Terminal velocity

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レッスンノート

Key Concepts

Newton's first law: An object's speed stays constant unless a resultant force acts on it.
Newton's second law: Acceleration is proportional to the resultant force; larger force → larger acceleration.
Newton's third law: Forces between two objects are equal in size and opposite in direction.
Terminal velocity is the maximum constant speed reached when forces are balanced.

Stages of a Skydive

1. Just jumped: Only weight acts → skydiver accelerates downwards.
2. Speeding up: Air resistance increases with speed; resultant force decreases → acceleration decreases.
3. Terminal velocity: Air resistance = weight → balanced forces, no resultant force → constant speed (terminal velocity).
4. Parachute opens: Larger surface area → air resistance increases greatly → resultant force upwards → deceleration.
5. Second terminal velocity: Slower speed reduces air resistance until it equals weight again → new, slower constant speed.

Graph of a Skydive

A speed–time graph shows speed increasing then levelling off at terminal velocity.
After parachute opens, speed drops rapidly then becomes constant at a lower terminal velocity.
The gradient of the graph represents acceleration (positive gradient = accelerating, negative = decelerating, flat = constant speed).

Factors Affecting Terminal Velocity

Weight: Heavier objects have a higher terminal velocity (larger weight requires larger air resistance to balance).
Surface area: Larger surface area increases air resistance, reducing terminal velocity (e.g., parachute).
Shape: Streamlined shapes reduce air resistance, allowing higher terminal velocity.

Examples and Applications

A car travelling at constant speed on a motorway has balanced forces (driving force = resistive forces).
If a resultant forward force acts on a car, it accelerates (speeds up).
Sky divers reach terminal velocity twice: first without parachute (fast), then with parachute (slow).

Particle arrangement in solids, liquids, and gases. In a solid, particles are closely packed in a regular pattern; in a liquid, they are close but irregular; in a gas, they are far apart and random. This model helps explain density and state changes.

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練習問題

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1.What happens to air resistance as the speed of an object increases?
Easy
- AIt increases
- BIt decreases
- CIt stays the same
- DIt becomes zero
2.A car is travelling at a constant speed. All the forces on the car are balanced. What happens to the speed of the car?
Easy
- AIt stays the same
- BIt increases
- CIt decreases
- DIt becomes zero
3.A car has a resultant force forwards. What happens to the speed of the car?
Easy
- AIt increases
- BIt decreases
- CIt stays the same
- DIt becomes zero
4.A skydiver has just jumped out of an aeroplane. The only force acting is their weight. What is the motion of the skydiver?
Medium
- AAccelerating downwards
- BConstant speed downwards
- CDecelerating downwards
- DStationary
5.A skydiver has reached terminal velocity. Which statement about the forces is correct?
Medium
- AWeight equals air resistance
- BWeight is greater than air resistance
- CWeight is less than air resistance
- DThere is no weight
6.A skydiver opens their parachute. What happens to the air resistance immediately after opening?
Easy
- AIt increases dramatically
- BIt decreases dramatically
- CIt stays the same
- DIt becomes zero
7.After opening the parachute, the skydiver decelerates. What is the direction of the resultant force?
Medium
- AUpwards
- BDownwards
- CHorizontal
- DZero
8.A skydiver reaches a second terminal velocity after opening the parachute. How does this second terminal velocity compare to the first?
Medium
- AIt is slower
- BIt is faster
- CIt is the same
- DIt is zero

