Forces Revision Notes

What is Fluid Pressure?

Pressure in fluids (which include both liquids and gases) arises from the continuous, random motion of the fluid particles. These particles collide with each other and with the surfaces of any object or container they are in. Each collision exerts a tiny force. The collective effect of these countless collisions over a specific area is what we define as pressure. Pressure is calculated as force per unit area, typically measured in Pascals (Pa), where 1 Pa = 1 N/m².

Direction of Force due to Fluid Pressure

A key characteristic of fluid pressure is the direction of the force it produces on a surface. The net force caused by pressure in a fluid always acts at right angles (or perpendicularly) to any surface it is in contact with. This applies whether the surface is the wall of a container, the bottom of a pool, or the surface of an object submerged within the fluid. If the force were not perpendicular, there would be a component of force parallel to the surface, which would cause the fluid to flow along the surface, contradicting the equilibrium state where pressure is being measured.

Examples of Perpendicular Pressure Force

Consider several real-world examples:

1. A diver underwater experiences pressure on all parts of their body, and the force from this water pressure pushes inwards, perpendicular to the diver's skin at every point.
2. The air inside a car tyre exerts pressure, and this pressure creates an outward force that is perpendicular to the inner surface of the tyre wall, keeping it inflated.
3. A dam holding back water experiences immense pressure from the water, and the force exerted on the wall of the dam is always perpendicular to its surface at any given point.

Why is it always perpendicular?

The reason the net force is always perpendicular is due to the nature of fluids. If there were a component of force parallel to the surface, the fluid would move along that surface. In a static fluid (one that is not flowing), any tangential forces would cause movement until the forces were balanced. Therefore, for a fluid at rest, the only sustained force it can exert on a surface is one that is normal (perpendicular) to that surface.

Uniform Motion: Speed, Distance, Time

Uniform motion refers to an object moving at a constant speed in a straight line. The fundamental formula linking these quantities is: Speed = Distance / Time.

This can be rearranged to find any of the variables if the other two are known: Distance = Speed × Time Time = Distance / Speed

Ensure consistency in units when performing calculations. For example, if speed is in metres per second (m/s), distance should be in metres (m) and time in seconds (s).

Motion with Uniform Acceleration

Uniform acceleration means an object's velocity is changing at a constant rate. Velocity is speed in a given direction. For uniformly accelerated motion, two primary formulae are used:

1. Change in velocity: Final speed (v) = Initial speed (u) + (acceleration (a) × time (t))

This is written as: v = u + at

1. Distance travelled: Distance (s) = (initial speed (u) × time (t)) + (½ × acceleration (a) × time (t)²)

This is written as: s = ut + ½at²

'Initial speed' (u) is the speed at the beginning of the timed interval, and 'final speed' (v) is the speed at the end of the interval. If an object starts 'from rest', its initial speed (u) is 0.

Units and Conversions

Accurate calculations depend on using consistent units. Common units are:

• Distance: metres (m)
• Time: seconds (s)
• Speed (or velocity): metres per second (m/s)
• Acceleration: metres per second squared (m/s²)

Sometimes, quantities might be given in different units, such as kilometres per hour (km/h) for speed, or minutes for time. It's crucial to convert these to the standard SI units (m, s, m/s, m/s²) before applying the formulae to avoid errors. For example, to convert km/h to m/s, divide by 3.6.

Practical Application: Measuring Speed and Acceleration

PAG P3 involves methods for determining speed and acceleration. For uniform speed, you can measure the distance travelled and the time taken using a ruler and stopwatch. For acceleration, more sophisticated methods are needed. For instance, using light gates connected to a data logger can measure the time taken for an object to pass through each gate, allowing calculation of instantaneous speeds at different points. From these speeds and the time between gates, acceleration can be determined. Variables to control in such experiments might include friction, the angle of a ramp, or external forces, ensuring that only the intended variables (like mass) are changed.

Understanding Inertia (Higher)

Inertia is the natural tendency of an object to resist changes in its state of motion. This means an object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction, unless acted upon by an external resultant force. The more mass an object has, the greater its inertia. For instance, it is much harder to stop a moving train than to stop a moving bicycle, even if they are travelling at the same speed, because the train has significantly more inertia due to its greater mass.

Defining Inertial Mass (Higher)

Inertial mass is a quantitative measure of an object's inertia. It is formally defined using Newton's Second Law of Motion. If a resultant force (F) acts on an object and causes it to accelerate (a), then the inertial mass (m) of that object is given by the ratio of the force to the acceleration: m = F / a. This formula highlights that for a given resultant force, a larger inertial mass results in a smaller acceleration, and conversely, to achieve a specific acceleration, a larger force is required for objects with greater inertial mass. The unit for inertial mass is the kilogram (kg).

Calculating Inertial Mass (Higher)

To calculate inertial mass, you need to know the resultant force acting on an object and the acceleration it experiences. For example, if a resultant force of 10 N causes an object to accelerate at 2 m/s², then its inertial mass is m = 10 N / 2 m/s² = 5 kg. This calculation is a direct application of the definition. It's essential to use the resultant force, meaning the vector sum of all forces acting on the object. If multiple forces are acting, they must be combined to find the net force before calculating the inertial mass.

Definition and Calculation of Momentum

Momentum (p) is a measure of the 'quantity of motion' an object possesses. It is a vector quantity, meaning it has both magnitude and direction. Momentum is calculated using the formula: momentum = mass × velocity (p = mv). The unit of momentum is kilogram metres per second (kg m/s). A larger mass or a higher velocity results in greater momentum. For example, a fast-moving bullet has high momentum due to its velocity, while a slow-moving train has high momentum due to its large mass.

Conservation of Momentum in Collisions (Higher Tier)

The principle of conservation of momentum states that in a closed system, the total momentum before a collision or explosion is equal to the total momentum after the collision or explosion. A 'closed system' means that no external forces act on the interacting objects. This principle is a direct consequence of Newton's third law of motion. During a collision, forces between objects are internal to the system, so the total momentum remains constant, even though momentum can be transferred between the colliding objects.

Types of Collisions: Elastic vs. Inelastic (Higher Tier)

Collisions are categorised based on whether kinetic energy is conserved. In an elastic collision, both momentum and kinetic energy are conserved. Ideal elastic collisions are rare in real life but are approximated by interactions like billiard balls. In an inelastic collision, momentum is conserved, but kinetic energy is not. Some kinetic energy is converted into other forms, such as heat, sound, or energy used to permanently deform the objects. Most everyday collisions, such as a car crash or a ball of clay hitting a wall, are inelastic.

Practical Investigation: Momentum in Collisions (PAG P3 Higher Tier)

A practical investigation could involve studying collisions using two trolleys on a track. The independent variable could be the mass or initial velocity of one trolley. The dependent variable would be the velocities of the trolleys after collision. Control variables include ensuring a level track and using the same type of trolleys and track. Velocities can be measured using light gates and data loggers. The total momentum before and after the collision can be calculated and compared to demonstrate conservation. Safety precautions include ensuring the track is stable and trolleys do not roll off. This practical helps confirm the conservation of momentum principle.