Chapter Summary
- Forces can change an object's speed, direction, shape, or size
- Resultant force is the single net force that represents all forces acting on an object
- Balanced forces cancel out (resultant = 0); unbalanced forces cause acceleration
- Newton's First Law: Objects stay at rest or move at constant velocity unless a resultant force acts on them
- Newton's Second Law: F = ma — the bigger the force or smaller the mass, the greater the acceleration
- Hooke's Law: Springs extend in proportion to the force applied (F = kx) up to a limit
- Circular motion is acceleration because direction constantly changes, requiring a centripetal force
- Friction opposes motion in solids and fluids, causing heating and energy loss
Resultant Forces
What is a Resultant Force?
Imagine pushing a box while your friend also pushes it from the other side. The box doesn't respond to both forces separately — it responds to the net effect of both forces combined. This combined effect is the resultant force.
A resultant force is a single force that has the same effect as all the individual forces acting on an object combined. It tells you:
- The direction the object will accelerate
- The size (magnitude) of the net force the object experiences
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Key Point: Whenever multiple forces act on an object, you can always replace them with a single resultant force that produces exactly the same effect.
Balanced vs Unbalanced Forces
Forces can either balance (cancel out) or remain unbalanced (cause acceleration). This distinction is fundamental to understanding motion.
| Balanced Forces |
Unbalanced Forces |
| Equal magnitude, opposite direction |
Different magnitudes or same direction |
| Resultant force = 0 N |
Resultant force ≠ 0 N |
| Object stays at rest or moves at constant velocity |
Object accelerates (speeds up, slows down, or changes direction) |
| Example: A book resting on a table (weight balances normal force) |
Example: A tennis ball being hit by a racket (unbalanced force causes it to accelerate) |
Balanced Forces:
←——— 5 N ——— ——— 5 N ———→
[Box]
Resultant = 0 N (no motion)
Unbalanced Forces:
←——— 3 N ——— ——— 7 N ———→
[Box]
Resultant = 4 N to the right
How balanced and unbalanced forces behave
Calculating Resultant Forces on a Straight Line
When all forces act in the same plane (e.g., left-right), you can add them algebraically by assigning direction signs:
- Choose a positive direction (e.g., rightward = +, leftward = −)
- Assign each force a sign based on its direction
- Add them together: Resultant = F₁ + F₂ + F₃ + ...
- The sign of the answer tells you the direction of the resultant
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Common Mistake:
Example: Forces on a Book at Rest
Newton's Laws of Motion
Friction