1. Overview
Forces are pushes or pulls that act on an object due to its interaction with another object. This topic explores how forces can change an object’s shape (deformation) and its motion (acceleration and circular paths), providing the foundation for all mechanical physics.
Key Definitions
- Force: An influence that can change the motion or shape of an object (measured in Newtons, N).
- Resultant Force: The single force that has the same effect as all the individual forces acting on an object combined.
- Extension: The increase in length of an object when a load is applied (Extension = New Length – Original Length).
- Spring Constant ($k$): A measure of a spring's stiffness; the force required per unit extension.
- Friction: A force that opposes motion between two surfaces in contact.
- Limit of Proportionality: The point beyond which extension is no longer directly proportional to the force applied.
Core Content
Changes in Size and Shape
When forces act on an object, they can cause it to compress (squash), stretch, or bend.
- Elastic Deformation: The object returns to its original shape once the force is removed.
- Plastic Deformation: The object is permanently stretched and does not return to its original shape.
Load-Extension Graphs & Experiment
To investigate the extension of a spring:
- Measure the original length of the spring using a ruler.
- Add a known mass (load) to the spring.
- Measure the new length and calculate extension ($Extension = \text{New Length} - \text{Original Length}$).
- Repeat by adding more masses and record the results.
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Resultant Force along a Straight Line
- Forces in the same direction: Add them together ($5\text{N} \rightarrow + 3\text{N} \rightarrow = 8\text{N} \rightarrow$).
- Forces in opposite directions: Subtract the smaller force from the larger force. The resultant force acts in the direction of the larger force ($10\text{N} \rightarrow - 3\text{N} \leftarrow = 7\text{N} \rightarrow$).
Newton’s First Law
- If the resultant force is zero, an object at rest stays at rest, and an object in motion continues at a constant speed in a straight line.
- If there is a resultant force, the object will change its velocity (accelerate, decelerate, or change direction).
Friction and Drag
- Solid Friction: Occurs between two surfaces. It impedes (slows down) motion and transforms kinetic energy into heat.
- Drag (Fluid Friction): The resistive force acting on an object moving through a liquid or a gas (e.g., air resistance). Drag increases as the speed of the object increases.
Extended Content (Extended Curriculum Only)
The Spring Constant ($k$)
The relationship between force and extension is defined by the equation: $$k = \frac{F}{x}$$
- A "stiff" spring has a high spring constant.
- Limit of Proportionality: On a load-extension graph, this is the point where the line begins to curve. Before this point, the spring obeys Hooke’s Law ($F \propto x$).
Worked Example: A force of 10N causes a spring to stretch from 5cm to 9cm. Calculate the spring constant.
- Extension ($x$) = $9 - 5 = 4\text{cm} = 0.04\text{m}$
- $k = \frac{F}{x} = \frac{10\text{N}}{0.04\text{m}} = 250\text{N/m}$
Newton’s Second Law
A resultant force causes an object to accelerate. The force and acceleration are always in the same direction. $$F = ma$$
Circular Motion
When an object moves in a circle, a force acts perpendicular to the motion (towards the center). Qualitatively:
- Speed: To move faster in the same circle, a larger force is needed.
- Radius: To move in a smaller circle at the same speed, a larger force is needed.
- Mass: A larger mass requires a larger force to keep the same speed and radius.
Key Equations
| Equation | Symbols | Units |
|---|---|---|
| $k = \frac{F}{x}$ | $k$ = Spring constant, $F$ = Force, $x$ = Extension | $k$ (N/m or N/cm), $F$ (N), $x$ (m or cm) |
| $F = ma$ | $F$ = Resultant Force, $m$ = Mass, $a$ = Acceleration | $F$ (N), $m$ (kg), $a$ (m/s²) |
| $F_{res}$ | Resultant Force | Newtons (N) |
Common Mistakes to Avoid
- ❌ Wrong: Adding two forces that are acting in opposite directions.
- ✓ Right: Subtract the magnitudes of opposing forces to find the resultant.
- ❌ Wrong: Using the "total length" of a spring in $F = kx$ calculations.
- ✓ Right: Always subtract the original length from the new length to find the extension ($x$).
- ❌ Wrong: Assuming a resultant force is required to keep an object moving at a constant speed.
- ✓ Right: If the speed and direction are constant, the resultant force must be zero.
- ❌ Wrong: Adding forces together when they act at right angles (perpendicular).
- ✓ Right: IGCSE Core/Extended focuses on forces in a straight line; do not simply add/subtract them if they are not on the same axis.
Exam Tips
- Read the Graph Axes: Check if the graph is Load-Extension or Load-Length. If it's Load-Length, the line will not start at (0,0); it starts at the original length.
- Direction Matters: When asked for a resultant force, always state the magnitude and the direction (e.g., "5N to the right").
- Units: Ensure mass is in kg before using $F=ma$. If given in grams, divide by 1000.