constant speed reached during free fall through a fluid. Ensure the object is actually falling at a constant rate, not just stationary.
• Label interpretation: The diagram labels are crucial. 'Accelerating' means speed is changing. 'Not accelerating' means speed is constant. Match the physics definition to the label.