Forces, Movement & Changing Shape

Balanced forces

• The forces on an object are balanced when they add up to a zero resultant
• A balanced object either stays still or carries on at a constant velocity in a straight line, because its motion does not change at all
• Example: a book at rest on a desk feels a downward weight and an equal upward reaction force from the desk. The two cancel out

Unbalanced forces and Newton's second law

• The forces are unbalanced when they do not add to zero, so there is a non-zero resultant
• A non-zero resultant force makes the object accelerate: it can speed up, slow down, or change direction
• The size of the acceleration is given by Newton's second law of motion:

F = m × a

• where:
  • F = resultant force (N)
  • m = mass (kg)
  • a = acceleration (m/s²)
• Rearranges to a = F / m and m = F / a

Example A — a delivery lorry of mass 1200 kg accelerates uniformly from rest to 18 m/s in 6.0 s. Calculate (i) the acceleration and (ii) the resultant force driving the lorry forward.

• (i) a = (v − u) / t = (18 − 0) / 6.0 = 3.0 m/s²
• (ii) F = m × a = 1200 × 3.0 = 3600 N

Example B — a cyclist plus bicycle have a combined mass of 85 kg. They brake from 12 m/s to a halt in 4.0 s. Calculate the size of the braking force.

• a = (v − u) / t = (0 − 12) / 4.0 = −3.0 m/s²
• F = m × a = 85 × (−3.0) = −255 N
• The negative sign tells you the resultant force points opposite to the motion, i.e. it is the brakes pushing backwards against the cyclist's forward travel