もっと問題

9.According to Newton's second law, what happens to acceleration if the resultant force decreases?
Medium
- AAcceleration decreases
- BAcceleration increases
- CAcceleration stays the same
- DAcceleration becomes zero
10.A skydiver is falling at constant speed. Which of Newton's laws explains this?
Medium
- ANewton's first law
- BNewton's second law
- CNewton's third law
- DNewton's law of gravitation
11.What name is given to the maximum constant speed reached by a falling object when air resistance equals weight?
Easy
- ATerminal velocity
- BAcceleration
- CResultant force
- DWeight
12.A skydiver's speed-time graph shows a horizontal line. What does this indicate?
Easy
- ATerminal velocity
- BAcceleration
- CDeceleration
- DFree fall
13.A skydiver of mass 80 kg has a weight of 800 N. When falling at terminal velocity, the air resistance acting on the skydiver is:
Medium
- A800 N
- B0 N
- Cgreater than 800 N
- Dless than 800 N
14.A skydiver jumps from a plane. At one point, the air resistance is 600 N and their weight is 800 N. What is the resultant force on the skydiver?
Medium
- A200 N downwards
- B200 N upwards
- C1400 N downwards
- D1400 N upwards
15.The graph shows the speed of a skydiver against time. During the first 10 seconds, the gradient of the graph decreases. This indicates that:
Medium
- Aacceleration is decreasing
- Bacceleration is increasing
- Cspeed is decreasing
- Dspeed is constant
16.A skydiver opens their parachute. The air resistance immediately becomes 1200 N, and their weight is 800 N. What is the direction and magnitude of the resultant force?
Medium
- A400 N upwards
- B400 N downwards
- C2000 N upwards
- D2000 N downwards
17.A falling object reaches terminal velocity when:
Easy
- Aair resistance equals weight
- Bair resistance is zero
- Cweight is zero
- Dair resistance is greater than weight
18.A skydiver falls with an acceleration of 9.8 m/s² just after jumping. As speed increases, air resistance increases. According to Newton's second law, the acceleration:
Hard
- Adecreases because resultant force decreases
- Bincreases because resultant force decreases
- Cremains constant because weight is constant
- Ddecreases because mass decreases
19.A skydiver has just opened their parachute. The speed-time graph shows a steep negative gradient. This means the skydiver is:
Medium
- Adecelerating
- Baccelerating
- Cat terminal velocity
- Dmoving upwards
20.A feather and a coin are dropped from the same height in a vacuum. Which statement is correct?
Medium
- AThey reach the ground at the same time.
- BThe coin reaches the ground first.
- CThe feather reaches the ground first.
- DNeither falls because there is no air.
21.A skydiver reaches terminal velocity of 50 m/s. Their parachute opens, and they decelerate to a new terminal velocity of 10 m/s. The air resistance at the lower terminal velocity is:
Medium
- Aequal to the weight
- Bless than the weight
- Cgreater than the weight
- Dzero
22.Which of Newton's laws states that the acceleration of an object is proportional to the resultant force on it?
Easy
- ANewton's second law
- BNewton's first law
- CNewton's third law
- DNewton's law of gravitation
23.A skydiver falls at terminal velocity. Which statement about the forces is correct?
Medium
- AAir resistance equals weight and there is no resultant force.
- BAir resistance is greater than weight and there is a resultant force upwards.
- CAir resistance is less than weight and there is a resultant force downwards.
- DAir resistance is zero and weight is the only force.
24.A student drops a ball bearing into a tube of viscous oil. The ball bearing accelerates initially, then reaches a constant speed. This constant speed is called:
Easy
- Aterminal velocity
- Binitial velocity
- Caverage velocity
- Dmaximum acceleration
25.A student drops a ball bearing into a tall tube filled with viscous oil. The ball bearing accelerates initially, then reaches a constant speed. Which statement explains why the ball bearing reaches a constant speed?
Medium
- AThe weight of the ball bearing becomes zero.
- BThe upward force from the oil equals the weight of the ball bearing.
- CThe ball bearing loses all its energy.
- DThe tube creates a vacuum around the ball bearing.
26.In an experiment to measure terminal velocity, a student drops small spheres of different diameters into a column of water. Which graph shows the expected relationship between terminal velocity and sphere diameter?
Medium
- AA straight line through the origin with positive slope.
- BA curve that increases and then levels off.
- CA curve that decreases as diameter increases.
- DA horizontal line showing no change.
27.A skydiver of mass 60 kg jumps from a plane. At one instant, the air resistance is 400 N and the weight is 600 N. According to Newton's second law, what is the acceleration of the skydiver at that instant? (Take g = 10 N/kg)
Medium
- A3.3 m/s² downwards
- B10 m/s² downwards
- C6.7 m/s² upwards
- D3.3 m/s² upwards
28.A student investigates terminal velocity by dropping paper cones of different masses but the same shape. Which variable should the student keep constant to ensure a fair test?
Medium
- AThe mass of the cone
- BThe height from which the cone is dropped
- CThe surface area of the cone
- DThe time taken to fall
29.A skydiver jumps from a plane and reaches terminal velocity. She then opens her parachute. Which of the following correctly describes the motion immediately after the parachute opens?
Medium
- AShe continues at the same speed because the forces are balanced.
- BShe accelerates upwards because the resultant force is upwards.
- CShe decelerates because the air resistance is greater than her weight.
- DShe accelerates downwards because her weight is still greater than air resistance.
30.The graph shows the speed of a skydiver against time. Which part of the graph corresponds to the skydiver falling at terminal velocity?
Easy
- AA steeply sloping upward section
- BA horizontal line
- CA downward sloping section
