Applying Newton's Laws

This lesson covers the practical application of Newton's three laws of motion, particularly F = ma, to real-world problems — as required by the Edexcel GCSE Physics specification (1PH0), Topic 2: Motion and Forces. You need to be able to apply F = ma to a range of situations, understand inertial mass, and describe the core practical investigating force, mass and acceleration.

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Newton's Three Laws — Quick Recap

Newton's First Law

An object remains at rest or continues to move at constant velocity unless acted upon by a resultant force.

• No resultant force → no change in velocity (object stays still or moves at constant speed in a straight line).
• This is the law of inertia — objects resist changes to their motion.

Newton's Second Law

The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass:

F = m × a

Quantity	Symbol	Unit
Resultant force	F	Newtons (N)
Mass	m	Kilograms (kg)
Acceleration	a	Metres per second squared (m/s²)

Newton's Third Law

When object A exerts a force on object B, object B exerts an equal and opposite force on object A.

• The forces act on different objects.
• They are the same type of force.
• They are equal in magnitude and opposite in direction.

Exam Tip: Newton's Third Law pairs always act on different objects. Weight of a book (Earth pulls book down) and the reaction pair is the book pulling the Earth up — NOT the normal contact force from the table. This is a very common misconception.

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Applying F = ma to Real-World Problems

Worked Example 1: Car Accelerating

A car of mass 1200 kg accelerates at 2.5 m/s². What is the resultant force?

F = ma = 1200 × 2.5 = 3000 N

Worked Example 2: Finding Acceleration

A 70 kg sprinter is pushed forward by a resultant force of 280 N. What is the acceleration?

a = F / m = 280 / 70 = 4 m/s²

Worked Example 3: Finding Mass

A resultant force of 450 N accelerates an object at 5 m/s². What is the mass?

m = F / a = 450 / 5 = 90 kg

Worked Example 4: Multi-Step Problem — Car with Friction

A car engine produces a driving force of 4000 N. The total resistive forces (friction + air resistance) are 1500 N. The car has a mass of 1250 kg.

Step 1: Find the resultant force. Resultant force = 4000 − 1500 = 2500 N (forward)

Step 2: Find the acceleration. a = F / m = 2500 / 1250 = 2 m/s²

Worked Example 5: Rocket Launch

A rocket has a mass of 5000 kg. Its engines produce a thrust of 80,000 N. Weight = 5000 × 9.8 = 49,000 N.

Resultant force = 80,000 − 49,000 = 31,000 N (upward)

Acceleration = F / m = 31,000 / 5000 = 6.2 m/s²

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Estimating Forces in Everyday Situations

The Edexcel specification expects you to be able to estimate forces for common scenarios:

Situation	Approximate Force
Weight of an apple	~1 N
Weight of a person (70 kg)	~700 N
Friction on a sliding book	~2–5 N
Braking force of a car	~5,000–10,000 N
Thrust of a jet engine	~100,000–250,000 N
Gravitational pull of the Sun on Earth	~3.5 × 10²² N

Exam Tip: When estimating forces, think about the mass of the object and the likely acceleration. Use F = ma to check if your estimate is reasonable. For example, a car (1000 kg) accelerating at 3 m/s² needs about 3000 N — plus some extra to overcome friction.

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Inertial Mass

Inertial mass is a measure of how difficult it is to change the velocity of an object. It is defined as:

Inertial mass = Force ÷ Acceleration

m = F / a

• An object with a large inertial mass is hard to accelerate — it resists changes in motion (high inertia).
• An object with a small inertial mass is easy to accelerate.
• Inertial mass is the same as the mass you measure on a balance — it is measured in kilograms (kg).

Example

A force of 500 N causes a trolley to accelerate at 10 m/s². What is its inertial mass?

m = F / a = 500 / 10 = 50 kg

The larger the inertial mass, the smaller the acceleration for a given force.

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Core Practical: Investigating F = ma

This is a required practical in the Edexcel GCSE Physics specification.

Method

1. Set up a dynamics trolley on a smooth, flat track.
2. Attach a string over a pulley at the end of the track, with hanging masses on the string to provide the accelerating force.
3. Use a light gate (or ticker tape / motion sensor) to measure the acceleration of the trolley.
4. To investigate the effect of force: keep the total mass constant, vary the hanging mass (which changes the force). Record the acceleration for each force.
5. To investigate the effect of mass: keep the force constant, add masses to the trolley (which changes the total mass). Record the acceleration for each mass.

Key Points for the Practical

• The total mass of the system = mass of trolley + mass on the string. This must be kept constant when investigating force (move masses between the trolley and the string).
• The track should be slightly tilted (compensated) so the trolley moves at constant speed without any push — this compensates for friction.
• The accelerating force is the weight of the hanging masses (F = mg).
• Repeat each measurement at least three times and calculate a mean to improve reliability.

Expected Results

Investigation	Independent Variable	Dependent Variable	Expected Relationship
Effect of force on acceleration	Force (N)	Acceleration (m/s²)	Directly proportional (a ∝ F)
Effect of mass on acceleration	Mass (kg)	Acceleration (m/s²)	Inversely proportional (a ∝ 1/m)

Graphs

• a vs F (constant mass): a straight line through the origin. Gradient = 1/m.
• a vs 1/m (constant force): a straight line through the origin. Gradient = F.