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ASPhysicsCIERevision Notes3. Dynamics3.1 Momentum & Newton’s Laws of MotionForce & Acceleration

Force & Acceleration (CIE AS Physics)

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Leander

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Leander

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Force & acceleration

  • Newton's second law of motion tells us that objects will accelerate if there is a resultant force acting upon them
  • This acceleration will be in the same direction as this resultant force

 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)

Resultant force

  • Since force is a vector, every force on a body has a magnitude and direction
  • The resultant force is therefore the vector sum of all the forces acting on the body
  • The direction of the force is indicated as either positive or negative 

Resultant forces on a body

4-4-newtons-2nd-law-example-calcs

 

Resultant forces on a body are indicated by a positive or negative value

  • The resultant force could also be at an angle, in which case vector addition is used to find the magnitude and direction of the resultant force.

Acceleration

  • Newton’s second law can be used to find the acceleration of an object of a known mass
  • Since acceleration is also a vector, it can be either positive or negative depending on the direction of the resultant force
  • An object will speed up (positive acceleration) if the resultant force acts in the same direction as the direction of motion
  • An object will slow down (negative acceleration) if the resultant force acts in the opposite direction to the direction of motion 
  • The acceleration will always be in the same direction as the resultant force

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.
Calculate the resultant force on the rocket.

(b)
The mass of the rocket is 0.8 × 105 kg.
Calculate the acceleration of the rocket and state the direction of the acceleration.

Answer:

(a)

Step 1: Sketch a diagram of the forces acting on the rocket

3-1-2-we-forces-diagram-rocket-cie-new

Step 2: Convert all the forces into SI units (newtons)

  • Upward acting force (positive direction):
    • Thrust = 15 MN = 15 cross times 10 to the power of 6 space straight N
  • Downward acting forces (negative direction):
    • Weight = 8 MN = 8 cross times 10 to the power of 6 space straight N
    • Air resistance = 500 kN = 500 cross times 10 cubed space straight N

Step 3: Calculate the resultant force acting on the rocket

F space equals space open parentheses 15 cross times 10 to the power of 6 close parentheses space minus space open parentheses 8 cross times 10 to the power of 6 close parentheses space minus space open parentheses 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 upwards

(b)

Step 1: List the known quantities

  • Force, F = 6.5×106 N
  • Mass, m = 0.8 × 105 kg

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

F space equals space m a

Step 3: Rearrange to make acceleration the subject

a space equals space F over m

Step 4: Substitute in the known values and calculate the acceleration

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

Step 5: State the direction of the acceleration

a space equals space 81 space straight m space straight s to the power of negative 2 end exponent space Upwards

  • Remember that acceleration is always in the same direction as the resultant force

Examiner Tip

You can choose which direction is positive as long as you are consistent throughout your calculation. However, the general convention is for the direction of motion to be the positive direction.

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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.