Resultant forces and Newton's laws

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Lesson notes

Big idea: resultant forces and newton's laws

Key concept: Relationships. Resultant force equals mass times acceleration. Zero resultant force means constant velocity, which can include rest.
Related concepts: Models and evidence. Use a scientific explanation to make predictions, then test it against observations.
Global context: Scientific and technical innovation. Force models explain vehicle acceleration and safety systems.

Resultant Forces

A force is a push or pull that acts on an object due to interaction with another object.
Forces can change an object's speed, direction, shape, or size.
A resultant force is a single force that represents the combined effect of all forces acting on an object.
Balanced forces are equal in magnitude and opposite in direction; they cancel out, giving zero resultant force.
Unbalanced forces produce a non-zero resultant force, causing a change in motion.
To calculate resultant force, assign positive/negative signs to directions and sum the forces.

Forces acting on a book rests on a desk

Newton's First Law

Newton's First Law: An object remains at rest or moves with constant velocity unless acted on by a resultant force.
Constant velocity means no change in speed and no change in direction.
If resultant force is zero, the object is either stationary or moving at constant velocity.
Example: A car moving at constant speed in a straight line has balanced driving and frictional forces.
The Moon orbits Earth at constant speed but changes direction, so it does not obey Newton's First Law (it has a resultant force).

Examples of Newton's First Law

Newton's Second Law

Newton's Second Law: The acceleration of an object is proportional to the resultant force and inversely proportional to its mass.
Equation: F = ma (force in N, mass in kg, acceleration in m/s²).
Acceleration occurs in the same direction as the resultant force.
For a given force, a larger mass gives a smaller acceleration.
Example: A 900 kg car accelerating at 9 m/s² requires a force of 8100 N.

Examples of resultant forces causing acceleration in a baseball and a lawnmower.

Investigating Force & Extension

Aim: Investigate the relationship between force and extension of a spring.
Independent variable: Force (weight added). Dependent variable: Extension.
Use a clamp stand, spring, masses, ruler, and pointer to measure extension.
Calculate extension: extension = final length – original length.
Plot a graph of force vs. extension; a straight line through origin shows direct proportionality (Hooke's Law).
Take readings at eye level to avoid parallax error; repeat for reliability.

Hooke's Law

Hooke's Law: The extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality.
Equation: F = kx, where k is the spring constant (N/m) and x is extension (m).
Spring constant k = F/x; a high k means a stiff spring.
On a force-extension graph, the gradient of the linear region equals the spring constant.
Beyond the limit of proportionality, the graph curves and Hooke's Law no longer applies.

Circular Motion

In circular motion, the velocity changes because direction changes, even if speed is constant.
A force acting perpendicular to motion causes the object to travel in a circle.
The force is always directed toward the centre of the circle (centripetal force).
Factors affecting required force: mass (greater mass needs more force), speed (faster needs more force), radius (smaller radius needs more force).

Friction

Friction opposes motion and causes heating (energy transfer).
Solid friction arises from surface imperfections; can be reduced by lubrication or smoothing.
Drag (air resistance) is friction in fluids; it slows objects and heats them.
Air resistance can be reduced by streamlining the object's shape.

Think like a scientist

Apply different measured horizontal pulls to the same low-speed trolley and measure its acceleration.
Comparison: the resultant horizontal force. Outcome: acceleration in metres per second squared.
Control: keep the trolley's mass constant. Explain why this makes the comparison fairer.
Evidence: Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause.
Safety: Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it.
Inquiry task: State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction.

