CIE IGCSE Physics (0625) Effects of forces Study Notes - New Syllabus
CIE IGCSE Physics (0625) Effects of forces Study Notes
LEARNING OBJECTIVE
- Understanding the concepts of Effects of forces
Key Concepts:
- Effects of Forces on Objects
- Load–Extension Graphs
- Newton’s Laws of Motion
- Friction
- Circular Motion
Effects of Forces on Objects
Effects of Forces on Objects:
- A force is a push or pull that can cause an object to:
- Accelerate (change velocity)
- Change direction
- Change shape or size
- Rotate
- When a force is applied to a solid object, it may:
- Stretch (tension)
- Compress (compression)
- Bend or deform
- These changes are often temporary (elastic) or permanent (plastic).
Hooke’s Law:
- For elastic materials (e.g. springs), the extension is proportional to the applied force, up to a limit.
- This relationship is called Hooke’s Law.
Spring Constant (k):
- The spring constant measures how stiff or flexible a spring is.
- Defined as the force per unit extension of the spring.
\( k = \dfrac{F}{x} \)
- \( k \) = spring constant (N/m)
- \( F \) = force applied (N)
- \( x \) = extension (m)
Important: Hooke’s Law is valid only up to the elastic limit of the spring. Beyond that, permanent deformation may occur.
Example:
A spring stretches by 0.05 m when a force of 2.0 N is applied. What is the spring constant?
▶️ Answer/Explanation
Use \( k = \dfrac{F}{x} \)
\( k = \dfrac{2.0}{0.05} = \boxed{40~\text{N/m}} \)
Example:
A spring has a spring constant of \( 200~\text{N/m} \). What will be the extension if a force of 5 N is applied?
▶️ Answer/Explanation
Rearrange: \( x = \dfrac{F}{k} \)
\( x = \dfrac{5}{200} = \boxed{0.025~\text{m}} \)
Load–Extension Graphs
Load–Extension Graphs:
- A load–extension graph shows how much a material (usually a spring or wire) stretches (extension) when different forces (loads) are applied.
- This helps to determine how the material behaves under tension — whether it follows Hooke’s Law or not.
Key Terms:
- Load (F): The force applied to the material (in newtons, N)
- Extension (x): The increase in length compared to the original length (in metres, m or centimetres, cm)
Hooke’s Law Region:
- For small loads, the extension is directly proportional to the applied load.
- The graph is a straight line from the origin in this region.
Limit of Proportionality:
- This is the point up to which the load and extension remain proportional (i.e. Hooke’s Law applies).
- Beyond this point, the graph begins to curve — the extension increases more rapidly than the load.
- The material may still return to its original shape, but no longer obeys Hooke’s Law.
Important: The term “limit of proportionality” is not the same as the “elastic limit”.
Procedure: Plotting a Load–Extension Graph for a Spring
- Set up a clamp stand with a spring suspended from it and a meter rule alongside.
- Measure the original length of the spring (without any load).
- Add weights gradually (e.g. 0.5 N, 1 N, 1.5 N, …).
- Record the new length of the spring after each load is added.
- Calculate the extension:
\( \text{Extension} = \text{Stretched length} – \text{Original length} \)
- Plot a graph of load (y-axis) vs extension (x-axis).
Mass (g) Mass (Kg) Load (N) Spring Length (cm) Extension (cm) 0 0 0 20 0 20 0.02 0.2 22 2 40 0.04 0.4 24 4 60 0.06 0.6 26 6 80 0.08 0.8 28 8 100 0.1 1 30 10 120 0.12 1.2 34 14 140 0.14 1.4 42 22
Interpreting the Load–Extension Graph
- Straight Line Region: Obeys Hooke’s Law (linear relationship).
- Point where curve starts: Limit of proportionality.
- Curved Region: Extension increases more than proportionally to the load.
