Forces Revision Notes

Defining Momentum (Higher)

Momentum (symbol, p) is a measure of an object's mass in motion. It is a vector quantity, meaning it has both magnitude and direction. Momentum is directly proportional to an object's mass and its velocity. The formula for momentum is p = m × v, where 'm' is the mass in kilograms (kg) and 'v' is the velocity in metres per second (m/s). Therefore, the standard unit for momentum is kilogram metres per second (kg m/s).

Conservation of Momentum in Collisions (Higher)

The principle of conservation of momentum states that in a closed system, where no external forces act, the total momentum before a collision (or explosion) is equal to the total momentum after. This means that momentum is transferred between objects but not lost or gained overall. For example, if two objects collide, the sum of their individual momenta before the impact will be the same as the sum of their individual momenta after the impact, taking into account their new velocities and directions.

Types of Collisions (Higher)

Collisions can generally be categorised as elastic or inelastic. In an elastic collision, both momentum and kinetic energy are conserved. Objects typically rebound without deformation. In contrast, in an inelastic collision, momentum is still conserved, but kinetic energy is not; some kinetic energy is converted into other forms like heat, sound, or deformation energy. Objects often stick together or deform significantly in inelastic collisions, such as a car crash where vehicles crumple.

Practical Investigation of Momentum (Higher) - PAG P3

PAG P3 involves investigating the conservation of momentum using trolleys and light gates. In such an experiment, the masses of the trolleys are measured using a balance, and their velocities before and after collision are measured using light gates connected to a data logger. The independent variable is typically the initial velocity or mass of one trolley, the dependent variable is the final velocity of the trolleys, and control variables include ensuring a level track to minimise friction. Safety involves ensuring the track is stable and trolleys do not fall off. Momentum is calculated for each trolley before and after, to verify if total momentum is conserved within experimental error. Percentage error calculation for momentum requires comparing the initial and final total momentum, highlighting the importance of minimising external forces in a closed system.

Energy Definition and Forms

Energy is defined as the capacity to do work or cause change. It is a scalar quantity, meaning it only has magnitude, not direction. Energy exists in many forms, including kinetic energy (due to motion), gravitational potential energy (due to height), elastic potential energy (stored in stretched or compressed objects), thermal energy (heat), chemical energy (stored in substances), electrical energy, light energy, and sound energy. The Law of Conservation of Energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another.

Energy Transfers and Work Done

Energy is transferred when work is done. Work done is a measure of the energy transferred when a force causes an object to move through a distance. For example, lifting an object against gravity involves work being done on the object, transferring energy to its gravitational potential store. Similarly, accelerating an object involves work being done, increasing its kinetic energy. Energy transfers can also occur through heating (e.g., conduction, convection, radiation) or by electrical means.

Units of Energy and Work Done

The standard unit for all forms of energy and for work done is the joule (J). The joule is part of the International System of Units (SI). Work done is calculated using the formula: Work Done = Force × Distance. Force is measured in newtons (N) and distance in metres (m). Therefore, the derived unit for work done is the newton-metre (N m). It is critical to understand that one newton-metre (1 N m) is exactly equivalent to one joule (1 J). This equivalence allows for direct conversion and understanding of energy transfers.

Calculating Energy Values

To calculate energy values, you need to apply the correct formulas. For work done, it's Force × Distance. For kinetic energy, it's 0.5 × mass × velocity². For gravitational potential energy, it's mass × gravitational field strength × height. In all these calculations, ensure you use the correct SI units for mass (kg), velocity (m/s), height (m), force (N), and gravitational field strength (N/kg or m/s²). The result will be in joules, or if calculating work done, in newton-metres, which can be directly converted to joules.

What is a Resultant Force? (Higher Tier)

A resultant force is the single force that represents the combined effect of all individual forces acting on an object. It dictates whether an object accelerates, decelerates, or remains in equilibrium (either stationary or moving at a constant velocity). If the resultant force is zero, the object's velocity will not change. If the resultant force is non-zero, the object will accelerate in the direction of the resultant force, with the acceleration being directly proportional to the resultant force and inversely proportional to the object's mass (Newton's Second Law, F=ma).

