Lesson summary
3.2.2 Terminal Velocity — AS PHYSICS 9702 notes: Explain the stages of a fall with drag, the shape of the velocity-time graph and the idea of terminal velocity.With no air resistance, as on the Moon — the only force is weight, the resultant force equals weight and the body accele…
- With air resistance, as on Earth
- The body accelerates according to F = ma
- When drag equals weight
- At terminal velocity the resultant force is zero
- In symbols (air, upthrust ignored)
- If drag is kv2
Section 1 of 10Free fall with and without air resistance
1With no air resistance, as on the Moon
- With no air resistance, as on the Moon the only force is weight, the resultant force equals weight and the body accelerates at g.
2With air resistance, as on Earth
- With air resistance, as on Earth weight is greater than drag at first, so the resultant force is in the direction of motion.
3The body accelerates according to F = ma
- The body accelerates according to F = ma as velocity increases the drag increases and the acceleration decreases.
4When drag equals weight
- When drag equals weight the resultant force is zero and the body falls at constant velocity.
Section 2 of 10Terminal velocity
Terminal velocity
Terminal velocity
Terminal velocity the constant maximum velocity reached when the resistive forces balance the weight.
At terminal velocity the resultant force is zero
- At terminal velocity the resultant force is zero so by the first law the acceleration is zero.
In symbols (air, upthrust ignored)
- In symbols (air, upthrust ignored) mg = Fd at v = vt.
If drag is kv2
- If drag is kv2 vt = √(mg ÷ k).
A heavier object, or a smaller area or more streamlined shape (smaller k)
- A heavier object, or a smaller area or more streamlined shape (smaller k) has a higher terminal velocity.
Section 3 of 10Stages of the fall
1
At release (v = 0) there is no drag, the resultant force is the weight and the acceleration is g.
2
As v increases the drag increases, so the resultant force (weight minus drag, minus upthrust in a liquid) decreases.
3
The object keeps speeding up, but more slowly, as the acceleration decreases.
4
At terminal velocity drag (plus upthrust) equals weight, so the resultant force is zero, a = 0 and v is constant.
Section 4 of 10The velocity-time graph
The graph starts at the origin
- The graph starts at the origin with gradient g = 9.8 m s-2.
The gradient decreases steadily
- The gradient decreases steadily showing the acceleration falls from g toward zero.
The graph levels off to a horizontal line
- The graph levels off to a horizontal line at the terminal velocity, approached asymptotically.
The gradient at any point
- The gradient at any point is the acceleration, found with a tangent.
The area under the graph
- The area under the graph gives the distance fallen.
Section 5 of 10A skydiver's two terminal velocities
1Arms and legs spread
- Arms and legs spread terminal speed about 55 m s-1.
2After the parachute opens
- After the parachute opens the area is much larger, so drag at 55 m s-1 far exceeds the weight.
3The resultant force is upward
- The resultant force is upward so the skydiver decelerates and the drag falls as the speed falls.
- (upward acceleration)
4Drag equals weight again at a much lower terminal velocity
- Drag equals weight again at a much lower terminal velocity about 5 m s-1, which allows a safe landing.
5The skydiver does not move upwards when the parachute opens
- The skydiver does not move upwards when the parachute opens they decelerate to a lower terminal velocity.
6A more massive skydiver of the same shape
- A more massive skydiver of the same shape has a larger terminal velocity, so should jump later than a lighter skydiver if they want to meet.
Section 6 of 10Falling in a liquid
Falling in a liquid
Three forces act on a sphere in a viscous liquid
- Three forces act on a sphere in a viscous liquid weight mg down, upthrust U up and drag Fd up.
At terminal velocity mg = U + Fd.
Time the sphere between two marks on a tall tube
- Time the sphere between two marks on a tall tube after it has reached steady speed, to find the terminal velocity.
This method gives the viscosity of liquids such as oil
- This method gives the viscosity of liquids such as oil a more viscous liquid gives a lower terminal velocity.
A bigger or denser sphere falls faster.
Section 7 of 10Describing the graph precisely
1At the start the speed is zero
- At the start the speed is zero so there is no drag, the resultant force equals the weight and the acceleration is g.
2As the speed increases the drag increases
- As the speed increases the drag increases so the resultant force and the acceleration decrease and the gradient decreases.
3When drag equals weight
- When drag equals weight the resultant force is zero, the acceleration is zero and the graph is horizontal.
4Use the words resultant force and gradient
- Use the words resultant force and gradient not gravity cancels.
Section 8 of 10More from the specification
More from the specification
Forces acting on falling bodies
- A body falling through fluid experiences downward gravitational weight opposed by upward drag and buoyancy;
- resultant force determines acceleration: Fnet = W - Fdrag - Fbuoy.
Attainment of terminal velocity
- As velocity increases, viscous drag force increases until the sum of upward forces equals downward weight,
- resulting in zero net force and constant terminal velocity.
Velocity-time graphs of falling objects
- The gradient of a velocity-time graph represents acceleration;
- the curve starts with gradient g and flattens asymptotically to a horizontal line at terminal speed.
Fluid resistance drag
- Fluid resistance drag frictional resistive forces acting on a body moving through a fluid increase in magnitude with higher speeds.
Terminal velocity condition
- Terminal velocity condition occurs when upward fluid drag forces equal downward weight, causing resultant force and acceleration to become zero.
Streamlining bodies
- Streamlining bodies aerodynamic shaping reduces fluid drag magnitude,
- allowing vehicles to reach higher speeds before resistive forces balance driving power.
Driving force
- Force applied by an engine or motor to produce motion.
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Terminal velocity | The constant maximum velocity reached when the resistive force equals the weight. |
| Drag force | A resistive force opposing motion through a fluid. |
| Resultant force | The vector sum of the forces on the object, zero at terminal velocity. |
| Upthrust | The upward force from the fluid on an immersed object. |
| Free fall | Falling under the action of gravity alone. |
| Viscosity | The resistance of a fluid to flow. |
| Asymptote | A level that a curve approaches but never reaches. |
| Streamlined | Shaped to reduce drag. |
Section 10 of 10Exam technique
1
Saying that at terminal velocity there are no forces — the forces balance and the resultant is zero.
2
Thinking the object stops accelerating because gravity stops acting.
3
Drawing the v-t graph as a straight line then a sharp kink — it is a smooth curve.
4
Forgetting upthrust when the object falls in a liquid.
5
Saying terminal velocity means zero velocity.
Marked practiceQuizzes for this lesson
Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).