Three worked examples
Whichever one value in F = m a you do not know, the other two will give it to you. Three examples, one for each way.
Example 1 — find the force
The problem
What force is needed to give a mass of 5 kg an acceleration of 2 m s−2?
Solution
F = m a
F = 5 kg × 2 m s−2
F = 10 N
Since 1 kg m s−2 = 1 N, the answer comes out in newtons.
Example 2 — find the acceleration
The problem
An object of mass 6 kg is travelling at uniform velocity. A force of 12 N is applied in the direction it is moving. Find the acceleration produced.
Solution
F = m a
12 = 6 × a
a = 12 ÷ 6
a = 2 m s−2
The force is applied along the direction of motion, so the acceleration is positive — the velocity increases.
Example 3 — find the mass
The problem
A force of 8 N applied to an object produces an acceleration of 2 m s−2 in it. Find the object's mass.
Solution
F = m a
8 = m × 2
m = 8 ÷ 2
m = 4 kg
Remember the method
Always write F = m a, substitute the values you have, and solve for the letter left over. There is no need to memorise three formulas — one is enough.
If a mass is given in grams, convert it to kilograms first.