In space there is no external matter for a rocket to ‘push off’ in order to accelerate; however, when force is applied to the fuel within the rocket to expel it, an equal and opposite force is applied on the rocket causing it to accelerate.
F = ma
This hugely important formula is a special case of Newton’s second law. At ordinary level, this formula is acceptable as the law itself. However, at higher level it won’t be.
The reason it is considered a ‘special case’ is that it relies on the fact that the standard unit of force, the newton, is defined as 1 N 1 kg m s2.
The ability to use this equation is required for both higher and ordinary level, while its derivation is for higher level only.
DERIVATION OF FORMULA F ma Derivation: Based on Newton’s second law we have:
F ˜ change in momentum time taken
F ˜ final momentum initial momentum time
F ˜ mv mu t
F ˜ ma
F ˜ ma F kma
F ma
v u t b
subbing ‘v u’ t
for ‘a’
in order to go from ‘proportional to . . .’ to ‘equal to . . .’ we must multiply by a constant
the unit ‘newton’ is defined in such a way as to make k 1.
SAMPLE PROBLEM 3D Calculate the force required to give a football of mass 420 g an acceleration of 200 m s2.
SAMPLE ANSWER 3D 3
NEWTON’S SECOND LAW
F ma F force
m mass a acceleration
Using the formula for force, making sure all values are in their standard unit: 420 g 0.42 kg F ma (0.42)(200) 84 The football requires a force of 84 N.
