Forces and their interactions

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レッスンノート

Scalars and Vectors

Scalar quantities have only a magnitude (size) and no direction.
Vector quantities have both a magnitude and a direction.
Examples of scalars: mass, distance, speed, time, energy, temperature.
Examples of vectors: force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength.
A vector can be represented by an arrow: the length shows the magnitude and the arrowhead shows the direction.
Distance is a scalar; displacement is the corresponding vector (distance in a given direction).
Speed is a scalar; velocity is the corresponding vector (speed in a given direction).

Contact and Non-Contact Forces

A force is a push or a pull that acts on an object due to an interaction with another object.
Forces can change an object's speed, direction, or shape.
Contact forces act between objects that are physically touching.
Examples of contact forces: friction, air resistance (drag), tension, normal contact force (reaction force).
Non-contact forces act at a distance without the objects touching, due to a field.
Examples of non-contact forces: gravitational force, electrostatic force, magnetic force.
Friction opposes motion and occurs when surfaces rub together; air resistance is a type of friction acting on objects moving through air.
Tension is the pulling force in a cable, rope or string when forces act on its ends.

Forces as Vectors and Force Pairs

Force is a vector quantity: it has both magnitude (in newtons, N) and direction.
The direction of a force can be described as left, right, up, down, or using an angle to the horizontal or vertical.
When two objects interact, they exert forces on each other; these are called force pairs.
Example: a laptop resting on a desk pushes down on the desk, and the desk pushes up on the laptop.
Example: a person standing on the Earth pulls the Earth gravitationally, and the Earth pulls the person gravitationally.
Force pairs can be shown using arrows in vector diagrams.

Weight, Mass and Gravity

Mass is a measure of the amount of matter in an object; it is measured in kilograms (kg) and is a scalar.
Weight is the force acting on an object due to gravitational attraction; it is measured in newtons (N) and is a vector.
Weight depends on the object's mass and the gravitational field strength (g) at its location.
The weight of an object acts at a single point called the centre of mass (or centre of gravity).
For a symmetrical object of uniform density, the centre of mass is at the point of symmetry.
Mass stays the same everywhere, but weight changes if the gravitational field strength changes (e.g., on the Moon).
Weight is measured directly using a calibrated spring-balance (newton-meter); mass is measured using a top-pan balance.

Mass and Weight on Earth and the Moon

Calculating Weight

The equation linking weight, mass and gravitational field strength is: W = m × g.
W is weight in newtons (N), m is mass in kilograms (kg), and g is gravitational field strength in newtons per kilogram (N/kg).
On Earth, g is approximately 9.8 N/kg (often taken as 10 N/kg for simpler calculations).
Weight and mass are directly proportional: doubling the mass doubles the weight (for a given g).
An object in free fall falls solely under gravity and accelerates towards Earth at about 9.8 m/s².
To find mass from weight, rearrange: m = W ÷ g.

Resultant Forces

A resultant force is a single force that has the same effect as all the original forces acting together.
Forces acting in the same direction are added; forces acting in opposite directions are subtracted.
If the forces cancel out completely, the resultant force is zero and the forces are balanced.
If the forces do not cancel out, there is an unbalanced force (resultant force) and the object's motion changes.
Always state both the magnitude and direction of a resultant force (e.g., '2 N to the left').
Example: a tug-of-war with 80 N left and 100 N right gives a resultant of 20 N to the right.

Illustrations of a baseball player hitting a ball and a person pushing a lawnmower, demonstrating resultant forces and acceleration.

Free Body Diagrams

A free body diagram shows all the forces acting on a single object as labelled arrows.
Each arrow is scaled to the magnitude of the force and points in the direction the force acts.
Forces are drawn acting from the centre of mass of the object.
Common forces to include: weight (down), normal contact force (perpendicular to surface), friction (opposing motion), tension (along string/rope), upthrust (upwards in a fluid).
Free body diagrams help identify balanced and unbalanced forces and can be used to find the resultant force.
If the force arrows form a closed loop, the forces are balanced (no resultant force).

A free-body diagram: two applied forces (F1, F2), friction, and weight drawn as arrows from a central point representing the object.

