Forces Revision Notes

What is Non-Uniform Motion?

Non-uniform motion describes movement where an object's speed changes over time. This is common in everyday life, such as a car accelerating from traffic lights, a person jogging and then walking, or a ball rolling down a hill. In these scenarios, the object is not covering equal distances in equal intervals of time. Therefore, we cannot simply use a speed for a specific segment to represent the entire journey. Average speed provides a summary of the overall rate of motion.

Calculating Average Speed

To calculate average speed for any motion, uniform or non-uniform, the key is to use the formula: Average Speed (m/s or km/h) = Total Distance Travelled (m or km) / Total Time Taken (s or h). It is essential to work with the total distance covered from the start to the end of the journey and the total time elapsed for the entire journey. Ensure that all units are consistent; for instance, if distance is in metres and time is in minutes, convert minutes to seconds before calculating speed in m/s.

Example Calculation

Consider a cyclist who travels 1000 metres in the first 100 seconds and then 500 metres in the next 50 seconds. To find the average speed over the entire journey, first find the total distance: 1000 m + 500 m = 1500 m. Next, find the total time: 100 s + 50 s = 150 s. Now, apply the formula: Average Speed = Total Distance / Total Time = 1500 m / 150 s = 10 m/s. This single value represents the overall average rate of travel.

Units and Consistency

Precise use of units is vital in physics calculations. The standard SI unit for distance is the metre (m) and for time is the second (s), which gives average speed in metres per second (m/s). Other common units include kilometres (km) for distance and hours (h) for time, leading to speeds in kilometres per hour (km/h). Always check that the units for distance and time are compatible before performing the division. If they are not, convert one or both quantities to a consistent set of units first.

What is a Gravitational Field?

A gravitational field is a region of space surrounding an object with mass, in which another object with mass will experience an attractive force. It's an invisible area of influence that extends infinitely outwards from any object, pulling other objects towards it. The concept explains how gravity acts without direct physical contact between objects; rather, objects interact through their respective gravitational fields. The Earth's gravitational field, for instance, is responsible for keeping us on the ground and for the Moon's orbit.

Gravitational Attraction and Mass

All matter, meaning anything that has mass, possesses a gravitational field. This field causes an attractive force between any two objects with mass. A key characteristic of gravitational fields is that their strength is directly proportional to the mass of the object creating the field. This means that if an object has a larger mass, its gravitational field will be significantly stronger. Consequently, it will exert a much greater attractive force on other objects within its field. This explains why massive celestial bodies like planets and stars have such noticeable gravitational effects.

Massive Objects and Field Strength

Objects with very large masses, such as planets, stars, and galaxies, generate extremely powerful gravitational fields. These strong fields are responsible for the large-scale structures and motions observed in the universe, including planetary orbits and the formation of galaxies. For example, the Sun's immense mass creates a gravitational field strong enough to hold all the planets in our solar system in their orbits. Comparatively, everyday objects like a chair or a car also have gravitational fields, but their masses are so small that the gravitational attraction they exert is negligible and unnoticeable in our daily lives.

Understanding Deformation

Deformation refers to any change in the shape or size of an object caused by an applied force. When a force is applied to a material, its constituent particles are displaced from their equilibrium positions. The nature of these changes determines whether the deformation is elastic or plastic. Tensile forces, which try to stretch an object, are a common example of forces causing deformation. The response of a material to these forces is critical in engineering and material science, dictating its suitability for specific applications. For example, materials in structural components must resist permanent changes to maintain integrity, focusing on elastic behaviour.

Elastic Deformation

Elastic deformation is a temporary change in the shape or size of an object. A key characteristic is that the object fully returns to its original dimensions once the external force or load is removed. During elastic deformation, the interatomic forces between particles within the material temporarily stretch or compress, but the particles do not permanently change their relative positions. Think of a spring: it stretches when pulled but rebounds to its initial length when released. Every material has an 'elastic limit'. Up to this point, it behaves elastically. Exceeding this limit leads to permanent changes.

Plastic Deformation

Plastic deformation is a permanent change in the shape or size of an object. Unlike elastic deformation, the object does not return to its original state after the deforming force is removed. This occurs when the applied force is strong enough to cause the particles within the material to move past each other into new, stable positions. The interatomic bonds are broken and reformed in these new configurations, meaning the material's internal structure has been permanently altered. Bending a metal wire permanently or moulding clay are examples of plastic deformation. Materials that can undergo significant plastic deformation are described as ductile or malleable.

Practical Investigation (PAG P2)

A common practical investigation involves stretching a spring. The independent variable is the applied force (weights added), and the dependent variable is the extension of the spring. Control variables include the type of spring and the temperature. Start by measuring the initial length of the spring. Add small, incremental weights, recording the total force and the corresponding extension after each addition. Calculate extension by subtracting the initial length from the current length. Remove weights gradually, observing if the spring returns to its original length. Plot force against extension to identify the elastic limit, which is the point beyond which the spring no longer returns to its original length. Safety precautions include ensuring weights are securely attached to prevent them from falling and wearing eye protection if there's any risk of a spring snapping.

Understanding Velocity-Time Graphs

A velocity-time graph plots velocity (y-axis) against time (x-axis). The gradient of the line on a velocity-time graph represents acceleration. A horizontal line shows constant velocity (zero acceleration). A straight line with a positive gradient indicates constant acceleration, while a straight line with a negative gradient shows constant deceleration. A curved line indicates changing acceleration.

Calculating Displacement from Area (Higher Tier)

The area enclosed between the line on a velocity-time graph and the time axis represents the displacement (distance travelled) of the object. Displacement is a vector quantity, meaning it has both magnitude and direction. If the velocity is positive, the displacement is in the positive direction; if velocity is negative, the displacement is in the negative direction.

Methods for Area Calculation (Higher Tier)

To find the area (and thus displacement), divide the region under the graph into standard geometric shapes: rectangles, triangles, or trapezoids. For a rectangle, Area = length × width (velocity × time). For a triangle, Area = 0.5 × base × height (0.5 × time × change in velocity). For a trapezoid (useful for constant acceleration where initial velocity is not zero), Area = 0.5 × (sum of parallel sides) × height. The parallel sides are the initial and final velocities, and the height is the time interval. Sum the areas of all segments to find the total displacement.

Interpreting Negative Areas (Higher Tier)

If the velocity-time graph goes below the x-axis, it indicates that the object is moving in the opposite direction. The area below the x-axis contributes negatively to the overall displacement. However, if asked for the 'total distance travelled', you would take the absolute value of the area below the x-axis and add it to the areas above, as distance is a scalar quantity and always positive.