Effects of ForcesCambridge IGCSE Physics: Revision notes

Forces applied to objects can produce deformation, which means a change in the size or shape of that object. The effect depends on the type of material and the magnitude of the force applied.

• Elastic deformation occurs when an object returns to its original shape and size after the force is removed (e.g. stretching a spring)
• Plastic deformation occurs when an object does not return to its original shape after the force is removed (e.g. bending a paperclip)
• Materials have a limit of elasticity beyond which permanent deformation occurs
• Different materials respond differently to the same force; some are stiff (hard to deform) whilst others are flexible (easy to deform)

A load–extension graph plots the load (force) applied to a material against its extension (increase in length). These graphs reveal how materials behave under increasing stress and are essential for understanding elastic properties.

Key regions of a load–extension graph:

1. Linear (straight line) region: The material obeys Hooke's Law; extension is directly proportional to load. This is where the limit of proportionality lies – the point beyond which the relationship is no longer linear.
2. Curved region: The material still returns to its original length when unloaded (elastic), but Hooke's Law no longer applies.
3. Steep rise then plateau: The material undergoes plastic deformation and eventually breaks (yield point and breaking point).

Experimental procedure for load–extension:

• Measure the original length of the material (e.g. a spring or wire) using a ruler or calliper
• Attach a load and measure the new length
• Calculate extension = new length − original length
• Repeat, increasing the load in known increments (typically 0.5 N to 1 N intervals)
• Plot load (y-axis) against extension (x-axis)
• Draw a line of best fit through the points

What the graph shape tells us:

• A steep gradient indicates a stiff material (large load produces small extension)
• A shallow gradient indicates a flexible material (small load produces large extension)

A resultant force is the single force that has the same effect as all the individual forces acting together. Understanding resultant forces is crucial for predicting motion.

Calculating resultant forces along the same straight line:

• Forces in the same direction: Add the forces together. Example: 5 N + 3 N = 8 N
• Forces in opposite directions: Subtract the smaller from the larger. Example: 10 N − 4 N = 6 N (in the direction of the larger force)
• Zero resultant force: When forces balance, the resultant is 0 N

Newton's First Law of Motion:

An object either remains at rest or continues moving at constant velocity in a straight line unless acted upon by a resultant force. This means:

• If the resultant force is zero, the object will not accelerate
• Moving objects with zero resultant force will maintain their velocity indefinitely
• This explains why we feel pushed back in a car when it accelerates (the car's velocity changes, but your inertia keeps you moving forward)

Newton's Second Law of Motion:

The relationship between force, mass and acceleration is given by the equation:

$F = ma$

Where:

• F = resultant force (in Newtons, N)
• m = mass (in kilograms, kg)
• a = acceleration (in metres per second squared, m/s²)

Key points about F = ma:

• The resultant force and acceleration are always in the same direction
• Acceleration is directly proportional to the resultant force (larger force = larger acceleration)
• Acceleration is inversely proportional to mass (larger mass = smaller acceleration for the same force)
• The equation is valid for both positive (speeding up) and negative (slowing down) accelerations

Friction is the force that acts between two surfaces in contact and tends to oppose relative motion. It is a crucial concept in understanding real-world motion.

Solid friction (between two solid surfaces):

• Acts at the interface between two surfaces moving (or attempting to move) relative to one another
• Always opposes the direction of motion (or potential motion)
• Can produce heating as surfaces rub together; kinetic friction converts mechanical energy to thermal energy
• Magnitude depends on:
  • The nature of the surfaces (rough surfaces have more friction than smooth ones)
  • The normal force pressing the surfaces together (greater normal force = greater friction)
• Examples: friction between a sliding block and a table, friction between tyres and a road

Friction in fluids (drag or air resistance):

When an object moves through a liquid or gas (such as air), it experiences drag or friction, which opposes its motion:

• Drag in liquids: A swimmer moving through water, a falling raindrop, a submarine
• Air resistance: A falling object, an aeroplane, a cyclist
• Drag increases with:
  • Speed: Faster motion produces greater drag
  • Surface area: Larger objects experience more drag
  • Density of the fluid: Denser fluids (like water) produce more drag than less dense ones (like air)
  • Shape: Streamlined objects experience less drag than blunt ones

Terminal velocity: When a falling object reaches a speed where the drag force equals the gravitational force, the resultant force becomes zero and the object stops accelerating. It then falls at a constant speed called terminal velocity.

The spring constant is a measure of the stiffness of a material and defines the relationship between the applied force and the resulting extension.

Definition and equation:

The spring constant is defined as the force per unit extension:

$k = \frac{F}{x}$

Rearranged:

$F = kx$

Where:

• k = spring constant (in Newtons per metre, N/m)
• F = force or load applied (in Newtons, N)
• x = extension (in metres, m)

Interpreting spring constant values:

• A large spring constant (e.g. 500 N/m) indicates a stiff material – considerable force is needed to produce small extensions
• A small spring constant (e.g. 50 N/m) indicates a flexible material – small force produces large extensions
• The spring constant is constant only within the limit of proportionality; beyond this point, the relationship is no longer linear

Calculating spring constant from a load–extension graph:

• Choose two points on the linear region of the graph
• Calculate k = F/x using these points
• Alternatively, k is equal to the gradient of the linear (straight-line) portion of the graph
• The gradient method is preferred as it uses all your data points and is more reliable

When an object moves in a circular path, it is always accelerating because its direction is constantly changing. This acceleration is caused by a resultant force directed towards the centre of the circle (called centripetal force).

Key principles of circular motion:

• The centripetal force acts perpendicular to the direction of motion, always pointing towards the centre of the circle
• Without this force, the object would move in a straight line (Newton's First Law)
• The object's speed around the circle may remain constant, but its velocity is constantly changing due to the change in direction

How force relates to speed (constant mass and radius):

• If the centripetal force increases, the object can move faster around the same circle
• If the centripetal force decreases, the object moves slower around the same circle
• The relationship is directly proportional: double the force allows double the speed
• Example: A car on a banked curve needs more friction force to go faster without skidding

How force relates to radius (constant mass and speed):

• If the centripetal force increases, the radius of the circular path decreases (tighter circle)
• If the centripetal force decreases, the radius increases (wider circle)
• The relationship is inversely proportional: double the force allows half the radius
• Example: A satellite in a higher orbit (larger radius) requires less gravitational force to maintain its speed than a satellite in a lower orbit

How mass affects the required force (constant speed and radius):

• A more massive object requires a larger centripetal force to maintain the same speed around the same radius
• A less massive object requires a smaller centripetal force for the same conditions
• The relationship is directly proportional: double the mass requires double the force
• Example: A heavier person on a merry-go-round needs more grip (friction force) than a lighter person to stay on at the same speed and radius

Real-world examples:

• A car turning a corner depends on friction between tyres and road to provide centripetal force
• A satellite orbiting Earth depends on gravitational force to maintain circular orbit
• A ball on a string swinging in a circle depends on tension in the string
• A cyclist leaning into a turn relies on friction and the horizontal component of the normal force