Evaluate the science

Force models explain vehicle acceleration and safety systems.
The pulling force is not automatically the resultant force; friction must be considered.
Evaluation task: Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

Slides

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Practice questions

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1.Which of the following is the correct definition of a force?
Easy
- AA push or a pull that acts on an object due to interaction with another object
- BA measure of the amount of matter in an object
- CThe rate of change of velocity of an object
- DThe energy transferred when an object is moved
2.What is a resultant force?
Easy
- AA single force that describes all of the forces operating on a body
- BThe largest force acting on an object
- CThe sum of all forces ignoring direction
- DThe force that remains when all other forces are removed
3.A book is at rest on a table. Which statement about the forces acting on the book is correct?
Easy
- AThe weight of the book and the normal contact force are balanced
- BThe weight of the book is greater than the normal contact force
- CThe normal contact force is greater than the weight of the book
- DThere is no resultant force because no forces are acting on the book
4.A car is moving at a constant velocity. The driving force from the engine is 3 kN. What is the frictional force acting on the car?
Medium
- A3 kN
- B0 kN
- C6 kN
- D1.5 kN
5.The Moon orbits the Earth at a constant speed. Which statement about the Moon's motion is correct?
Medium
- AThe Moon is accelerating because its direction is changing
- BThe Moon is not accelerating because its speed is constant
- CThe Moon is not accelerating because no resultant force acts on it
- DThe Moon is accelerating only when its speed changes
6.A moving ball is struck sideways by a force. Which pair of changes is possible?
Easy
- AIts speed and direction change
- BIts mass and chemical element change
- CIts mass increases but its motion cannot change
- DIts direction cannot change
7.A 2 kg object accelerates at 3 m/s². What is the resultant force acting on it?
Easy
- A6 N
- B1.5 N
- C5 N
- D0.67 N
8.A spring has an unstretched length of 5 cm. When a 2 N weight is hung from it, its length becomes 9 cm. What is the spring constant?
Medium
- A50 N/m
- B0.5 N/m
- C0.22 N/m
- D22.2 N/m

Revision notes

## Big idea: resultant forces and newton's laws - **Key concept: Relationships.** Resultant force equals mass times acceleration. Zero resultant force means constant velocity, which can include rest. - **Related concepts: Models and evidence.** Use a scientific explanation to make predictions, then test it against observations. - **Global context: Scientific and technical innovation.** Force models explain vehicle acceleration and safety systems. ## Resultant Forces - A **force** is a push or pull that acts on an object due to interaction with another object. - Forces can change an object's **speed**, **direction**, **shape**, or **size**. - A **resultant force** is a single force that represents the combined effect of all forces acting on an object. - **Balanced forces** are equal in magnitude and opposite in direction; they cancel out, giving zero resultant force. - **Unbalanced forces** produce a non-zero resultant force, causing a change in motion. - To calculate resultant force, assign positive/negative signs to directions and sum the forces. ## Newton's First Law - Newton's First Law: An object remains at rest or moves with **constant velocity** unless acted on by a **resultant force**. - Constant velocity means no change in speed **and** no change in direction. - If resultant force is zero, the object is either stationary or moving at constant velocity. - Example: A car moving at constant speed in a straight line has balanced driving and frictional forces. - The Moon orbits Earth at constant speed but changes direction, so it does **not** obey Newton's First Law (it has a resultant force). ## Newton's Second Law - Newton's Second Law: The **acceleration** of an object is proportional to the resultant force and inversely proportional to its mass. - Equation: **F = ma** (force in N, mass in kg, acceleration in m/s²). - Acceleration occurs in the same direction as the resultant force. - For a given force, a larger mass gives a smaller acceleration. - Example: A 900 kg car accelerating at 9 m/s² requires a force of 8100 N. ## Investigating Force & Extension - Aim: Investigate the relationship between force and extension of a spring. - Independent variable: **Force** (weight added). Dependent variable: **Extension**. - Use a clamp stand, spring, masses, ruler, and pointer to measure extension. - Calculate extension: **extension = final length – original length**. - Plot a graph of force vs. extension; a straight line through origin shows direct proportionality (Hooke's Law). - Take readings at eye level to avoid parallax error; repeat for reliability. ## Hooke's Law - Hooke's Law: The **extension** of an elastic object is directly proportional to the **force** applied, up to the **limit of proportionality**. - Equation: **F = kx**, where k is the spring constant (N/m) and x is extension (m). - Spring constant k = F/x; a high k means a stiff spring. - On a force-extension graph, the gradient of the linear region equals the spring constant. - Beyond the limit of proportionality, the graph curves and Hooke's Law no longer applies. ## Circular Motion - In circular motion, the **velocity** changes because direction changes, even if speed is constant. - A force acting **perpendicular** to motion causes the object to travel in a circle. - The force is always directed toward the **centre** of the circle (centripetal force). - Factors affecting required force: **mass** (greater mass needs more force), **speed** (faster needs more force), **radius** (smaller radius needs more force). ## Friction - **Friction** opposes motion and causes heating (energy transfer). - Solid friction arises from surface imperfections; can be reduced by lubrication or smoothing. - **Drag** (air resistance) is friction in fluids; it slows objects and heats them. - Air resistance can be reduced by **streamlining** the object's shape. ## Think like a scientist - Apply different measured horizontal pulls to the same low-speed trolley and measure its acceleration. - **Comparison:** the resultant horizontal force. **Outcome:** acceleration in metres per second squared. - **Control:** keep the trolley's mass constant. Explain why this makes the comparison fairer. - **Evidence:** Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause. - **Safety:** Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it. - **Inquiry task:** State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction. ## Evaluate the science - Force models explain vehicle acceleration and safety systems. - The pulling force is not automatically the resultant force; friction must be considered. - **Evaluation task:** Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

