A LevelPhysicsCIERevision Notes3. Dynamics3.1 Momentum & Newton’s Laws of MotionNewton's Laws of Motion

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Newton's Laws of Motion (CIE A Level Physics)

Revision Note

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Newton's three laws of motion

Newton's first law

  • Newton’s First Law of Motion states that:

A body will remain at rest or move with constant velocity unless acted on by a resultant force

  • If the forces acting on an object are balanced, the object is said to be in equilibrium
    • There is no resultant force (the resultant force = 0)
    • There is no change in the object's motion
      • If the object was moving at a constant velocity, it will continue to move at that constant velocity
      • If the object was at rest, it will remain at rest

  • If the forces acting on an object are not balanced:
    • There is a resultant force
    • There is a change in the object's motion
      • The object may speed up (acceleration)
      • The object may slow down (negative acceleration)
      • The object may change direction (a change in velocity, hence acceleration)

Worked example

A car is moving at a constant velocity in the forward direction.

The driving force exerted by the engine on the car is 6 kN.

Frictional forces oppose the motion of the car. State the magnitude of the frictional forces acting on the car.

WE - Newtons first law question image, downloadable AS & A Level Physics revision notes

Answer:

Step 1: Determine whether the forces acting on the car are balanced

  • The car is traveling at a constant velocity
  • Therefore, there is no resultant force acting on the car
  • Hence, the forces are balanced

Step 2: Determine the magnitude of the frictional forces acting on the car

  • The forward and backward forces are balanced
  • Therefore, the frictional forces are equal to the driving force
  • The magnitude of the frictional forces = 6 kN

Newton's second law

  • Newton's second law of motion describes the change in motion that occurs when the forces acting on an object are not balanced
  • Newton's second law can be stated as:

A resultant force acting on a body will cause a change in the object's motion in the direction of the force

  • Newton's second law can also be stated in terms of momentum:

The rate of change in momentum is proportional to the magnitude of the force

  • Newton's second law can also be written as:

F space equals space m a

  • Where:
    • F = force in newtons (N)
    • m = mass in kilograms (kg)
    • a = acceleration in metres per second squared (m s-2)

Worked example

A girl is riding her skateboard down the road and increases her speed from 1 m s-1 to 4 m s-1 in 2.5 s.

The force driving her forward is 72 N. Calculate the combined mass of the girl and the skateboard.WE - Newtons second law question image, downloadable AS & A Level Physics revision notes

Answer: 

Step 1: List the known quantities

  • Force, F = 72 N
  • Initial velocity, vi = 1 m s-1
  • Final velocity, vf = 4 m s-1

Step 2: State the equation for Newton's Second Law

F space equals space m a

Step 3: State the equation for acceleration

a space equals space fraction numerator increment v over denominator increment t end fraction

Step 4: Substitute the acceleration equation into Newton's Second Law

F space equals space m space cross times space fraction numerator increment v over denominator increment t end fraction space equals space fraction numerator m open parentheses v subscript f space minus space v subscript i close parentheses over denominator increment t end fraction

  • Notice here that the change in momentum equation emerges
    • F space equals space fraction numerator m v subscript f space minus space m v subscript i over denominator increment t end fraction

Step 5: Rearrange to solve for mass

m space equals space F over a space equals space fraction numerator F increment t over denominator v subscript f space minus space v subscript i end fraction space

Step 6: Substitute the known values to calculate

m space equals space fraction numerator 72 space cross times 2.5 over denominator 4 minus 1 end fraction

m space equals space 60 space kg

Newton's third law

  • Newton’s third law of Motion describes the force interaction between two different objects

Whenever two bodies interact, the forces they exert on each other are equal and opposite

  • If body A exerts a force on body B, then body B will exert a force on body A of equal magnitude but in the opposite direction
  • Therefore, forces always occur in pairs 

  • A Newton's third law force pair must be: 
    • the same type of force
    • the same magnitude 
    • opposite in direction 
    • acting on different objects

Worked example

A physics textbook is at rest on a dining room table. Eugene draws a free-body force diagram for the book and labels the forces acting on it.WE Newton Third law Question image, downloadable IGCSE & GCSE Physics revision notes

Eugene says the diagram is an example of Newton's third law of motion. William disagrees with Eugene and says the diagram is an example of Newton's first law of motion.

By referring to the free-body force diagram, state and explain who is correct.

Answer:

Step 1: State Newton's first law of motion

  • Objects will remain at rest, or move with a constant velocity unless acted on by a resultant force

Step 2: State Newton's third law of motion

  • Whenever two bodies interact, the forces they exert on each other are equal and opposite

Step 3: Check if the diagram satisfies all of the conditions for identifying Newton's third law

  • Newton's third law applies for pairs of equal and opposite forces of the same type, acting on two different objects
  • The forces in the diagram act on only one object
  • Furthermore, the forces acting on the object are different types of force; one is the normal contact force (of the table on the book) and the other is the gravitational force (of the Earth on the book); its weight
  • The image below shows how to apply Newton's third law correctly in this case, considering the pairs of forces acting:

WE Newton Third law Answer image, downloadable IGCSE & GCSE Physics revision notes

Step 4: Conclude which person is correct

  • In this case, William is correct
  • The free-body force diagram in the question is an example of Newton's first law 
  • The book is at rest because the two forces acting on it are balanced - i.e. there is no resultant force

Examiner Tip

Just because you see two forces in opposite directions doesn't mean they are a Newton's third law force pairs! You must remember the specific criteria.

Worked example - Newton's third law pairs, downloadable AS & A Level Physics revision notes

Newton’s Third Law force pairs are only those that act on different objects

You may also have heard Newton’s Third Law as: ‘For every action is an equal and opposite reaction’. However, try and avoid using this definition since it is unclear which forces are acting on which object and can therefore be misleading.

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    Leander

    Author: Leander

    Expertise: Physics

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.