Forces and Free-Body Diagrams
Introduced| English | Meaning |
|---|---|
| force/fɔːs/ | An interaction that can change an object’s motion or shape. |
| contact forces/ˈkɒntækt ˈfɔːsɪz/ | contact forces |
| field forces/fiːld ˈfɔːsɪz/ | field forces |
| free-body diagram/friː ˈbɒdi ˈdaɪəɡræm/ | A diagram showing all external forces acting on a selected object. |
| components/kəmˈpəʊnənts/ | The parts of a vector resolved along specified directions. |
| net force/net fɔːs/ | The vector sum of all forces acting on an object. |
The forces you cannot see
- A book lies still on a table — so nothing is happening, right?
- Wrong: gravity pulls it down and the table pushes it up, in perfect balance.
- Every object is a tug-of-war of hidden forces.
- To solve any mechanics problem, you first have to draw those forces.
What a force is
- A force 力 is a push or a pull one object exerts on another, measured in newtons.
- Contact forces 接触力 need touching — the normal force, friction, tension.
- Field forces 场力 act at a distance — gravity is the everyday one.
A free-body diagram 受力图 shows every force acting on one object
Which of these is a field force (acts without contact)?
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Gravity is a field force acting at a distance; friction, normal, and tension all require contact.
Select all contact forces.
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Normal, friction, and tension all need contact; gravity is a field force.
Draw a free-body diagram
- A free-body diagram shows the object as a single dot.
- Every force on it becomes an arrow, pointing the right way, labeled.
- Draw only the forces acting on the object — never the forces it exerts on other things.
Build a free-body diagram
Add each force as an arrow and read off the net force and resulting acceleration.
The force an object exerts on your hand belongs on that object's free-body diagram.
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A free-body diagram shows forces on the object. The force it pushes back on your hand goes on your hand's diagram.
Resolve into components
- Forces rarely line up with your axes, so split each into components 分量.
- On a ramp, tilt the axes along and across the slope.
- Gravity then splits into $mg\sin\theta$ down the slope and $mg\cos\theta$ into it.
On a ramp of angle $\theta$, the component of gravity along the slope is $mg\,____\,\theta$.
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The along-slope pull is $mg\sin\theta$; the into-slope part is $mg\cos\theta$.
Add them to a net force
- The net force 合力 is the vector sum of every arrow.
- Add components axis by axis: $\sum F_x$ and $\sum F_y$ separately.
- That net force is what $\sum F = ma$ then turns into acceleration.
Forces on a box (rightward positive):$+15\ \text{N}$, $-6\ \text{N}$, $+1\ \text{N}$. What is the net horizontal force (in N)?
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$15 - 6 + 1 = 10\ \text{N}$ to the right -- just add the components with their signs.
If every force on an object cancels, its net force is zero.
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Balanced forces sum to zero, so there is no net force and no acceleration.
A $2\ \text{kg}$ box on the floor is pushed right with $12\ \text{N}$; friction resists with $4\ \text{N}$.
- Horizontal net force: $12 - 4 = 8\ \text{N}$ to the right.
- Vertical: the normal force and gravity cancel, so $\sum F_y = 0$.
A free-body diagram shows forces on the object only. The force the box pushes back on your hand belongs on your hand's diagram, not the box's — mixing them up is the most common mistake in all of mechanics.
A free-body diagram draws every force on an object as a labeled arrow. Split them into components along your axes, then add to get the net force ($\sum F_x$, $\sum F_y$). Only forces on the object appear — that net force drives its acceleration.
Write from a net force of 7 N
- The horizontal forces are +8 N, -3 N and +2 N.
- Find the net force.
Forces on a box, with rightward positive, are +8 N, -3 N and +2 N. What is the net horizontal force?
8 minus 3 is 5, and 5 plus 2 is 7.
What is the net force?
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8 minus 3 plus 2 is 7 N to the right. Other options — 10 N (the lesson net force); 13 N (the sum of the positive forces only).