- Use graph to find spring constant (gradient of linear portion):
\( k = \dfrac{F}{x} \)
Example:
A load-extension graph shows a straight line from 0 to 4 N, and then curves from 4 N onward. What is the limit of proportionality?
▶️ Answer/Explanation
Since the graph is straight up to 4 N, the load and extension are proportional up to this point.
Limit of proportionality = \( \boxed{4~\text{N}} \)
Example:
A spring is stretched by 0.04 m when a 2 N load is applied within the linear region. What is the spring constant?
▶️ Answer/Explanation
Use \( k = \dfrac{F}{x} \)
\( k = \dfrac{2}{0.04} = \boxed{50~\text{N/m}} \)
Newton’s First Law of Motion
Newton’s First Law of Motion:
- An object remains at rest or continues to move in a straight line at constant speed unless acted upon by a resultant (net) force.
- This law describes the behavior of objects when there is no net force acting on them.
Key Concept:
- If the resultant force is zero:
- An object at rest stays at rest.
- An object in motion continues to move with constant velocity in a straight line.
- If there is a , the object’s state of motion will change (it will accelerate, decelerate, or change direction).
Inertia: The tendency of an object to resist changes in its motion.
Example:
A book rests on a table. No external horizontal forces are acting on it. What will happen to the book?
▶️ Answer/Explanation
There is no resultant force. The book remains at rest.
This is Newton’s First Law in action.
Example:
A trolley is moving at constant speed. A force is suddenly applied in the opposite direction. What will happen?
▶️ Answer/Explanation
Now there is a non-zero resultant force acting opposite to the motion.
The trolley will decelerate and eventually stop or change direction.
Resultant of Forces Along a Straight Line
Resultant of Forces Along a Straight Line:
- When multiple forces act along the same straight line, the resultant force is the single force that has the same effect as all the individual forces combined.
- Forces in the same direction are added.
- Forces in opposite directions are subtracted.
Resultant force: \( F_{\text{net}} = F_{\text{forward}} – F_{\text{backward}} \)
If:
- \( F_{\text{net}} = 0 \): The object is in equilibrium (no change in motion).
- \( F_{\text{net}} \ne 0 \): The object accelerates in the direction of the resultant force.
Newton’s Second Law:
- States that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
\( F = m \cdot a \)
- \( F \) = net force (N)
- \( m \) = mass (kg)
- \( a \) = acceleration (m/s²)
Direction: The direction of acceleration is the same as the direction of the net force.
Example:
A 5 N force pulls a crate to the right and another 5 N force resists to the left. What is the resultant force and motion of the object?
▶️ Answer/Explanation
\( F_{\text{net}} = 5~\text{N} – 5~\text{N} = \boxed{0~\text{N}} \)
The crate is in equilibrium — it stays at rest or moves with constant velocity.
Example:
A 10 N force pulls a box to the right, while a 4 N friction force resists to the left. What is the resultant force?
▶️ Answer/Explanation
Forces are in opposite directions: \( F_{\text{net}} = 10~\text{N} – 4~\text{N} = \boxed{6~\text{N to the right}} \)
Example:
A car of mass 800 kg has a resultant force of 1600 N acting forward. What is its acceleration?
▶️ Answer/Explanation
Use \( F = ma \) ⇒ \( a = \dfrac{F}{m} \)
\( a = \dfrac{1600}{800} = \boxed{2.0~\text{m/s}^2} \)
Solid Friction
What is Solid Friction?
- Solid friction is the force that resists the motion of one solid surface sliding (or trying to slide) over another.
- It acts parallel to the surfaces in contact and in the opposite direction to motion or attempted motion.
Key Points about Solid Friction:
- It occurs between two solid surfaces.
- Friction tries to impede (oppose) relative motion.
- It causes heating due to energy being converted into thermal energy (vibration of particles).
- Rougher surfaces usually produce more friction.
- Lubricants (like oil or grease) can reduce friction by forming a smoother, slippery layer.
Types of Solid Friction:
- Static friction: Acts when there is no motion but a force is trying to move the object.
