The shape of the lesson
By the end of the lesson, learners can
- Drag catches up with weight: Drop an object and watch the two arrows.
- The fall in three stages: Drag depends on speed and on the size and shape of the object.
- The skydiver story.
- At release: drag is zero, so acceleration is g.
- Terminal velocity: drag equals weight, resultant is zero.
- Constant velocity means zero acceleration, not zero force.
One picture every idea returns to
Frictional, viscous and drag forces oppose motion and grow with speed. An object released in air first accelerates at g while the drag is small. As it speeds up the drag rises until it equals the weight; the resultant force is then zero, the acceleration is zero, and the object continues at a constant terminal velocity.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, When the air pushes back.. Real objects do not fall forever faster. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Drag catches up with weight | Drop an object and watch the two arrows. Project tab 2 of the lab (Motion with resistance) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: The fall in three stages | Drag depends on speed and on the size and shape of the object. | Pairs |
| 21 to 30 min | Teach and check: The skydiver story | The skydiver story. | Think-Pair-Share |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 15 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in The skydiver story, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Think-Pair-Share
Pose the question, give thirty seconds of silent thinking, then a minute to compare with a partner before a few pairs share with the class. The silent minute is the part that cannot be cut.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Terminal velocity is a constant velocity, which means the acceleration is zero, not that there are no forces. | The weight and the drag are both still acting; they are simply balanced. A second trap: when a parachute opens the diver slows down but does not stop and does not move upward. The drag exceeds the weight only while the diver is moving fast, so it decelerates the diver to a new, lower terminal velocity. Saying the diver "moves back up" is wrong. |
Motion with resistance: worksheet
6 questions, 15 marks. Written in the style of the papers; no past paper question is reproduced.
An object is released from rest and falls through air. Describe the forces on it and its acceleration at three stages: immediately after release, partway down while speeding up, and at terminal velocity.
A raindrop of weight 4.0 × 10⁻⁵ N falls at terminal velocity. State the drag force acting on it, and the resultant force.
A ball of mass 0.20 kg falls through a liquid in which the drag force is D = 0.40v (D in N, v in m s⁻¹). Taking g = 9.8 m s⁻², find its terminal velocity.
Sketch in words the velocity-time graph for a stone dropped from rest into deep water where there is significant drag, until it reaches terminal velocity.
A skydiver is falling at a steady terminal velocity and then opens a parachute. Explain, in terms of forces, why the diver slows down and then falls at a new steady speed.
A student claims that at terminal velocity "there is no force on the object". Correct this statement and give the precise condition that holds at terminal velocity.
Answer key and marking notes
- At release: drag is zero, so the only force is weight and the acceleration is g (maximum). ✓
- Speeding up: drag has grown but is still less than weight, so the resultant is downward and the acceleration is positive but decreasing. ✓
- Terminal velocity: drag equals weight, the resultant is zero, so the acceleration is zero and the speed is constant. ✓
- At terminal velocity drag = weight = 4.0 × 10⁻⁵ N, acting upward. ✓
- The resultant force is zero. ✓
- Weight = mg = 0.20 × 9.8 = 1.96 N. ✓
- At terminal velocity drag = weight: 0.40v = 1.96. ✓
- v = 1.96 / 0.40 = 4.9 m s⁻¹. ✓
- The curve starts steep (gradient g) at the origin. ✓
- The gradient decreases as drag builds, and the curve flattens to a horizontal line at the terminal velocity. ✓
- The parachute increases the area, so the drag suddenly becomes much larger than the weight. ✓
- The resultant force is now upward, so the diver decelerates. ✓
- As the speed falls, the drag decreases until it again equals the weight, giving a new, lower terminal velocity. ✓
- There are still two forces, the weight and the drag; they are equal and opposite. ✓
