AP Physics 1 Unit 2 Forces Study GuideAP Physics 1 Unit 2 Forces Study Guide

APPHYSICS1 · UNIT2 · 1 D A N D 2 D F O R C E S T E S T

Forces & Newton's Laws

Study guide for the Unit 2 test (MCQ + FRQ). It covers Newton's three laws, free-body diagrams, F = ma (including v–t graphs), weight and apparent weight, tension, friction, modified Atwood machines, forces at angles, inclines, springs and center of mass. It's built from the class slides, worksheets, notes and keys, and matched to the College Board CED Unit 2. It uses g = 9.8 m/s², the same as the class. THE 6-STEP METHOD FROM THE SLIDES. EVERY FORCE PROBLEM USES IT.

1. Draw a FBD for each object: a dot plus arrows for every force on that object.

2. Pick positive directions. Choose the direction of acceleration as +. For Atwood machines the notes say "right and down are positive."

3. Write ΣF = ma for each axis (ΣFx = max, ΣFy = may).

4. Plug in what you know. If there's no motion along an axis, then a = 0 on that axis. 5. Rearrange to isolate the unknown.

6. Solve, then check the units and whether the sign makes sense.

1 · Forces and free-body diagrams

A force is a push or pull from an interaction between two objects. An object cannot exert a force on itself. Every force needs a partner object you can name: "the floor pushes up on the box," "Earth pulls down on the box."

Force Symbol Direction Remember

Weight

(gravity)

Fg = mg Straight down, always Earth pulls on the object. Weight is in newtons

and mass is in kg.

Normal FN Perpendicular to the surface It only exists when objects touch. It is not always mg, and it doesn't always point up (a wall pushes

sideways).

Tension FT Along the rope, away from the

object

It can only pull. It's the same everywhere in an

ideal rope.

Friction fs, fk Parallel to the surface, opposing

sliding (or attempted sliding)

fk = μkFN, and fs ≤ μsFN.

Spring Fs Back toward the equilibrium

position

|Fs| = k|x|

Applied, drag,

buoyant

FA, FD,

FB

Applied: given. Drag: opposes v.

Buoyant: up.

Drag is "friction with fluids."

Book at restBook at rest

FFNN

FFgg

Car, constant v →Car, constant v →

FFNN

FFgg

FFengineengine

FFdragdrag

Leaning on a wallLeaning on a wall

FFNN

ffss

FFgg

FBD RULES THAT COST POINTS (AP SCORING AND THE "DON'T LOSE POINTS ON FBDS" VIDEO)

Every arrow starts on the dot and points away from it. Use one straight arrow per force. Don't draw components (Fx, Fy, mg sinθ) on the FBD itself. Draw them on a separate "component diagram," like the notes do.

Forces in the same direction go side by side, not on top of each other.

Use a distinct label for every arrow. Never draw "ma," a "force of motion," or a "net force" arrow. Those aren't forces.

Arrow lengths should be roughly proportional. If the object is at constant velocity, the opposing arrows must match.

2 · Newton's three laws

First law (inertia)

If ΣF = 0, the velocity stays constant. That means staying at rest, or moving in a straight line at constant speed. Inertia = mass: the more mass, the more an object resists changes in its motion. Forces can be balanced on one axis and unbalanced on another, and velocity only changes along the unbalanced axis.

TRAP · MOVING DOESN'T MEAN THERE'S A NET FORCE

A car cruising at a constant 30 m/s has ΣF = 0. The engine force equals the drag force. You need a net force to change velocity, not to keep it.

Second law: ΣF = ma

Acceleration is in the same direction as the net force. It's proportional to ΣF and inversely proportional to m. Double the net force and a doubles. Double the mass and a is halved.

Worked example (slides). A person pushes a 3 kg box to the left against 10 N of friction. What push gives a = 2 m/s² left? Take left as +: ΣFx = FA − f = ma, so FA = (3)(2) + 10 = 16 N.

Third law: equal and opposite pairs

If A pushes on B, then B pushes on A with a force of equal magnitude and opposite direction, every time, even when A and B are accelerating. Third-law pairs always:

act on two different objects, so they never cancel on one FBD

are the same type of force (contact–contact or gravity–gravity)

are written FA on B = −FB on A

Force on a book resting on a table Its third-law partner

Earth pulls the book down (Fg) The book pulls Earth up, not the normal force

The table pushes the book up (FN) The book pushes the table down

TRAP · FN AND FG ARE NOT A THIRD-LAW PAIR

They act on the same object (the book) and are different types of force. They're equal here only because a = 0, and that's Newton's second law. In an accelerating elevator, they aren't equal.

QUICK CHECK

1. A truck hits a mosquito. Which feels the bigger force? Neither. The forces are equal. The mosquito has the bigger acceleration, because a = F/m and its m is tiny.

2. A 2 kg box has 10 N right and 4 N left acting on it. Find a. ΣF = 6 N, so a = 3 m/s² to the right.

3 · Connecting to Unit 1: graphs give you a, and a gives you ΣF

The slope of a v–t graph is a, and then ΣF = ma. A straight-line v–t graph means constant ΣF. A flat segment means ΣF = 0. A downward slope means ΣF points opposite your + direction.

Elevator velocity (up +)

2468 10

−1

1

2

3

4

5

6

t (s)

v (m/s)

ΣF upΣF up

ΣF = 0ΣF = 0

ΣF downΣF down

Worked example (2nd-law practice). A 1000 kg car speeds up from rest to 20 m/s in 10 s against 1000 N of drag. Then a = 2 m/s², so ΣF = 2000 N. Since Fengine − Fdrag = ma, Fengine = 3000 N. Kinematics still applies: once you have a from forces, use v = v0 + at, Δx = v0t + ½at² and v² = v0² + 2aΔx. In the couch example from the slides, 15 N + 20 N − 5 N = 20a gives a = 1.5 m/s², so v after 3 s = 4.5 m/s. 4 · Weight, mass, and apparent weight (elevators)

Mass (kg) is the same everywhere. Weight Fg = mg (N) changes with g: a 30 kg person weighs 294 N on Earth but less on the Moon. A scale reads the normal force, and that's your apparent weight. Take up as +: ΣFy = FN − mg = ma, so FN = m(g + a).

Elevator is… a Scale

at rest, or moving at

constant v (up or down)

0 = mg

speeding up going up, or

slowing down going

down

up > mg

speeding up going down,

or slowing down going

up

down < mg

in free fall (cable cut) −g 0, so you're

"weightless"

TRAP · DIRECTION OF MOTION VS. DIRECTION OF ACCELERATION