Newton's Second Law – Advanced Calculations

A small experimental rocket is tested using two different types of rocket boosters.

The speed of the rocket is measured on the Mach scale, where Mach 1 = 340 m/s.

• The solid-fuel booster accelerates the rocket to Mach 1.2.

• The liquid-fuel booster then further accelerates the rocket to Mach 4.8 in a time of 15 s.

The average resultant force on the rocket while this liquid-fuel booster is pushing it is 2400 N.

Calculate the mass of the rocket.

Assume the mass remains constant.

Give your answer to 2 significant figures.

[6 marks]

• How do we use Mach number?

  Mach 1 is the assumed speed of sound. It is used as a reference value.

  • You should use it as a multiplier.

  So

  • Multiply the Mach number by 340 m/s to find the velocity at each point.

• Key values?

  • Initial velocity = 408 m/s

  • Final velocity = 1632 m/s

  • Time = 15 s

  • Acceleration ?

• Change in velocity?

  change in velocity = final - initial

  1632 - 408 = 1224 m/s

  *Remember: Velocity is speed with direction.

  Since the car travels in the same direction throughout, we can use the given speeds as velocity values when calculating its acceleration.

• Which formula?

  change in velocity = acceleration x time

• How do we find acceleration?

  a = change in V / t

  1224 / 15 = 81.6 m/s²

Second Equation:

• New key values?

  • force = 2400

  • acceleration = 81.6 m/s²

  • mass = ?

• Which formula?

  Newton’s Second Law:

  force = mass x acceleration

  f = ma

• How do we find mass?

  • m = F / a

  • 2400 / 81.6 = 29.41 kg

  To 2 significant figures:

  • 29kg

Continue Revising Paper 2

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