- The correct condition is that the resultant force is zero, so the acceleration is zero and the velocity is constant. ✓
17 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
An object falling at terminal velocity has an acceleration of:
- Ag
- Bgreater than g
- Czero
- Dequal to its velocity
As a falling object speeds up, the drag force on it:
- Adecreases
- Bincreases
- Cstays constant
- Dreverses direction
At the instant an object is released from rest in air, its acceleration is:
- Azero
- Bgreater than g
- Cequal to the terminal velocity
- Dg, because drag is zero
The drag force on a moving object always acts:
- Aopposite to the velocity
- Bin the direction of motion
- Cdownward
- Dtoward the centre of the Earth
An object reaches terminal velocity when:
- Athe drag is zero
- Bthe weight is zero
- Cthe drag equals the weight
- Dthe acceleration equals g
An object of weight 10 N falls where the drag is D = 2.0v (D in N, v in m s⁻¹). Its terminal velocity is:
- A20 m s⁻¹
- B5.0 m s⁻¹
- C0.2 m s⁻¹
- D8.0 m s⁻¹
A dense metal ball and a light plastic ball of the same size and shape are dropped in air. The metal ball's terminal velocity is:
- Alower
- Bthe same
- Czero
- Dhigher
The velocity-time graph for an object dropped in air and reaching terminal velocity is:
- Aa curve that flattens to a constant value
- Ba straight line through the origin
- Ca horizontal line from the start
- Da curve that steepens
When a skydiver opens a parachute at terminal velocity, the diver immediately:
- Aspeeds up
- Bmoves upward
- Cdecelerates
- Dstays at the same speed
Increasing the surface area of a falling object, with its weight unchanged, gives it a terminal velocity that is:
- Ahigher
- Blower
- Cunchanged
- Dzero
The resistive force on an object moving through a liquid is best described as a:
- Agravitational force
- Bnormal contact force
- Cmagnetic force
- Dviscous drag force
On the Moon, which has no atmosphere, a hammer and a feather are released together from the same height. They:
- Aland at the same time
- Bthe hammer lands first
- Cthe feather lands first
- Dnever land
While a dropped object is still speeding up but before terminal velocity, its acceleration is:
- Aincreasing
- Bconstant at g
- Cdecreasing
- Dzero
A raindrop of weight 0.60 mN falls where the drag is D = 0.10v (D in mN, v in m s⁻¹). Its terminal velocity is:
- A0.6 m s⁻¹
- B6.0 m s⁻¹
- C60 m s⁻¹
- D1.7 m s⁻¹
Once an object is moving at terminal velocity, its kinetic energy is:
- Aincreasing
- Bdecreasing
- Czero
- Dconstant
A parachute is useful for landing because it:
- Aincreases drag and lowers the terminal velocity
- Breduces the weight
- Cremoves air resistance
- Dincreases the acceleration
An object falling at terminal velocity loses gravitational potential energy steadily, yet its kinetic energy stays constant. The energy is mainly transferred to:
- Akinetic energy of the object
- Belastic potential energy
- Cinternal energy of the air and object
- Dgravitational field energy
Quiz key
At terminal velocity the velocity is constant, so the acceleration is zero.
Drag increases with speed, always opposing the motion.
At release the speed is zero so drag is zero; the only force is weight and a = g.
Drag and other resistive forces always oppose the relative motion, so they act opposite to the velocity.
At terminal velocity the upward drag has grown to equal the downward weight, so the resultant is zero.
2.0v = 10, so v = 5.0 m s⁻¹.
The heavier ball needs a larger drag to balance its weight, which means a higher speed, so its terminal velocity is higher.
The gradient (acceleration) starts at g and falls to zero, so the curve rises then levels off.
The larger area increases drag above the weight, giving an upward resultant, so the diver decelerates to a new lower terminal velocity.
More area means more drag at a given speed, so the drag balances the weight at a lower speed.
Motion through a fluid such as a liquid produces a viscous drag force opposing the motion.
With no air resistance both have acceleration g, so they fall together and land at the same time.
As drag grows, the resultant force falls, so the acceleration decreases from g toward zero.
0.10v = 0.60, so v = 6.0 m s⁻¹.
At terminal velocity the speed is constant, so the kinetic energy is constant.
The large area greatly increases drag, lowering the terminal velocity to a safe landing speed.
Since KE is constant, the work done by gravity is transferred against drag into internal energy (heating the air and object).
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.