- DA curved section with decreasing slope
31.What is the name given to the constant speed reached by a falling object when air resistance equals weight?
Easy
- AAcceleration
- BTerminal velocity
- CFree fall
- DEquilibrium speed
32.According to Newton's first law, if the forces on a moving object are balanced, what happens to its speed?
Easy
- AIt increases.
- BIt decreases.
- CIt stays the same.
- DIt becomes zero.
33.A skydiver of weight 800 N is falling at terminal velocity. What is the magnitude of the air resistance force acting on the skydiver?
Easy
- A0 N
- B400 N
- C800 N
- D1600 N
34.A student drops a feather and a coin from the same height in a vacuum. Which statement is correct?
Easy
- AThe feather falls slower because it is lighter.
- BThe coin falls faster because it is heavier.
- CBoth fall at the same rate because there is no air resistance.
- DThe feather falls faster because it has a larger surface area.
35.A skydiver reaches a terminal velocity of 50 m/s. After opening the parachute, they decelerate to a new terminal velocity of 10 m/s. What is the ratio of the air resistance at the lower terminal velocity to that at the higher terminal velocity? (Assume weight is constant.)
Hard
- A1:5
- B5:1
- C1:1
- D1:25
36.In an experiment to measure the terminal velocity of a ball bearing in oil, a student records the time to fall between two marks. Which of the following would improve the accuracy of the measurement?
Medium
- AUsing a longer tube so the ball bearing reaches terminal velocity before the first mark.
- BUsing a ball bearing with a larger mass.
- CUsing a less viscous oil.
- DTiming with a stopwatch instead of a light gate.
37.What is the name given to the constant maximum speed reached by a falling object when air resistance equals weight?
Easy
- ATerminal velocity
- BAcceleration
- CDeceleration
- DResultant force
38.According to Newton's first law, if no resultant force acts on a moving object, what happens to its speed?
Easy
- AIt remains constant
- BIt increases
- CIt decreases
- DIt becomes zero
39.A skydiver has just jumped out of an aeroplane and is falling. At one instant, the air resistance is 400 N and the weight is 600 N. What is the resultant force on the skydiver?
Medium
- A200 N downwards
- B200 N upwards
- C1000 N downwards
- D1000 N upwards
40.A skydiver is falling at terminal velocity. Which statement about the forces is correct?
Easy
- AWeight equals air resistance
- BWeight is greater than air resistance
- CWeight is less than air resistance
- DThere is no air resistance
41.What is terminal velocity?
Easy
- AThe maximum speed a falling object reaches when air resistance equals weight
- BThe speed at which an object first starts to fall
- CThe speed at which air resistance is zero
- DThe speed at which weight is zero
42.At terminal velocity, the resultant force on a falling object is zero.
Easy
True or false?
43.According to Newton's second law, if the resultant force on a falling object decreases, what happens to its acceleration?
Medium
- AIt decreases
- BIt increases
- CIt stays the same
- DIt becomes zero
44.Put the following events in the correct order for a skydiver reaching terminal velocity before opening the parachute.
Medium
- Air resistance equals weight
- Skydiver accelerates due to weight
- Air resistance increases as speed increases
- Skydiver reaches terminal velocity
45.Match each stage of a skydive to the correct description of forces.
Hard
- Just after jumping
- Falling at terminal velocity
- Just after opening parachute
- Resultant force upwards
- Only force is weight
- Forces are balanced
46.Which of the following statements about terminal velocity are true? (Select all that apply.)
Hard
- ATerminal velocity is reached when air resistance equals weight
- BTerminal velocity is the same for all falling objects
- CA larger surface area leads to a lower terminal velocity
- DAt terminal velocity, acceleration is zero
47.A skydiver opens their parachute and immediately decelerates because the resultant force is upward.
Medium
True or false?
48.The graph shows the speed of a skydiver against time. Which part of the graph corresponds to the skydiver falling at terminal velocity? (Assume the graph has a flat horizontal section after an initial curve.)
Easy
- AA horizontal line after the curve
- BThe initial upward curve
- CA downward sloping line
- DThe point where the graph starts
49.The graph shows the speed of a skydiver against time. Which part of the graph corresponds to the skydiver falling at terminal velocity? (Assume the graph has a curve that flattens twice.)
Medium
- AThe initial steep upward slope
- BThe first horizontal section
- CThe downward slope after the peak
- DThe final horizontal section
50.A skydiver of mass 70 kg jumps from a plane. At one instant, the air resistance is 500 N and the weight is 700 N. What is the resultant force acting on the skydiver?
Medium
- A200 N downwards
- B200 N upwards
- C1200 N downwards
- D1200 N upwards
51.Complete the sentence using the correct term.
Easy
The force that opposes the motion of an object through air is called ____.
52.A skydiver of weight 800 N is falling at terminal velocity. What is the magnitude of the air resistance force acting on the skydiver? (Give your answer in newtons.)
Easy
53.State what happens to air resistance as the speed of an object increases.
Easy
54.A skydiver of mass 80 kg falls at terminal velocity. Calculate the magnitude of the air resistance force acting on the skydiver. (Take g = 10 N/kg)
Medium
55.Explain how a skydiver reaches a terminal velocity.
Hard
56.A skydiver of weight 800 N is falling at terminal velocity. What is the magnitude of the air resistance force acting on the skydiver? (Give your answer in newtons.)
Easy
- A800 N
- B880 N
- C960 N
- D720 N
57.A skydiver of mass 80 kg falls at terminal velocity. Calculate the magnitude of the air resistance force acting on the skydiver. (Take g = 10 N/kg)
Medium
- A720 N
- B880 N
- C960 N
- D800 N

