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Newton's laws of motion — KCSE Physics

KCSE Physics · 116 practice questions · 11 syllabus objectives · 11 revision lessons

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Last updated · Aligned to the KNEC KCSE syllabus

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Solve numerical problems involving Newton's laws and conservation of linear momentum

State Newton's three laws of motion and identify examples of each law in everyday situations

Apply Newton's second law (F = ma) to calculate net force, mass or acceleration for a given system

Define linear momentum and impulse, and apply the law of conservation of momentum to collisions and explosions

State Newton's first law of motion and define inertia

State Newton's second law and derive F=ma; define momentum and impulse

State the law of conservation of linear momentum and distinguish elastic and inelastic collisions

State Newton's third law of motion

Describe frictional forces, define coefficient of friction and solve related problems

Define viscosity, explain terminal velocity and sketch relevant graphs

Newton's laws of motion

Revision Notes

Concise lesson notes for Newton's laws of motion, written to the KCSE Physics marking standard. Read the first lesson free below.

Solving Problems with Newton's Laws

Newton's laws of motion describe the relationship between the motion of an object and the forces acting on it. To solve numerical problems involving these laws, follow these steps:

  1. Identify the forces acting on the object. This includes gravitational force, friction, tension, etc.
  2. Apply Newton's Second Law (F = ma) to find acceleration. Here, F is the net force, m is mass, and a is acceleration.
  3. For problems on conservation of momentum, remember that the total momentum before an event equals the total momentum after.

Example: A 5 kg object is pushed with a net force of 20 N. What is its acceleration?

  • Solution: Using F = ma, we rearrange to a = F/m. Thus, a = 20 N / 5 kg = 4 m/s².

Example: Two cars collide. Car A (mass = 1000 kg, velocity = 20 m/s) and Car B (mass = 1500 kg, velocity = 0 m/s). What is the total momentum before the collision?

  • Solution: Total momentum = (mass of A × velocity of A) + (mass of B × velocity of B) = (1000 kg × 20 m/s) + (1500 kg × 0 m/s) = 20000 kg·m/s.

Key points to remember

  • Identify all forces acting on the object.
  • Use F = ma to calculate acceleration.
  • Apply conservation of momentum principle.
  • Momentum before = Momentum after in collisions.
  • Units for force: Newtons (N), mass: kilograms (kg), acceleration: m/s².

Worked example

A 10 kg cart is pulled with a force of 30 N. Calculate the acceleration.

  • Acceleration a = F/m = 30 N / 10 kg = 3 m/s².

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Lesson 2: Newton's Laws of Motion Explained

Objective: State Newton's three laws of motion and identify examples of each law in everyday situations

Newton's three laws of motion describe the relationship between a body and the forces acting on it. They are fundamental to understanding physics.

  1. First Law (Law of Inertia): An object at rest stays at rest, and an object in motion continues in motion at a constant velocity unless acted upon by a net external force.

    • Example: A book on a table remains still until someone pushes it.

  2. Second Law (F=ma): The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be expressed as F = ma.

    • Example: Pushing a shopping cart harder makes it accelerate faster.

  3. Third Law (Action and Reaction): For every action, there is an equal and opposite reaction.

    • Example: When you jump off a small boat, the boat moves backward as you move forward.
  • First Law explains inertia and motion persistence.
  • Second Law relates force, mass, and acceleration.
  • Third Law highlights action-reaction pairs.
  • Real-life examples help illustrate each law.
  • Understanding these laws is crucial for physics.

State Newton's Second Law of Motion and provide an example.

  • Newton's Second Law states that F = ma, where F is force, m is mass, and a is acceleration.
  • Example: A car accelerates faster when the engine exerts more force.
Lesson 3: Applying Newton's Second Law (F = ma)

Objective: Apply Newton's second law (F = ma) to calculate net force, mass or acceleration for a given system

Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. This relationship can be expressed with the formula: F = ma.

To apply this law, follow these steps:

  • Identify the mass (m) of the object in kilograms (kg).
  • Determine the acceleration (a) in meters per second squared (m/s²).
  • Calculate the net force (F) using the formula: F = ma.

Example: If a car has a mass of 1,000 kg and accelerates at 2 m/s², find the net force acting on the car.