Newton's First Law: Newton's First Law: An object remains at rest or moves with **constant velocity** unless acted on by a **resultant force**.
Circular Motion: In circular motion, the **velocity** changes because direction changes, even if speed is constant.
Newton's Second Law: Newton's Second Law: The **acceleration** of an object is proportional to the resultant force and inversely proportional to its mass.
Friction: **Friction** opposes motion and causes heating (energy transfer).
Hooke's Law: Hooke's Law: The **extension** of an elastic object is directly proportional to the **force** applied, up to the **limit of proportionality**.
Resultant Forces: A **force** is a push or pull that acts on an object due to interaction with another object.
Force & Extension Investigation: Describe the experiment to investigate the relationship between force and extension of a spring, including variables, method, and analysis.
Designing scientific inquiries: Plan a fair comparison: Apply different measured horizontal pulls to the same low-speed trolley and measure its acceleration.
Evaluating evidence and impacts: Force models explain vehicle acceleration and safety systems. The pulling force is not automatically the resultant force; friction must be considered.
Investigating Force & Extension: Aim: Investigate the relationship between force and extension of a spring.
force: Hooke's Law: The **extension** of an elastic object is directly proportional to the **force** applied, up to the **limit of proportionality**.
speed: Factors affecting required force: **mass** (greater mass needs more force), **speed** (faster needs more force), **radius** (smaller radius needs more force).
direction: Forces can change an object's **speed**, **direction**, **shape**, or **size**.
shape: Forces can change an object's **speed**, **direction**, **shape**, or **size**.
size: Forces can change an object's **speed**, **direction**, **shape**, or **size**.
resultant force: Newton's First Law: An object remains at rest or moves with **constant velocity** unless acted on by a **resultant force**.

Flashcards

Which of the following is the correct definition of a force?

A push or a pull that acts on an object due to interaction with another object A force is a push or a pull that acts on an object due to the interaction with another object. The other options describe mass, acceleration, and work respectively.

What is a resultant force?

A single force that describes all of the forces operating on a body A resultant force is a single force that describes all of the forces operating on a body. The other options are incorrect because direction must be considered, and resultant force is not simply the largest or remaining force.

A book is at rest on a table. Which statement about the forces acting on the book is correct?

The weight of the book and the normal contact force are balanced For a book at rest, the gravitational pull (weight) and the push force of the table (normal contact force) are equal in magnitude and opposite in direction, so they are balanced. A resultant force of zero does not mean no forces act.