Balanced and Unbalanced Forces

Balanced forces produce no resultant force; the object remains at rest or moves at constant velocity.
Unbalanced forces produce a resultant force; the object accelerates, decelerates, or changes direction.
An object moving at constant speed in a straight line has balanced forces acting on it.
If the resultant force on an object is zero, it is in equilibrium.
When several forces act at angles, the resultant can be found by resolving forces into horizontal and vertical components or by using a scale drawing.
A single force can be resolved into two perpendicular components that together have the same effect.

A car with balanced forces at constant speed, and a seesaw with balanced moments, illustrating equilibrium.

スライド

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練習問題

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1.Which of the following is a vector quantity?
Easy
- AVelocity
- BSpeed
- CMass
- DDistance
2.Which of the following is a contact force?
Easy
- AFriction
- BGravitational force
- CElectrostatic force
- DMagnetic force
3.A student has a mass of 50 kg. What is their weight on Earth? Use g = 9.8 N/kg.
Medium
- A490 N
- B50 N
- C9.8 N
- D0.2 N
4.Mass is a scalar quantity and weight is a vector quantity.
Easy
True or false?
5.A resultant force of zero means that no forces are acting on the object.
Easy
True or false?
6.Which of the following are non-contact forces? (Select all that apply.)
Medium
- AGravitational force
- BElectrostatic force
- CMagnetic force
- DFriction
- EAir resistance
7.Match each force with its correct description.
Medium
- Weight
- Friction
- Tension
- Upthrust
- The force of gravity on a mass
- A force that opposes motion between surfaces in contact
- A pulling force transmitted through a cable or rope
- The upward force exerted by a fluid on an object
8.Place the steps for calculating the resultant force of two forces acting in opposite directions in the correct order.
Medium
- Identify the direction of the larger force
- Subtract the smaller force from the larger force
- State the magnitude and direction of the resultant force

