Physics › Mechanics › Drag and terminal speed
Drag and terminal speed
Friction and drag are the forces the idealised problems leave out, and AQA wants them back in, qualitatively. Their defining habit is that drag grows with speed, and that single fact produces terminal speed, two-stage skydives and the top speed of every vehicle.
Builds on Newton's laws and the resultant force and Motion graphs and the SUVAT equations.
IN THIS TOPIC
- Describe friction, lift and drag qualitatively, including that air resistance increases with speed.
- Explain terminal speed using Newton's laws, and sketch the velocity-time graph it produces.
- Apply the same balance argument to a parachutist's two terminal speeds and to a vehicle's maximum speed.
WHAT YOU PROBABLY THINK
Falling objects just keep speeding up.
The resistive cast
Friction acts between solid surfaces and opposes relative motion, or attempted motion, between them. AQA asks for a qualitative treatment only, and the distinction between static and dynamic friction is explicitly not tested. Drag is the resistive force from moving through a fluid, air or water, and lift is the component of the fluid's force perpendicular to the flow, the force that holds aircraft up.
The property that drives everything else in this topic: air resistance increases with speed. Move faster and you sweep more air aside each second, and each parcel of it more violently. Friction, by contrast, has no such appetite; that difference in behaviour is why drag, not friction, sets speed limits.
Terminal speed
Drop an object and follow the forces. At the moment of release the speed is zero, so drag is zero and the resultant is the full weight: the acceleration is g. As speed builds, drag grows, the resultant shrinks, and the acceleration fades.
Eventually drag has grown to equal the weight. The resultant force is zero, and by Newton's first law the object stops accelerating and falls at constant velocity: the terminal speed. Nothing has switched off; two forces have merely reached a stalemate.
The velocity-time graph carries the whole argument: initial gradient g, curvature as the resultant shrinks, and a horizontal asymptote at terminal speed. Sketching this graph, with those three features labelled, is a standard question in its own right.
Two terminal speeds, one argument
A parachutist runs the argument twice. In freefall the body reaches a high terminal speed. Opening the parachute multiplies the area meeting the air, so at that speed drag now vastly exceeds weight: the resultant points upward, the parachutist decelerates, and drag falls with the speed until the two balance again, at a much lower, survivable terminal speed.
Note what the deceleration is not: it is not the parachute “pulling upward” in any new sense. It is the same drag force as before, made suddenly enormous by area, and dying back as the speed falls.
The top speed of a vehicle
A car's maximum speed is the same stalemate wearing different clothes. The engine provides a driving force; drag rises with speed until the total resistive force equals it. Resultant zero, acceleration zero: that speed is the maximum. Anything that raises the driving force or trims the drag, more power, better streamlining, raises the speed at which the stalemate happens, which is the entire business model of sports-car design.
THE EXAM BIT
- The terminal-speed explanation is a chain, and every link scores: drag increases with speed, so the resultant force falls, so the acceleration falls, until drag equals weight, resultant zero, constant velocity. Write it in that order.
- At terminal speed the forces are balanced, but the object is still moving and still has weight. “The forces cancel so it stops” is the planted error.
- On the skydiver graph, the parachute moment shows a steep negative gradient, not a vertical cliff to zero: the speed falls to the new terminal value, not to rest.
- Heavier means faster terminal speed, not slower: more weight needs more drag to balance it, and more drag needs more speed. Questions about raindrops and hailstones lean on this.
- For a vehicle's top speed, the sentence examiners want: at maximum speed the driving force equals the total resistive force, so the resultant force and acceleration are zero.
CHECK YOURSELF
A skydiver falls at a terminal speed of 55 m s−1, then opens a parachute and reaches a new terminal speed of 6 m s−1. Explain, in terms of forces, why the new terminal speed is lower.
Show a hint
The weight has not changed. What has, and what does that do to the speed at which drag can match it?
Show the answer
Opening the parachute greatly increases the area pushing through the air, so at any given speed the drag is far larger than before.
Drag therefore matches the unchanged weight at a much lower speed, and it is at that lower speed that the resultant returns to zero and the fall becomes steady.
Between the two plateaus, drag exceeds weight, the resultant acts upward, and the skydiver decelerates: the steep falling section of the velocity-time graph.
Drag grows with speed.
Terminal speed is where it catches the weight.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.