復習ノート

## Terminal Velocity (Skydiving) - **Newton's First Law**: Speed stays constant unless a resultant force acts. - **Newton's Second Law**: Acceleration ∝ resultant force. - **Newton's Third Law**: Forces between objects are equal and opposite. ### Stages of a Skydive: 1. **Just jumped**: Only weight acts → accelerates downwards. 2. **Speeding up**: Air resistance increases, resultant force decreases → acceleration decreases. 3. **Terminal velocity**: Air resistance = weight → no resultant force → constant speed (terminal velocity). 4. **Parachute opens**: Surface area increases → air resistance > weight → resultant force upward → deceleration. 5. **New terminal velocity**: Slower speed reduces air resistance until balanced → second, slower terminal velocity. ### Key Points: - Air resistance increases with speed. - Terminal velocity is the maximum constant speed when forces balance. - Opening parachute increases air resistance, causing deceleration to a lower terminal velocity.

Terminal velocity: The constant maximum speed reached when the resultant force on an object is zero, e.g., when air resistance equals weight.
Newton's first law: The speed of an object will remain the same unless a resultant force acts on the object.
Newton's second law: The acceleration of an object is proportional to the resultant force on the object.
Newton's third law: If object A exerts a force on object B, then object B exerts a force of equal size and opposite direction on object A.
Air resistance: A frictional force that opposes motion through air; increases with speed and surface area.

フラッシュカード

What is terminal velocity?

Terminal velocity is the constant maximum speed reached when the force of air resistance equals the weight of the falling object, resulting in zero net force and zero acceleration.

According to Newton's first law, what happens to the speed of an object if no resultant force acts on it?

The speed of the object remains the same (constant speed).

According to Newton's second law, how is acceleration related to resultant force?

Acceleration is proportional to the resultant force; larger resultant force gives larger acceleration.

State Newton's third law.

If object A exerts a force on object B, then object B exerts a force of equal size and opposite direction on object A.

What is the only force acting on a skydiver just after jumping out of a plane (before falling fast)?

Their weight (downward force).

How does air resistance change as a skydiver's speed increases?

Air resistance increases as speed increases.

What happens to the resultant downward force on a skydiver as they speed up?

The resultant downward force decreases because air resistance increases, opposing weight.

What happens to the acceleration of a skydiver as they approach terminal velocity?

Acceleration decreases, eventually becoming zero at terminal velocity.

At terminal velocity, how do the forces on a skydiver compare?

The forces are balanced: air resistance equals weight, so resultant force is zero.

What does Newton's first law say about a skydiver at terminal velocity?

Since the resultant force is zero, the skydiver continues moving at constant speed (terminal velocity).

What happens to air resistance when a skydiver opens their parachute?

Air resistance increases dramatically because the parachute increases surface area.

What is the direction of the resultant force just after a parachute opens?

Upward, because air resistance becomes greater than weight.

What happens to the skydiver's motion just after the parachute opens?

The skydiver decelerates (slows down) due to the upward resultant force.

After decelerating with the parachute open, what happens to air resistance?

As the skydiver slows, air resistance decreases until it equals weight again.

Does a skydiver reach a second terminal velocity after opening the parachute?

Yes, a slower terminal velocity when forces are balanced again.

In the speed-time graph of a skydiver, what does a horizontal line indicate?

Constant speed, which occurs at terminal velocity (before and after parachute opening).

In the speed-time graph, what does a decreasing slope (downward curve) indicate?

Deceleration, which happens after the parachute opens.

In the speed-time graph, what does an increasing slope (upward curve) indicate?

Acceleration, which occurs at the start of the fall.

What is the relationship between resultant force and acceleration according to Newton's second law?

The acceleration of an object is proportional to the resultant force on it.

If a car is travelling at constant speed on a motorway, what can be said about the forces?

All forces on the car are balanced; resultant force is zero.

If a car has a resultant force forwards, what happens to its speed?

The car accelerates (speed increases).

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