もっと問題

9.Which of the following quantities is a scalar?
Medium
- Adisplacement
- Bvelocity
- Cdistance
- Dforce
10.Which of the following is a non-contact force?
Medium
- Afriction
- Btension
- Cair resistance
- Dmagnetic force
11.A student has a mass of 50 kg. The gravitational field strength on Earth is 9.8 N/kg. What is the student's weight on Earth?
Medium
- A5.1 N
- B50 N
- C490 N
- D490 kg
12.A box is pushed to the right with a force of 30 N while friction acts to the left with a force of 12 N. What is the resultant force on the box?
Medium
- A18 N to the right
- B42 N to the right
- C18 N to the left
- D42 N to the left
13.An object is moving at a constant velocity in a straight line. Which statement is correct?
Medium
- AA resultant force acts in the direction of motion.
- BThe resultant force on the object is zero.
- CThe object must have no forces acting on it.
- DA resultant force acts opposite to the direction of motion.
14.Which of the following are contact forces? (Select all that apply.)
Medium
- Afriction
- Bgravitational force
- Ctension
- Delectrostatic force
- Eair resistance
15.Which of the following statements about weight and mass are correct? (Select all that apply.)
Hard
- AMass is measured in kilograms.
- BWeight is measured in newtons.
- CMass changes depending on the gravitational field strength.
- DWeight is a vector quantity.
- EWeight is a scalar quantity.
16.Gravitational force is a non-contact force.
Easy
True or false?
17.The weight of an object is the same on the Moon as it is on Earth.
Easy
True or false?
18.Match each quantity with whether it is a scalar or a vector.
Medium
- Distance
- Displacement
- Speed
- Velocity
- Scalar
- Vector
19.Put the steps for drawing a free body diagram in the correct order.
Medium
- Draw the object as a dot
- Identify all forces acting on the object
- Draw arrows from the dot to show each force
- Label each arrow with the force name and value
20.Put the steps for finding the resultant of two forces acting in opposite directions in the correct order.
Medium
- Identify the size and direction of each force
- Subtract the smaller force from the larger force
- State the direction of the resultant force as the direction of the larger force
- Write the final answer with magnitude and direction
21.The results show force (N) and acceleration (m/s²). Which point is anomalous?
Medium
- A0.2 N, 0.29 m/s²
- B0.4 N, 0.57 m/s²
- C0.6 N, 0.86 m/s²
- D0.8 N, 1.24 m/s²
22.A student writes down four quantities. Which one is a vector quantity?
Easy
- ASpeed
- BDistance
- CAcceleration
- DTemperature
23.A boat is travelling at a constant speed of 8 m/s due north. Which statement about the forces on the boat is correct?
Medium
- AThe resultant force on the boat is zero.
- BThe resultant force on the boat is directed due north.
- CThe resultant force on the boat is equal to its weight.
- DThe resultant force on the boat is directed due south.
24.Air resistance is a contact force.
Easy
True or false?
25.A skydiver of mass 70 kg is falling at terminal velocity. What is the air resistance acting on the skydiver? Use g = 9.8 N/kg.
Medium
- A686 N upwards
- B686 N downwards
- C70 N upwards
- D0 N
26.Match each force to the correct description.
Medium
- Friction
- Upthrust
- Tension
- Normal contact force
- The force that pushes touching objects apart, acting perpendicular to a surface
- The force that opposes motion when two surfaces rub together
- The upward force on an object in a fluid
- The pulling force in a rope or cable when it is stretched
27.A box is sliding down a rough slope at constant speed. Which statements are correct? (Select all that apply.)
Medium
- AThe forces on the box are balanced.
- BThe box has a resultant force down the slope.
- CFriction acts up the slope.
- DThe normal contact force acts parallel to the slope.
- EThe weight of the box acts vertically downwards.
28.A student uses a newton-meter to measure the weight of a metal block on Earth. The reading is 14.7 N. The student then takes the same block to a planet where g = 3.7 N/kg. What is the mass of the block and its weight on the new planet? Use g = 9.8 N/kg on Earth.
Hard
- AMass = 1.5 kg, weight on new planet = 5.6 N
- BMass = 1.5 kg, weight on new planet = 14.7 N
- CMass = 4.0 kg, weight on new planet = 14.8 N
- DMass = 1.5 kg, weight on new planet = 3.7 N
29.Put the steps for drawing a free body diagram of a car accelerating along a straight road into the correct order.
Medium
- Draw the object as a simple shape or dot.
- Identify all the forces acting on the car (thrust, friction, weight, normal contact force).
- Draw each force as an arrow starting at the object, pointing in the direction the force acts.
- Make the length of each arrow represent the magnitude of that force.
- Label each arrow with the name of the force.
30.For a stationary object, the forces acting on it must be balanced.
Medium
True or false?
31.A satellite orbits Earth in a circular path at constant speed. Which statements are correct? (Select all that apply.)
Hard
- AThe satellite's velocity is constantly changing.
- BThe satellite has zero acceleration.
- CThe gravitational force provides the centripetal force.
- DThe satellite's speed is constant but its direction changes.
- EThe resultant force on the satellite is zero.
32.Which of the following correctly describes the difference between mass and weight?
Medium
- AMass is a force and weight is a scalar.
- BMass is a scalar and weight is a force.
- CMass is measured in newtons and weight in kilograms.
- DMass and weight are the same quantity measured in different units.
33.A student measures the weight of a metal block using a spring-balance (newton-meter). What is the correct unit for the reading?
Medium
- ANewtons
- BKilograms
- CNewtons per kilogram
- DMetres per second squared
34.A student uses a newton-meter to measure the weight of a metal block on Earth. The reading is 14.7 N. The student then takes the same block to a planet where g = 3.7 N/kg. What is the weight of the block on that planet?
