02 · 20 min
Forces
Resultant force, weight, Newton’s laws, and Hooke’s law for a spring.
F = ma
The idea
A force is a push or a pull, measured in newtons. Draw the forces, choose a positive direction, and add them to get the resultant. If the resultant is zero, the velocity does not change: the object stays at rest or moves in a straight line at constant speed.
Newton’s second law says resultant force = mass × acceleration. Mass is how much matter is there, in kilograms. Weight is the pull of gravity, W = mg, so weight changes when g changes and mass does not.
For a spring inside its elastic limit, force and extension are proportional: F = kx. Extension is the extra length, not the total length. Convert centimetres to metres before you calculate k.
Formulas
Weight
W = mg
The gravitational force on a mass. On Earth in this course, g = 10 N/kg.
- W
- weight
- N
- m
- mass
- kg
- g
- gravitational field strength
- N/kg
Newton’s second law
F = ma
F is the resultant force, in the direction of a. Balanced forces mean F = 0 and a = 0.
- F
- resultant force
- N
- m
- mass
- kg
- a
- acceleration
- m/s²
Hooke’s law
F = kx
A spring or wire within its limit of proportionality. x is the extension.
- F
- force
- N
- k
- spring constant
- N/m
- x
- extension
- m
Worked examples
Resultant force on a trolley
A 4.0 kg trolley is pulled forward with 18 N. Friction is 6.0 N backward. Find the acceleration.
- Mass
- 4.0 kg
- Forward force
- 18 N
- Friction
- 6.0 N
Try it on paper first. Then open the working one step at a time.
Mass and weight are not the same
An astronaut has mass 70 kg. Find her weight on Earth (g = 10 N/kg) and on Mars (g = 3.7 N/kg).
- Mass
- 70 kg
- g on Earth
- 10 N/kg
- g on Mars
- 3.7 N/kg
Try it on paper first. Then open the working one step at a time.
Checks
A 1 200 kg car has a resultant force of 3 600 N. What is its acceleration, in m/s²?
An object weighs 40 N where g = 10 N/kg. What is its mass, in kg?
When the resultant force on an object is zero, the object
A spring extends by 4.0 cm when a 2.0 N weight hangs on it. What is the spring constant, in N/m?
Easy places to lose a mark
- Putting the pulling force into F = ma while ignoring friction.
- Writing mass in grams. 200 g is 0.20 kg.
- Using the stretched length instead of the extension in Hooke’s law.
Practical
Force trolley
See that acceleration depends on the resultant force and the mass.