Forces and Free-Body Diagrams
Introduced| English |
|---|
| force/fɔːs/ |
| contact forces/ˈkɒntækt ˈfɔːsɪz/ |
| field forces/fiːld ˈfɔːsɪz/ |
| free-body diagram/friː ˈbɒdi ˈdaɪəɡræm/ |
| components/kəmˈpəʊnənts/ |
| net force/net fɔːs/ |
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.
Which of these is a field force (acts without contact)?
Gravity is a field force acting at a distance; friction, normal, and tension all require contact.
Select all contact forces.
Normal, friction, and tension all need contact; gravity is a field force.
Draw a free-body diagram
- A free-body diagram 受力图 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.
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 $mg\,____\,\theta$.
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)?
$15 - 6 + 1 = 10\ \text{N}$ to the right -- just add the components with their signs.
If every force on an object cancels, its net force is zero.
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.