Forces Revision Notes

What is Extension and Force?

Extension refers to the increase in length of an object, like a spring or piece of rubber, when a force is applied to it. Force is a push or pull that can cause an object to accelerate, deform, or change its state of motion. When discussing elastic materials, we are concerned with forces that cause deformation. For example, hanging weights from a spring applies a downward force, causing the spring to extend. The units for force are Newtons (N) and for extension, typically metres (m) or centimetres (cm).

Linear Relationship: Key Features

A linear relationship between force and extension means that the extension is directly proportional to the applied force. This occurs within the elastic limit of the material. On a force-extension graph, a linear relationship is represented by a straight line that passes through the origin (0,0). This implies that if you double the force, the extension will also double. Materials exhibiting this behaviour will return to their original shape once the force is removed, showing elastic deformation. Metal springs are good examples of materials that often display a clear linear relationship over a significant range before reaching their elastic limit.

Non-Linear Relationship: Key Features

A non-linear relationship occurs when the extension is no longer directly proportional to the applied force. This typically happens when the elastic limit of the material has been exceeded. On a force-extension graph, a non-linear relationship is shown by a curve. In this region, a small increase in force can lead to a much larger increase in extension compared to the linear region. When a material is stretched beyond its elastic limit, it undergoes plastic deformation, meaning it will not return to its original shape even after the force is removed. Materials like rubber often exhibit non-linear behaviour over a wider range of forces before breaking.

Practical Investigation (PAG P2)

To investigate force and extension, you can set up a spring or rubber band clamped to a stand. Measure its initial length. Then, attach known masses (which apply a force due to gravity, F=mg) and measure the new length. The extension is the new length minus the original length. Repeat this for increasing masses. Plot a graph of force (y-axis) against extension (x-axis). Independent variable: Applied force (mass hooked on). Dependent variable: Extension of the spring/material. Control variables: Type of spring/material, temperature. Safety: Wear eye protection to guard against snapping springs. Ensure the stand is stable and cannot topple. Results analysis: Observe the shape of the graph. A straight line indicates a linear relationship, while a curve indicates a non-linear relationship. Identify the elastic limit if visible.

Measuring Distances

The method and equipment used to measure distance depend on the length being measured and the required precision. For short distances, such as the length of a desk or the width of an object, a standard ruler or a measuring tape is suitable. These instruments typically have markings down to millimetres, allowing for measurements to the nearest millimetre or half-millimetre with careful reading. For longer distances, for example, the length of a sports field or a corridor, a trundle wheel is often used. A trundle wheel measures distance by clicking for every metre it rolls, providing a straightforward way to cover larger distances. For very large distances, such as those outdoors or between points that are not easily accessible, technologies like GPS or surveyor's tapes become more appropriate, though a measuring tape can still be used for lengths of up to perhaps 30 or 50 metres, requiring careful handling to prevent sagging and ensure accuracy.

Measuring Time

Similar to distance, the measurement of time also requires different tools based on the duration and precision needed. For short time intervals, especially those in experiments where human reaction time significantly affects accuracy, a stopwatch is commonly employed. Digital stopwatches can read to hundredths of a second, but human reaction time typically introduces an error of around 0.1 to 0.2 seconds. To minimise this error, especially for very short events, automated systems like light gates connected to a data logger are used. Light gates start and stop a timer automatically as an object passes through them, eliminating reaction time errors and providing highly precise measurements. For longer time periods, such as the duration of an entire experiment or an activity, digital or analogue clocks are sufficient. When using any timing device, it is important to understand its resolution and potential sources of error inherent in its operation.

Accuracy and Precision in Measurement

When measuring distance and time, it's important to differentiate between accuracy and precision. Accuracy refers to how close a measurement is to the true value, while precision refers to how close repeated measurements are to each other. To improve accuracy, instruments should be calibrated correctly and read meticulously, avoiding errors like parallax (reading a scale from an angle). For improving precision and reducing the impact of random errors, it is good practice to take multiple measurements and calculate an average. For example, when measuring the time for an object to fall, conducting three to five trials and averaging the results will provide a more reliable value than a single measurement. Considering the resolution of the measuring device is also key; a ruler marked in millimetres cannot give a reading more precise than half a millimetre, and a stopwatch reading to 0.01 seconds cannot give a more precise time.

