Short on time? This page is the recap. For explanations, diagrams and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- A force is an interaction: a push or pull on one object by another. It is a vector, measured in newtons (N).
- An object or system cannot exert a net force on itself. Only external interactions change the motion of a system as a whole.
- Contact forces (normal, friction, tension, applied) are the large-scale result of electric forces between atoms at the touching surfaces. Long-range forces such as gravity need no contact.
- A free-body diagram shows the forces exerted on the chosen object or system by its environment, drawn from a dot at its center of mass.
- Choose axes with one axis along the acceleration. On a ramp, that means axes parallel and perpendicular to the surface.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| F_g = mg | m in kg, g = 9.8 N/kg, F_g in N | find the size of the gravitational force near Earth |
| F_g along a ramp = mg sin θ | θ = ramp angle | find gravity’s down-slope component |
| F_g into a ramp = mg cos θ | θ = ramp angle | find gravity’s component into the surface |
| F_x = F cos θ, F_y = F sin θ | θ measured from the +x axis | split a force at an angle (in a separate sketch) |
| Force | Direction |
|---|---|
| Gravitational, F_g | straight down (towards Earth’s centre) |
| Normal, F_N | perpendicular to the surface, away from it |
| Friction, F_f | along the surface, opposing sliding or the tendency to slide |
| Tension, F_T | along the string, pulling away from the object |
Diagram conventions
- One dot for the object or system (its center of mass).
- One straight arrow per force, starting on the dot, pointing the way the force acts, and labelled.
- Same-direction forces side by side, never overlapping.
- No components, no velocity, no acceleration and no net-force arrow on the diagram.
Mistakes to avoid
- A “force of motion” along the velocity. Nothing exerts it.
- Forces the object exerts on other things. They belong on the other objects’ diagrams.
- F_N = mg every time. Not on a ramp, and not when something else pulls up or pushes down.
- Gravity drawn perpendicular to a ramp. Gravity is always vertical.
- Internal forces drawn on a system’s diagram.
- Sine and cosine swapped on a ramp. Check with θ = 0: the down-slope part must vanish.
Quick self-check
- What is the size of the gravitational force on a 5.0 kg bag? (49 N, downward)
- How many forces act on a stone in flight after it is thrown, with air resistance negligible? (One: gravity, Earth on stone.)
- A 10 kg box sits on a 30° ramp. Find gravity’s components along and into the ramp. (49 N down the slope; 85 N into the surface)
- Is the normal force on a book resting on a level desk a contact or a long-range force, and what causes it at the atomic scale? (Contact; electric repulsion between atoms of the two surfaces.)
Next: practice questions.