- Kinetic (sliding) friction: Acts when objects are sliding past each other.
Example:
A wooden block is pushed but does not move. What force prevents the motion?
▶️ Answer/Explanation
Static friction balances the applied force, preventing motion.
As long as the applied force is less than the maximum static friction, the block remains stationary.
Example:
When you rub your hands together quickly, they feel warm. What causes the heating?
▶️ Answer/Explanation
Friction between the surfaces of your hands converts mechanical energy into thermal energy.
Frictional heating raises the temperature of your skin.
What is Drag in a Liquid?
- Drag is a type of frictional force that acts on an object moving through a fluid (liquid or gas).
- In a liquid, this is often called viscous drag or fluid resistance.
- Drag always acts in the opposite direction to the object’s motion.
Cause of Drag:
- As an object moves through a liquid, it must push liquid particles out of the way.
- This interaction slows down the object due to resistance from the liquid particles.
Factors Affecting Drag in Liquids:
- Speed of the object – higher speed means more drag.
- Viscosity of the liquid – thicker (more viscous) liquids like oil cause more drag than thinner ones like water.
- Shape and surface area – streamlined shapes experience less drag.
Important: In liquids, drag increases with speed but not always linearly.
Example:
A small ball is dropped into a beaker of oil. As it falls, it slows down and then moves at a constant speed. Why?
▶️ Answer/Explanation
At first, weight is greater than drag, so the ball accelerates.
As speed increases, drag increases until it balances the weight.
The ball then moves at constant speed — this is called terminal velocity.
Example:
Two identical marbles are dropped: one in water and one in honey. Which experiences more drag?
▶️ Answer/Explanation
Honey has higher viscosity than water, so it produces more resistance to motion.
The marble in honey experiences greater drag and falls more slowly.
What is Drag in a Gas?
- When an object moves through a gas like air, it experiences a frictional force known as air resistance or drag.
- This drag force acts in the opposite direction to the object’s motion.
- It is a form of fluid friction, just like drag in liquids.
Key Characteristics of Air Resistance:
- Acts only when the object is moving through the air.
- Always opposes the motion (slows the object down).
- Converts some of the object’s kinetic energy into heat.
Factors Affecting Air Resistance:
- Speed of the object: faster objects experience greater air resistance.
- Shape: streamlined shapes reduce air resistance (e.g., airplanes, bullets).
- Surface area: larger surfaces face more drag (e.g., parachutes).
- Density of the air: drag is higher in denser air (e.g., at sea level vs. high altitude).
Example:
A skydiver jumps out of a plane and starts falling. How does air resistance affect their motion?
▶️ Answer/Explanation
Initially, gravity causes the skydiver to accelerate downwards.
As speed increases, air resistance increases.
Eventually, air resistance balances weight → the skydiver reaches terminal velocity.
They fall at a constant speed from this point.
Example:
Why are sports cars designed with a curved, low body?
▶️ Answer/Explanation
The streamlined shape reduces air resistance, allowing the car to move faster with less force.
This improves fuel efficiency and top speed.
Example:
You drop a flat sheet of paper and a crumpled paper ball from the same height. Which hits the ground first?
▶️ Answer/Explanation
The crumpled ball has less surface area, so it experiences less air resistance.
It accelerates faster and hits the ground before the flat sheet.
Effect of a Resultant Force on an Object
Effect of a Resultant Force on an Object:
- A resultant force is a single force that has the same effect as all the individual forces acting on an object.
- When there is a non-zero resultant force, the object’s velocity changes.
- This change in velocity can occur in two ways:
- By changing the object’s speed (increase or decrease)
- By changing the object’s direction of motion
- A change in either speed or direction is called acceleration (or deceleration, if slowing down).
Key Point: If a resultant force acts on an object, it must accelerate in the direction of the force.
Example:
A car is moving at 10 m/s. The driver presses the accelerator, and the engine applies a forward force larger than the resistive forces. What happens?