Common Sources of Error

Several types of errors can affect measurements of distance and time. Reaction time is a significant random error when manually starting and stopping a stopwatch; it can be reduced by using automatic timing systems like light gates or by training to minimise reaction time. Parallax error occurs when the observer's eye is not directly perpendicular to the scale being read, leading to an incorrect reading; this is corrected by reading directly in front of the mark. Zero error happens when an instrument does not read zero when it should, for example, a ruler whose end is not precisely at the zero mark. This systematic error can be corrected by subtracting or adding the zero error to all readings. Environmental factors, such as temperature affecting the length of a measuring tape or air resistance affecting the motion of an object, can also introduce errors in measurements. Awareness of these potential errors allows for better experimental design and more reliable results.

What is a Free Body Diagram (Higher)?

A free body diagram is a simplified visual tool used to represent an object and all the external forces acting upon it. The object is typically shown as a pointmass or a simple shape, and each force is represented by an arrow (vector) originating from the object's centre. The arrow's direction indicates the direction of the force, and its length can be proportional to the force's magnitude. These diagrams are crucial for analysing motion and understanding how forces interact to produce a net effect on an object. They isolate the object from its surroundings, making it easier to identify and sum the forces.

Understanding Resultant Force (Higher)

The resultant force is the single force that has the same effect on an object as all the individual forces acting on it combined. If multiple forces push or pull an object, the resultant force is the 'net' force. If the resultant force is zero, the object is in equilibrium (either at rest or moving at a constant velocity). If the resultant force is non-zero, the object will accelerate in the direction of the resultant force, according to Newton's Second Law of Motion (F=ma). Calculating resultant force can involve simple addition/subtraction for collinear forces or vector addition (e.g., parallelogram method, trigonometry) for forces at angles.

Calculating Resultant Force for Collinear Forces (Higher)

When forces act along the same straight line (collinear), determining the resultant force is straightforward. Forces acting in the same direction are added together. Forces acting in opposite directions are subtracted. For example, if Force A is 10 N to the right and Force B is 5 N to the right, the resultant force is 15 N to the right. If Force A is 10 N to the right and Force B is 5 N to the left, the resultant force is 5 N to the right (10 N - 5 N). The direction of the larger force dictates the direction of the resultant.

Vector Addition for Non-Collinear Forces (Higher)

When two or more forces act on an object at an angle to each other, their resultant force is found using vector addition. One common graphical method is the parallelogram method. To use this, draw the two force vectors originating from the same point, scaled to their magnitudes. Complete a parallelogram using these two vectors as adjacent sides. The diagonal drawn from the common origin to the opposite corner of the parallelogram represents the resultant force, showing both its magnitude and direction. More complex scenarios may involve resolving forces into perpendicular components and then using Pythagoras' theorem and trigonometry.

What is an Interaction?

An interaction in physics refers to any situation where two or more objects mutually influence each other. This influence often manifests as forces. Forces are pushes or pulls that can change an object's motion (speed or direction) or its shape. It's crucial to remember that forces always occur in pairs, as per Newton's Third Law: if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These are called interaction pairs. Understanding interactions is key to explaining movement, stability, and energy transfers. Without interactions, objects would simply continue in their current state of motion indefinitely, as described by Newton's First Law.

Contact vs. Non-Contact Interactions

Interactions can be broadly categorised into two main types: contact interactions and non-contact interactions. Contact interactions occur when objects are physically touching each other. Examples include: friction (the force resisting motion between surfaces in contact), tension (force through a stretched rope or cable), air resistance (force opposing motion through air), normal force (the support force from a surface), and pushing/pulling (direct application of force). Non-contact interactions occur when objects exert forces on each other without direct physical contact. The primary examples are gravitational force (attraction between any two objects with mass), magnetic force (attraction or repulsion between magnetic poles or moving charges), and electrostatic force (attraction or repulsion between charged particles).

Examples of Interactions and Forces Involved

It's important to be able to identify specific examples of interactions and the forces involved.

Contact Interactions:

• Kicking a ball: Foot exerts a pushing force on the ball, accelerating it. The ball exerts an equal and opposite force on the foot.
• Pushing a trolley: Hand exerts a pushing force on the trolley. The trolley exerts an equal and opposite force on the hand.
• Friction on a sliding block: The surface exerts a friction force opposing the block's motion. The block exerts an equal and opposite force on the surface.
• Lifting a weight: Muscular force applied upwards on the weight. The weight pulls downwards on the muscles.

Non-Contact Interactions:

• An apple falling from a tree: The Earth exerts a gravitational force on the apple, pulling it downwards. The apple exerts an equal and opposite gravitational force on the Earth.
• Two magnets attracting/repelling: Magnets exert magnetic forces on each other without touching.
• A charged balloon attracting hair: The charged balloon exerts an electrostatic force on the hair, pulling it towards the balloon.