Medium
- A14.7 N
- B5.55 N
- C39.2 N
- D1.5 N
35.A student sets up a trolley on a runway, attached by a string over a pulley to a mass hanger. She places masses on the trolley and moves them one at a time to the hanger to change the accelerating force. Which of the following are correct experimental techniques? (Select all that apply.)
Medium
- AKeep the total mass of the moving system constant by leaving unused masses on the trolley
- BMeasure the acceleration using a light gate or video analysis
- CAdd all the masses to the hanger at once to get the largest possible force
- DTilt the runway slightly to compensate for friction acting on the trolley
- EMeasure the mass of the trolley using a newton-meter
36.Which piece of apparatus is used to measure the weight of an object directly?
Easy
- ATop-pan balance
- BNewton-meter (spring-balance)
- CMeasuring cylinder
- DMetre ruler
37.A newton-meter measures weight directly in newtons.
Easy
True or false?
38.A student investigates force and acceleration using a trolley. The graph of acceleration against force gives a straight line through the origin with gradient 1.43 m/s² per N. What does the gradient represent?
Medium
- AThe mass of the trolley and weight system
- BThe reciprocal of the mass of the trolley and weight system
- CThe weight of the trolley and weight system
- DThe gravitational field strength
39.A student is asked to improve a trolley experiment to compensate for friction. Which of the following are valid improvements? (Select all that apply.)
Hard
- ATilt the runway slightly until the trolley moves at constant speed when given a small push
- BAdd extra mass to the trolley to increase friction
- CUse a lubricant on the runway
- DIncrease the mass on the hanger to overcome friction
- EIgnore friction because it has no effect on the results
40.Match each piece of apparatus with what it measures.
Medium
- Newton-meter
- Top-pan balance
- Light gate
- Protractor
- Force in newtons
- Mass in kilograms
- Acceleration or speed
- Angle in degrees
41.A box has a mass of 12 kg. Calculate its weight on Earth using g = 9.8 N/kg. Give your answer in newtons.
Medium
42.Complete the sentences about scalars and vectors.
Easy
A scalar quantity has magnitude only, whereas a vector quantity has both magnitude and ____.
43.What is the name of the single force that has the same effect as all the forces acting on an object combined?
Medium
44.A book has a mass of 1.5 kg. Calculate its weight on Earth, where g = 9.8 N/kg. Give your answer in newtons.
Medium
45.A space probe has a weight of 5000 N on Earth. The gravitational field strength on Mercury is 3.7 N/kg and on Earth is 9.8 N/kg. Calculate the weight of the probe on Mercury. Give your answer to 2 significant figures.
Hard
46.Name the three non-contact forces listed in the notes.
Medium
The three non-contact forces are ____, ____, and ____.
47.Using the graph, the line of best fit has a gradient of 1.43 m/s² per N. Calculate the mass of the trolley and weight system. Give your answer in kg.
Hard
48.A bag of flour has a mass of 2.5 kg. Calculate its weight on Earth, where g = 9.8 N/kg. Give your answer in newtons.
Medium
49.Complete the sentence about gravitational field strength.
Easy
Gravitational field strength is measured in ____ and on Earth has a value of about ____.
50.An astronaut has a weight of 735 N on Earth, where g = 9.8 N/kg. On the Moon g = 1.6 N/kg. Calculate the astronaut's weight on the Moon. Give your answer in newtons.
Medium
51.A resultant force of 18 N acts on a trolley of mass 6.0 kg. Calculate the acceleration of the trolley. Give your answer in m/s².
Medium
52.A car of mass 1200 kg is travelling at a constant velocity of 15 m/s due east. What is the resultant force acting on the car? Give your answer in newtons.
Medium
53.Explain why weight is a vector quantity but mass is a scalar quantity.
Hard
54.A student is sitting still on a chair. Name the forces acting on the student and state whether each is a contact or non-contact force.
Hard
55.Explain why she keeps the unused masses on top of the trolley.
Hard
56.A car is moving along a straight road at a constant speed. Explain, in terms of the forces acting on the car, why the car is not accelerating.
Hard
57.A book is resting on a table. Describe the two forces acting on the book and explain why the book is in equilibrium.
Medium
58.A box has a mass of 12 kg. Calculate its weight on Earth using g = 9.8 N/kg. Give your answer in newtons.
Medium
- A129.4 N
- B105.8 N
- C117.6 N
- D141.2 N
59.A book has a mass of 1.5 kg. Calculate its weight on Earth, where g = 9.8 N/kg. Give your answer in newtons.
Medium
- A15.7 N
- B14.7 N
- C13.7 N
- D16.7 N
60.A space probe has a weight of 5000 N on Earth. The gravitational field strength on Mercury is 3.7 N/kg and on Earth is 9.8 N/kg. Calculate the weight of the probe on Mercury. Give your answer to 2 significant figures.
Hard
- A1710 N
- B2090 N
- C2280 N
- D1900 N
61.In an experiment on force and acceleration, the line of best fit on a graph of acceleration against force has a gradient of 1.43 m/s² per N. Calculate the mass of the trolley and weight system. Give your answer in kg.
Hard
- A1.7 kg
- B2.7 kg
- C0.7 kg
- D-0.3 kg
62.A bag of flour has a mass of 2.5 kg. Calculate its weight on Earth, where g = 9.8 N/kg. Give your answer in newtons.
Medium
- A24.5 N
- B22 N
- C27 N
- D29.5 N
63.An astronaut has a weight of 735 N on Earth, where g = 9.8 N/kg. On the Moon g = 1.6 N/kg. Calculate the astronaut's weight on the Moon. Give your answer in newtons.
Medium
- A132 N
- B108 N
- C144 N
- D120 N
64.A resultant force of 18 N acts on a trolley of mass 6.0 kg. Calculate the acceleration of the trolley. Give your answer in m/s².
Medium
- A4 m/s²
- B3 m/s²
- C2 m/s²
- D5 m/s²
65.A car of mass 1200 kg is travelling at a constant velocity of 15 m/s due east. What is the resultant force acting on the car? Give your answer in newtons.
Medium
- A2 N
- B-1 N
- C0 N
- D1 N