Using Free-Body Diagrams (Higher Tier)

Free-body diagrams simplify complex scenarios by representing the object as a point and drawing all forces acting on it as arrows originating from that point. The length of the arrow signifies the force's magnitude, and the arrow's direction indicates the force's direction. It is vital to only include forces acting *on* the object, not forces the object exerts. Common forces include weight (due to gravity, always vertically downwards), normal contact force (perpendicular to the surface), friction (opposing motion), and tension (in ropes/cables) or air resistance. These diagrams are crucial for visualising and later calculating resultant forces.

Calculating Resultant Forces Along a Single Line (Higher Tier)

When forces act along the same straight line, determining the resultant force is straightforward. Forces acting in the same direction are added together, while forces acting in opposite directions are subtracted. For instance, if a push force of 50 N acts right and friction of 10 N acts left, the resultant force is 50 N - 10 N = 40 N to the right. If two people pull a rope with forces of 30 N and 40 N in the same direction, the resultant force is 30 N + 40 N = 70 N in that direction. The direction of the larger force dictates the direction of the resultant force when forces are in opposition.

Calculating Resultant Forces at Angles (Higher Tier)

When forces act at angles, simple addition or subtraction is not enough. Forces must be treated as vectors. One common method is to resolve each force into its perpendicular components (e.g., horizontal and vertical components). Then, sum all horizontal components to find the net horizontal force (F_x_resultant) and sum all vertical components to find the net vertical force (F_y_resultant). The overall resultant force (F_resultant) can then be found using Pythagoras' theorem: F_resultant = sqrt(F_x_resultant^2 + F_y_resultant^2). The direction of this resultant force can be found using trigonometry (e.g., tan(theta) = F_y_resultant / F_x_resultant). This approach is essential for accurate analysis of angled forces.

Identifying Forces on Isolated Objects (Higher)

For any isolated solid object or system, it is crucial to identify all forces acting upon it. Forces are vector quantities, meaning they have both magnitude and direction. An 'isolated' object means we focus only on the forces directly affecting that object, ignoring its internal structure or external elements not interacting with it. Drawing a free-body diagram is the best way to visualise these forces; represent the object as a dot and draw arrows originating from it to show each force.

Common Types of Forces and Their Characteristics (Higher)

Key forces to consider include:

• Weight (W): Always acts vertically downwards towards the centre of the Earth. Calculated as W = mg, where m is mass and g is gravitational field strength.
• Normal Contact Force (N): Acts perpendicularly outwards from a surface supporting the object. It prevents the object from penetrating the surface. On a horizontal surface, it often balances weight.
• Tension (T): A pulling force in a string, cable, or chain. It acts along the length of the string, away from the object.
• Thrust/Push (F_thrust): A general force that drives an object forward or acts directly on it. For example, engine thrust or a direct push.
• Friction (F_f): Opposes relative motion or attempted motion between surfaces in contact. Acts parallel to the surface, in the direction opposite to motion. Can be static or kinetic.
• Air Resistance/Drag (D): A form of fluid friction opposing motion through air/fluid. Its magnitude increases with speed and depends on shape. Often represented as acting opposite to the direction of motion.
• Upthrust/Buoyancy (U): An upward force exerted by a fluid on an immersed object, according to Archimedes' principle. It opposes the object's weight.

Analysing a System (Higher)

When dealing with a 'system' of objects (e.g., two masses connected by a string), it's important to consider which forces are internal to the system and which are external. Internal forces cancel out within the system, while external forces determine the net acceleration of the entire system. You might also need to analyse each object in the system separately using free-body diagrams to resolve unknown forces or accelerations. For example, in a pulley system, the tension in the string is an internal force between the two connected masses, but it's an external force when considering each mass individually. Always clearly define the boundaries of your 'system'.