Newton's Second Law

Force Causes Acceleration

Newton's Second Law explains how forces affect the motion of objects. It states that when a force acts on an object, it causes the object to accelerate. Acceleration means a change in the object's velocity, which could be speeding up, slowing down, or changing direction. Acceleration is a vector quantity, meaning it has both magnitude and direction.

The greater the force applied to an object, the greater the acceleration it experiences. If no force acts on an object (or if forces are balanced), the object will not accelerate and will either remain at rest or continue moving at a constant speed.

Acceleration Proportional to Force

Acceleration ($a$) is directly proportional to the resultant force ($F$) acting on an object. This means if you double the force, the acceleration doubles, provided the mass stays the same.

Mathematically:

$$a \propto F$$

Acceleration Inversely Proportional to Mass

Acceleration is also inversely proportional to the mass ($m$) of the object. This means that the heavier the object, the smaller the acceleration for the same force.

Mathematically:

$$a \propto \frac{1}{m}$$

Newton's Second Law Formula: $F = ma$

Combining the two proportionalities, Newton's Second Law is written as the equation:

$$F = ma$$

• F is the resultant force in newtons (N)
• m is the mass of the object in kilograms (kg)
• a is the acceleration in metres per second squared (m/s²)

This formula allows you to calculate any one of the three variables if you know the other two.

For instance, if a car of mass 1000 kg accelerates at 2 m/s², the force required is:

$$F = 1000 \times 2 = 2000 \text{ N}$$

Understanding the Relationship Between Force, Mass and Acceleration

- If you increase the force on an object but keep its mass constant, acceleration increases.

- If you increase the mass but keep the force constant, acceleration decreases.

- If no net force acts on the object, acceleration is zero, so the object moves at a constant velocity or stays at rest.

Example: Calculating Acceleration

A cyclist and bike have a combined mass of 80 kg. They apply a force of 160 N to accelerate. What is their acceleration?

Using $F = ma$, rearranged to find acceleration:

$$a = \frac{F}{m} = \frac{160}{80} = 2 \text{ m/s}^2$$

So, the cyclist accelerates at 2 m/s².

Key Points to Remember

• Force and acceleration are directly proportional.
• Mass and acceleration are inversely proportional.
• The unit of force is the newton (N), where 1 N = 1 kg·m/s².
• Always use the resultant force (the overall force after all forces are combined) in calculations.
• Newton's Second Law applies to any object where forces cause changes in motion, from cars to falling objects (ignoring air resistance).