A car is moving at a constant velocity. The driving force from the engine is 3 kN. What is the frictional force acting on the car?

3 kN According to Newton's first law, if the car moves at constant velocity, the resultant force is zero. Therefore, the frictional force must equal the driving force in magnitude and oppose it, so frictional force = 3 kN.

The Moon orbits the Earth at a constant speed. Which statement about the Moon's motion is correct?

The Moon is accelerating because its direction is changing The Moon moves at constant speed but changes direction, so its velocity changes. Acceleration is a change in velocity, so the Moon is accelerating. Newton's first law states that a resultant force is needed to change velocity.

A moving ball is struck sideways by a force. Which pair of changes is possible?

Its speed and direction change A resultant force can change velocity, which includes speed and direction; it does not change the mass of the ball.

A 2 kg object accelerates at 3 m/s². What is the resultant force acting on it?

6 N Using Newton's second law, F = ma = 2 kg × 3 m/s² = 6 N. The other options result from incorrect operations (dividing instead of multiplying, etc.).

A spring has an unstretched length of 5 cm. When a 2 N weight is hung from it, its length becomes 9 cm. What is the spring constant?

50 N/m Extension = 9 cm - 5 cm = 4 cm = 0.04 m. Using Hooke's law F = kx, k = F/x = 2 N / 0.04 m = 50 N/m. Common errors include using length instead of extension or incorrect unit conversion.

What is the unit of the spring constant?

N/m The spring constant k is defined as force per unit extension, so its unit is newtons per metre (N/m). N is the unit of force, N·m is work, and m/N is the reciprocal.

Which of the following is true about an object moving in a circle at constant speed?

The object is accelerating because its direction changes Circular motion is acceleration because velocity changes direction even when speed is constant. A resultant force (centripetal force) is needed to keep an object moving in a circle; without it, the object would move in a straight line.

A sledge moves down a slope and friction acts on it. Which energy transfer occurs because of friction?

Kinetic energy is transferred to thermal energy Friction transfers energy from the moving sledge to thermal stores of the sledge and surroundings.

Which of the following would reduce friction between two solid surfaces?

Lubricating the surfaces Lubrication separates the solid surfaces and reduces friction. For dry friction, the apparent contact area alone does not generally determine the frictional force.

A student measures the unstretched length of a spring as 2.1 cm. When a load of 1.0 N is hung on the spring, the stretched length is 6.3 cm. What is the extension of the spring?

4.2 cm Extension = stretched length - unstretched length = 6.3 cm - 2.1 cm = 4.2 cm.

In an experiment to investigate the stretching of a spring, a student records the following data: Load = 2.0 N, stretched length = 10.5 cm, unstretched length = 2.1 cm. What is the spring constant?

0.24 N/cm Extension e = 10.5 - 2.1 = 8.4 cm. Spring constant k = F/e = 2.0 N / 8.4 cm = 0.24 N/cm.

A student determines the spring constant of a spring using two methods. In Method 1, a 300 g mass (weight 3.0 N) produces an extension of 23 mm. In Method 2, the mass oscillates and the period squared is 0.16 s². Using k = 0.040×m / T² with m = 0.300 kg, what is the spring constant from Method 2?

0.075 N/mm k = 0.040×0.300 / 0.16 = 0.075 N/mm. Note the unit is N/mm as the formula uses m in kg and T in s.

A student measures the unstretched length of a spring as 2.1 cm. Loads are added and the stretched lengths are recorded. For a load of 3.0 N, the stretched length is 14.7 cm. What is the extension?

12.6 cm Extension = stretched length - unstretched length = 14.7 cm - 2.1 cm = 12.6 cm.

How would you design the inquiry for resultant forces and newton's laws?

Apply different measured horizontal pulls to the same low-speed trolley and measure its acceleration. Compare the resultant horizontal force; record acceleration in metres per second squared; keep the trolley's mass constant.

What limitation matters when applying resultant forces and newton's laws?

The pulling force is not automatically the resultant force; friction must be considered.

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