フラッシュカード

What is a scalar quantity?

A scalar quantity has magnitude (size) only, with no direction. Examples include mass, distance, speed, time, energy and temperature.

What is a vector quantity?

A vector quantity has both magnitude and an associated direction. Examples include force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength.

How can a vector quantity be represented?

A vector can be represented by an arrow: the length of the arrow represents the magnitude, and the direction of the arrow represents the direction of the vector.

What is a force?

A force is a push or a pull that acts on an object due to the interaction with another object. Force is a vector quantity, measured in newtons (N).

What is a contact force? Give examples.

A contact force acts between objects that are physically touching. Examples include friction, air resistance, tension and normal contact force (reaction force).

What is a non-contact force? Give examples.

A non-contact force acts at a distance, without the objects touching, due to a field. Examples include gravitational force, electrostatic force and magnetic force.

What is weight?

Weight is the force acting on an object due to gravity. It is a vector quantity measured in newtons (N).

What is mass?

Mass is a measure of the amount of matter in an object. It is a scalar quantity measured in kilograms (kg).

State the equation linking weight, mass and gravitational field strength.

weight = mass × gravitational field strength (W = m g), where W is in newtons (N), m in kilograms (kg) and g in newtons per kilogram (N/kg).

What is gravitational field strength?

Gravitational field strength (g) is the force per unit mass, measured in N/kg. On Earth it is about 9.8 N/kg. It is equivalent to the acceleration of free fall.

What is the centre of mass of an object?

The centre of mass (or centre of gravity) is the point through which the weight of an object acts. For a symmetrical object of uniform density, it is at the point of symmetry.

What is a resultant force?

A resultant force is a single force that has the same effect as all the original forces acting together. It determines the direction and magnitude of the final force on an object.

How do you calculate the resultant of two forces acting in a straight line?

Add forces acting in the same direction; subtract forces acting in opposite directions. State both magnitude and direction, e.g. '2 N to the left'.

What are balanced forces?

Balanced forces cancel each other out, so there is no resultant force (resultant = 0 N). The object remains at rest or moves at constant velocity.

What are unbalanced forces?

Unbalanced forces do not cancel completely, so there is a resultant force. The object accelerates (changes speed and/or direction) in the direction of the resultant force.

What is a free body diagram?

A free body diagram shows the forces acting on a single object as vector arrows. Each arrow is scaled to the force's magnitude, points in the force's direction, and is labelled with the force's name.

What is equilibrium?

An object is in equilibrium when the forces acting on it are balanced, so the resultant force is zero. The object stays at rest or moves at constant velocity.

How can a single force be resolved into components?

A single force can be resolved into two components acting at right angles to each other (horizontal and vertical). The two components together have the same effect as the single force.

How do you find the resultant of two forces at right angles using a scale drawing?

Draw the two force vectors to scale, head to tail. The resultant is the vector from the tail of the first to the head of the last. Measure its length and convert using the scale to find magnitude; measure the angle for direction.

What is the difference between distance and displacement?

Distance is a scalar: it measures the total length of the path taken. Displacement is a vector: it measures the straight-line distance from start to finish, including direction.

What is the difference between speed and velocity?

Speed is a scalar: it has magnitude only. Velocity is a vector: it has both magnitude (speed) and direction.

Give an example of a force pair between two objects.

When two objects interact, each exerts a force on the other. For example, a book on a table: the book pushes down on the table, and the table pushes up on the book with equal and opposite forces.

How is weight measured?

Weight is measured directly using a calibrated spring-balance (newton-meter), which measures force in newtons. Mass is measured with a top-pan balance, and weight can then be calculated using W = m g.

Why does an object's weight change on different planets but its mass does not?

Mass is the amount of matter and stays the same everywhere. Weight depends on gravitational field strength (g), which varies from planet to planet, so weight changes with location.

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