Newton's Second Law
Newton's Second Law
- The first law says a resultant force changes motion. The second law says by how much.
- For a constant mass, the resultant force and the acceleration are linked by one short equation.
The equation
Symbols
- = resultant force (N)
- = mass (kg)
- = acceleration (m s⁻²)
- is always the resultant force: add every force on the object first, with directions.
- The acceleration is in the same direction as the resultant force.
- The same force gives a small mass a large acceleration and a large mass a small one: .
- This is the constant-mass form of Newton's second law. The full law uses momentum, and lesson 3.11 comes back to it.
- The equation also defines the unit of force. One newton is the force that gives a mass of 1 kg an acceleration of 1 m s⁻².
- So . These are the base units of force used in homogeneity checks (chapter 1).
Definition
1 markWhat is meant by one newton?
Model answer: The force that gives a mass of 1 kg an acceleration of 1 m s⁻² in the direction of the force.
Worked example
Smallest case: one force, one mass
A resultant force of 6.0 N acts on a 2.0 kg mass. Find the acceleration.
- .
Answer
Your turnquick check
The same resultant force acts first on mass m and then on mass 2m. What happens to the acceleration?
Show worked answer
It halves, because .