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Newton’s Second Law (HL IB Physics)

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Ashika

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Ashika

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Newton's Second Law

  • Newton's second law describes the change in motion that arises from a resultant force acting on an object

  • Newton's second law of motion states:

The resultant force on an object is directly proportional to its acceleration 

  • This can also be written as:

F thin space equals space m a

  • Where:
    • F = resultant force (N)
    • m = mass (kg)
    • a = acceleration (m s–2)

 

  • This relationship means that objects will accelerate if there is a resultant force acting upon them
  • The acceleration will always act in the same direction as the resultant force

  • When unbalanced forces act on an object, the object experiences a resultant force
  • If the resultant force acts along the direction of the object's motion, the object will:
    • Speed up (accelerate)
    • Slow down (decelerate)
  • If the resultant force acts on an object at an angle to its direction of motion, it will:
    • Change direction 

Resultant Force

  • Force is a vector quantity with both magnitude and direction
  • The resultant force is, therefore, the vector sum of all the forces acting on the body
  • If the object is in motion, then the positive direction is in the direction of motion

Resultant Force horizontal, downloadable AS & A Level Physics revision notes

Resultant forces on a body can be positive or negative depending on their direction

  • If the resultant force acts at an angle to the direction of motion, the magnitude and direction of the resultant force can be found by
    • Combing vectors
    • Scale drawings

Acceleration

  • Acceleration is a vector quantity with both magnitude and direction
  • If the resultant force acts in the direction of an object's motion, the acceleration is positive
  • If the resultant force opposes the direction of the object's motion, the acceleration is negative 
  • But the acceleration will always act in the same direction as the resultant force

Examiner Tip

It is important to understand that for an object in motion, a resultant force that opposes that motion will cause the object to decelerate, not to suddenly travel backwards. 

If no drag forces are present, then the acceleration of a falling object is independent of its mass. This unintuitive fact of physics has been proven by astronauts on the Moon, who simultaneously dropped both a hammer and a feather from equal heights and found that they hit the ground at the same time! (Because there is no air resistance on the Moon.)

Worked example

A rocket produces an upward thrust of 15 MN and has a weight of 8 MN.

(a)
When in flight, the force due to air resistance is 500 kN.
Determine the resultant force on the rocket.

(b)
The mass of the rocket is 0.8 × 105 kg.

Calculate the magnitude and direction of the acceleration of the rocket.

Answer

Part a)

Step 1: Draw a force diagram of the situation

we---newtons-second-law-on-rocket-answer-image1

Step 2: Convert the forces into newtons and assign directions

  • The direction of motion is upwards, therefore upwards is the positive direction
    • Air resistance (downward acting) = −500 kN = −500 × 103 N
    • Weight (downward acting) = −8 MN = −8 × 106 N
    • Thrust (upward acting) = 15 MN = 15 × 106 N

Step 3: Calculate the resultant force

F space equals space open parentheses 15 cross times 10 to the power of 6 close parentheses space plus space open parentheses negative 8 cross times 10 to the power of 6 close parentheses space plus space open parentheses negative 500 cross times 10 cubed close parentheses

F space equals space 6.5 cross times 10 to the power of 6 space straight N space equals space 6.5 space MN

  • The positive value indicates that the resultant force acts in the direction of motion i.e., upwards

 

Part b)

Step 1: State the equation for Newton's second law and rearrange to make acceleration the subject

F space equals space m a space space rightwards double arrow space space a space equals fraction numerator space F over denominator m end fraction

Step 2: Calculate the acceleration and state the direction

a space equals space fraction numerator 6.5 cross times 10 to the power of 6 over denominator 0.8 cross times 10 to the power of 5 end fraction

a space equals space 81 space straight m space straight s to the power of negative 2 end exponent space open parentheses 2 space straight s. straight f. close parentheses upwards

  • Acceleration is in the same direction as the resultant force

Examiner Tip

Air resistance is a type of fluid resistance because fluids are gases or liquids. The IB specification uses fluid resistance so you should use this term when referring to air resistance in the exam. Air resistance and fluid resistance are drag forces since drag is the force exerted by the particles in a fluid on an object moving it. The symbol for fluid resistance is therefore the same as symbol for drag, Fd.

Worked example

Three forces, 4 N, 8 N, and 24 N act on an object with a mass of 5 kg. Which acceleration is not possible with any combination of these three forces?

A.  1 m s–2

B.  4 m s–2

C.  7 m s–2

D.  10 m s–2

Answer:

Step 1: List the values given

  • Three possible forces at any angle of choice: 4 N, 8 N, and 24 N
  • Mass of object = 5 kg

Step 2: Consider the relevant equation

  • Newton's second law relates force and acceleration:

F = m × a

Step 3: Rearrange to make acceleration the focus

a space equals space F over m

Step 4: Investigate the minimum possible acceleration

  • The minimum acceleration would occur when the forces were acting against each other
  • This is when just the 4 N force is acting on the body
  • Now check the acceleration:

a space equals space 4 over 5 space equals space 0.8 space straight m space straight s to the power of negative 2 end exponent

Step 4: Investigate the maximum possible acceleration

  • The maximum acceleration would occur when all three forces are acting in the same direction
  • This is a total force of

a = 4 + 8 + 24 = 36 N

  • With acceleration:

a space equals space 36 over 5 space equals space 7.2 space straight m space straight s to the power of negative 2 end exponent

Step 5: Consider this range and the options

  • Since option D is higher than 7.2 m s–2; it is not possible that these three forces can produce 10 m s–2 acceleration for this mass
  • Option D is the correct answer, as it is the only one that is not possible

Examiner Tip

The direction you consider positive is your choice, as long as the signs of the numbers (positive or negative) are consistent throughout the question.

It is a general rule to consider the direction the object is initially travelling in as positive. Therefore all vectors in the direction of motion will be positive and opposing vectors, such as drag forces, will be negative.

Newton's Second Law and Momentum

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

The resultant force on an object is equal to its rate of change of momentum

  • This change in momentum is in the same direction as the resultant force

  • These two definitions are derived from the definition of momentum, as follows:

    • Momentum:

 p space equals space m v

    • Rate of change of momentum:

 fraction numerator increment p over denominator increment t end fraction space equals space m fraction numerator increment v over denominator increment t end fraction

    • Force:

 F space equals space m fraction numerator increment v over denominator increment t end fraction

    • Acceleration:

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

    • Therefore:

F space equals space m a 

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

WE - Newtons second law answer image, downloadable AS & A Level Physics revision notes

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    Ashika

    Author: Ashika

    Expertise: Physics Project Lead

    Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.