6.8 - Newton's 1st & 2nd Laws

Newton's First Law - Resultant force changes motion

• Newton's First Law - If the resultant force on an object is zero, its velocity doesn't change:
  • A stationary object stays stationary.
  • A moving object continues at the same velocity (same speed and direction).
• When an object is stationary or moving at a constant velocity, the forces on it are balanced.
• Velocity only changes if the forces are unbalanced, giving a non-zero resultant force that causes an acceleration in the direction of the force.

A non-zero resultant force can cause an object to:

• start moving
• stop moving
• speed up
• slow down
• change direction

Newton's Second Law - Acceleration and resultant force

• The larger the resultant force on an object, the more it accelerates - force and acceleration are directly proportional ($F\propto a$).
• Acceleration is inversely proportional to mass: for a fixed resultant force, a larger mass accelerates less than a smaller one.

Formula for Newton's Second Law

Where:

• $F$ = Resultant force, in newtons (N)
• $m$ = Mass, in kilograms (kg)
• $a$ = Acceleration, in metres per second squared (m/s²)

$F$ is always the resultant force, found by adding or subtracting the forces acting along the same line.

Worked example - Acceleration of a car

A car of mass 2,000 kg has an engine providing a driving force of 8,000 N. The drag force on the car is 2,000 N. Find its acceleration.

Inertia and inertial mass

• Inertia is the tendency of an object to continue in its current state of motion (at rest or moving at a constant velocity).
• The larger an object's mass, the larger its inertia, and the harder it is to change its velocity.

Inertial mass

• An object's inertial mass measures how difficult it is to change its velocity.
• It's defined as the ratio of resultant force to acceleration:

Newton's Second Law with changing mass

Newton's Second Law ($F=ma$) also applies when an object's mass changes during motion, such as a rocket burning fuel.

How a rocket's acceleration changes

1. A rocket's engines burn fuel to produce an upwards thrust.
2. When thrust is greater than weight and air resistance, there's an upwards resultant force ($F$), producing an upwards acceleration ($a=\frac{F}{m}$).
3. As fuel burns, the rocket's mass decreases, which increases its acceleration for a constant thrust.
4. As the rocket climbs, weight and air resistance also decrease, which further increases the upwards resultant force and acceleration.