Solution:

  • Given: m = 1,000 kg, a = 2 m/s²
  • Using F = ma: F = 1,000 kg × 2 m/s² = 2,000 N

Thus, the net force acting on the car is 2,000 Newtons.

  • Newton's second law formula is F = ma.
  • Net force is the product of mass and acceleration.
  • Use consistent units: kg for mass, m/s² for acceleration.
  • Calculate net force for systems with known mass and acceleration.

A 500 kg object accelerates at 3 m/s². Calculate the net force. F = ma = 500 kg × 3 m/s² = 1,500 N.

Lesson 4: Understanding Momentum and Impulse

Objective: Define linear momentum and impulse, and apply the law of conservation of momentum to collisions and explosions

Linear momentum is defined as the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction. The formula for linear momentum (p) is:

p = mv
where:

  • p = linear momentum
  • m = mass (kg)
  • v = velocity (m/s)

Impulse, on the other hand, is defined as the change in momentum of an object when a force is applied over a period of time. The impulse (J) can be calculated using:

J = FΔt
where:

  • J = impulse (Ns)
  • F = force (N)
  • Δt = time interval (s)

The law of conservation of momentum states that in a closed system, the total momentum before a collision or explosion is equal to the total momentum after the event. This principle can be applied to both elastic and inelastic collisions.

For example, in a two-object collision:

  • If object A (mass = 2 kg, velocity = 3 m/s) collides with object B (mass = 3 kg, at rest), the total momentum before the collision is:
    • Total momentum = (2 kg * 3 m/s) + (3 kg * 0 m/s) = 6 kg·m/s.
  • Linear momentum is mass times velocity (p = mv).
  • Impulse is the change in momentum due to force over time.
  • Conservation of momentum applies to closed systems during collisions.
  • Total momentum before equals total momentum after a collision.
  • Momentum is a vector quantity, having both magnitude and direction.

Calculate the momentum of a 5 kg object moving at 4 m/s.
Momentum (p) = mv = 5 kg * 4 m/s = 20 kg·m/s.

Sample Questions

Read 3 questions and answers free. Sign up to access all 116 questions with full KNEC-style marking schemes and a personalised study plan.

1
easySHORT ANSWER3 marks

List three factors that affect the coefficient of friction between two surfaces in contact. (3 marks)

Answer & marking scheme

Part (a) — 3 marks
The nature of the surfaces in contact (1 mk)
The normal force acting between the surfaces (1 mk)
The presence of lubricants or contaminants (1 mk)
2
easySHORT ANSWER2 marks

State Newton's third law of motion. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
For every action, there is an equal and opposite reaction (2 mks)
3
easySHORT ANSWER3 marks

Identify the definition of linear momentum and give its formula. (3 marks)

Answer & marking scheme

Part (a) — 1 mark
Linear momentum is the product of the mass and velocity of an object (1 mk)
Part (b) — 1 mark
p = mv (1 mk)
Part (c) — 1 mark
The unit of linear momentum is kilogram metre per second (kg m/s) (1 mk)
4

A cyclist of mass 70 kg accelerates from a stationary position to a speed of 14 m/s in 4 seconds. Calculate the net force applied to the cyclist. (3 marks)

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Frequently asked questions

What does the KCSE Physics topic "Newton's laws of motion" cover?

Newton's laws of motion covers Solve numerical problems involving Newton's laws and conservation of linear momentum; State Newton's three laws of motion and identify examples of each law in everyday situations; Apply Newton's second law (F = ma) to calculate net force, mass or acceleration for a given system, and more, all aligned to the official KNEC KCSE Physics syllabus.

How many practice questions are available for Newton's laws of motion?

HighMarks has 116 Newton's laws of motion practice questions for KCSE Physics, each with a full marking scheme. The first 3 are free; sign up to access the rest, plus all KCSE mock exams and past papers.

Are these aligned with the KNEC KCSE syllabus?

Yes. Every objective on this page is taken directly from the official KNEC KCSE Physics syllabus. Practice questions match the KCSE exam format and are graded against the standard KNEC marking scheme.

How should I revise Newton's laws of motion for the KCSE exam?

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