▶️ Answer/Explanation
The net (resultant) force is forward, so the car accelerates.
Its speed increases in the same direction of motion.
Example:
A ball on a string is swung in a circle. The tension in the string pulls toward the center. What effect does this have on the ball?
▶️ Answer/Explanation
The tension provides a resultant force toward the center of the circle.
This causes the ball to change direction continuously, keeping it in circular motion.
Its speed may stay constant, but its velocity changes because the direction changes.
Example:
A cyclist is moving forward, but friction and air resistance become greater than the forward force. What is the effect?
▶️ Answer/Explanation
There is a net force acting backward (resultant force is opposite to motion).
The cyclist slows down — their speed decreases (negative acceleration or deceleration).
Circular Motion
Circular Motion:
- When an object moves in a circular path, it is constantly changing direction.
- Even if its speed remains constant, the velocity changes due to the continuous change in direction.
- This means the object is accelerating, and a force must be acting to cause this acceleration.
- This force is called the centripetal force and always acts towards the center of the circle.
- The centripetal force is always perpendicular to the direction of motion (velocity) of the object.
(a) Speed increases if force increases, with mass and radius constant
- If an object is moving in a circular path and both its mass and radius of the circle are kept constant, then increasing the centripetal force will cause the object to move faster (its speed increases).
- This is because the object is being pulled harder toward the center, allowing it to turn more tightly without flying outward.
- The increase in force allows for greater acceleration, which results in an increase in speed while maintaining circular motion.
Example:
A toy car is attached to a string and spun in a circle on a smooth surface. If you pull the string tighter (increase the tension), the car speeds up. Why?
▶️ Answer/Explanation
The increased tension in the string provides more centripetal force.
With mass and radius constant, this allows the car to move faster without changing the path.
(b) Radius decreases if force increases, with mass and speed constant
- If the mass and speed of the object remain constant, increasing the centripetal force will cause the object to move in a smaller circle (i.e., the radius decreases).
- This happens because the extra inward force allows the object to curve more tightly, reducing the turning radius.
- The path bends more sharply, so the object moves in a tighter circle while keeping its speed the same.
Example:
A car turns in a circular path at a constant speed. The road gets stickier (more grip), increasing the frictional force. What happens to the turning radius?
▶️ Answer/Explanation
Frictional force increases — this is the centripetal force keeping the car in the curve.
With speed and mass constant, more force means the car can turn in a smaller radius.
(c) An increased mass requires an increased force to keep speed and radius constant
- If the speed and radius of the circular path are to remain constant, then increasing the object’s mass requires a greater centripetal force.
- This is because a heavier object has more inertia and resists changes in direction more strongly.
- To keep it moving in the same circle at the same speed, a stronger inward force is needed to overcome this increased inertia.
Example:
A truck and a motorcycle are turning around the same bend at the same speed. Which one needs more inward force to stay on the same curve?
▶️ Answer/Explanation
The truck has more mass, so it requires a greater centripetal force to follow the same curved path at the same speed.
This is why sharp turns are more dangerous for heavy vehicles at high speeds.
Example:
A student swings two different balls of the same size in horizontal circles using strings of the same length. Ball A has a mass of 0.2 kg and moves at 3 m/s. Ball B has a mass of 0.4 kg. The student wants Ball B to follow the same circular path at the same speed.
Compare the centripetal force required for both balls and explain what happens if:
- Ball B is swung at the same speed and radius.
- The force applied to Ball B is greater than needed.
- The same force is applied to both Ball A and Ball B.
▶️ Answer/Explanation
- Ball B (more massive) requires to maintain the same circular path at the same speed, since force is proportional to mass.
- If is applied to Ball B, the ball will move faster or the radius will decrease, depending on how it’s held — .
- If the is used for both, Ball B will at the same speed — it may fly outward or require a larger radius to compensate.
This tests understanding of the relationship between mass, speed, radius, and force in circular motion.