Chapter 1: Forces P2 Knowledge organiser

Scalar and Vector Quantities

Physical quantities are categorized into two types: scalars and vectors.
Scalars: These are quantities that possess magnitude (size) only. They do not have a specific direction associated with them. - Examples include: - Distance: Measured in meters ( $m$ ). - Speed: Measured in meters per second ( $\text{m/s}$ ). - Mass: Measured in kilograms ( $kg$ ). - Time: Measured in seconds ( $s$ ). - Energy: Measured in Joules ( $J$ ). - Temperature: Measured in degrees Celsius ( $^{\circ}C$ ) or Kelvin ( $K$ ).
Vectors: These are quantities that have both a magnitude and a defined direction. - Examples include: - Displacement: Distance in a specific direction ( $m$ ). - Velocity: Speed in a specific direction ( $\text{m/s}$ ). - Acceleration: Rate of change of velocity ( $\text{m/s}^2$ ). - Force: Measured in Newtons ( $N$ ). - Weight: The force of gravity acting on an object ( $N$ ). - Momentum: The product of mass and velocity ( $kg\,m/s$ ).
Vectors are typically represented by arrows. The length of the arrow signifies the magnitude of the vector, and the direction in which the arrow points signifies the vector's direction.

Contact and Non-Contact Forces

A force is a push or a pull that acts on an object due to its interaction with another object. All forces are measured in Newtons ( $N$ ).
Contact Forces: These forces occur when the objects are physically touching. - Friction: A force that opposes motion between two surfaces sliding or attempting to slide across each other. - Air Resistance: A type of frictional force (drag) that acts on objects moving through the air. - Tension: The force pulled through a string, rope, cable, or wire when it is pulled tight by forces acting from opposite ends. - Normal Contact Force: The support force exerted upon an object that is in contact with another stable object (e.g., a book resting on a table).
Non-Contact Forces: These forces act between objects that are not in physical contact. - Gravitational Force: The force of attraction between masses. It is responsible for weight. - Electrostatic Force: The force of attraction or repulsion between charged objects. - Magnetic Force: The force exerted by magnets or moving electric charges.

Gravity, Mass, and Weight

Mass: The amount of matter in an object, measured in kilograms ( $kg$ ). Mass is a scalar and is independent of location.
Weight: The force acting on an object due to gravity, measured in Newtons ( $N$ ). Weight is a vector and changes depending on the gravitational field strength of the location.
Gravitational Field Strength ( $g$ ): A measure of the strength of the gravity in a specific area. - On Earth, the gravitational field strength is approximately $g \approx 9.8\,N/kg$ . - On the Moon, it is approximately $g \approx 1.6\,N/kg$ .
The relationship between weight, mass, and gravitational field strength is defined by the formula: - $W = m \times g$
Weight is directly proportional to mass. If the mass of an object doubles, its weight also doubles ( $W \propto m$ ).
Weight is measured using a calibrated spring balance, commonly referred to as a newtonmeter.
The weight of an object is considered to act at a single point designated as the center of mass.

Resultant Forces and Work Done

Resultant Force: The single force that represents the combined effect of all individual forces acting on an object. - If multiple forces act along the same line, the resultant is found by adding forces in the same direction and subtracting forces in opposite directions. - A resultant force of zero indicates that the object is either stationary or moving at a constant speed in a straight line (equilibrium).
Work Done: When a force causes an object to move through a distance, energy is transferred. This is called work. - The formula for work done is: - $W = F \times s$ - Where: - $W$ is work done in Joules ( $J$ ). - $F$ is the applied force in Newtons ( $N$ ). - $s$ is the distance moved along the line of action of the force in meters ( $m$ ).
One Joule of work is done when a force of one Newton causes a displacement of one meter ( $1\,J = 1\,Nm$ ).
Work done against friction forces usually causes a rise in the temperature of the object as energy is transferred to the thermal store.

Forces and Elasticity

Changing an object's shape requires more than one force (e.g., stretching, compressing, or bending).
Elastic Deformation: The object returns to its original shape and length once the forces are removed.
Inelastic (Plastic) Deformation: The object does not return to its original shape; it is permanently changed.
Hooke's Law: For certain materials, the extension is directly proportional to the force applied, provided the limit of proportionality is not exceeded.
The formula for force and extension is: - $F = k \times e$ - Where: - $F$ is force ( $N$ ). - $k$ is the spring constant ( $N/m$ ). - $e$ is the extension ( $m$ ).
The spring constant ( $k$ ) is a measure of the stiffness of the spring. STiffer springs have higher values of $k$ .
The energy stored in a stretched spring (elastic potential energy) can be calculated if the limit of proportionality has not been exceeded: - $E_e = \frac{1}{2} \times k \times e^2$

Moments, Levers, and Gears

Moment: The turning effect of a force around a pivot.
The formula for a moment is: - $M = F \times d$ - Where: - $M$ is the moment in Newton-meters ( $Nm$ ). - $F$ is the force in Newtons ( $N$ ). - $d$ is the perpendicular distance from the pivot to the line of action of the force in meters ( $m$ ).
Balanced Moments: For an object in equilibrium, the total clockwise moment about a pivot equals the total anticlockwise moment about that same pivot.
Levers: These are simple machines that increase the distance from the pivot at which the force is applied, allowing a smaller force to lift a larger load (force multiplier).
Gears: Circular discs with teeth used to transmit the turning effect of a force. A smaller gear driving a larger gear increases the moment produced but reduces the speed of rotation.

Pressure and Fluids

A fluid is a substance that can flow (either a liquid or a gas).
Pressure: The force per unit area exerted on a surface. - $P = \frac{F}{A}$ - Where: - $P$ is pressure in Pascals ( $Pa$ ). - $F$ is force in Newtons ( $N$ ). - $A$ is area in square meters ( $m^2$ ).
Atmospheric Pressure: The earth's atmosphere creates pressure. It is most dense at the Earth's surface and decreases as altitude increases.
Pressure in a Liquid Column: The pressure at a certain depth depends on the height of the column above, the density of the liquid, and gravity. - $p = h \times \rho \times g$ - Where: - $p$ is pressure ( $Pa$ ). - $h$ is height (depth) of the column ( $m$ ). - $\rho$ is the density of the liquid ( $kg/m^3$ ). - $g$ is the gravitational field strength ( $9.8\,N/kg$ ).
Upthrust: When an object is submerged in a fluid, it experiences a higher pressure on its bottom surface than on its top surface, creating a resultant force upwards. This force is equal to the weight of the fluid displaced.

Speed, Velocity, and Acceleration

Speed: The distance traveled in a set amount of time ( $v = s / t$ ). Regular speeds include walking ( $\approx 1.5\,m/s$ ), running ( $\approx 3\,m/s$ ), and cycling ( $\approx 6\,m/s$ ).
Velocity: Speed in a specific direction. Motion in a circle involves constant speed but constantly changing velocity because the direction is changing.
Acceleration: The rate of change of velocity. - $a = \frac{\Delta v}{t} = \frac{v - u}{t}$ - Where: - $a$ is acceleration ( $m/s^2$ ). - $v$ is final velocity ( $m/s$ ). - $u$ is initial velocity ( $m/s$ ). - $t$ is time ( $s$ ).
Uniform Acceleration: For objects accelerating at a constant rate: - $v^2 - u^2 = 2 \times a \times s$
In velocity-time graphs, the gradient represents acceleration, and the area under the graph represents the distance traveled.

Newton's Laws of Motion

Newton's First Law: If the resultant force on a stationary object is zero, it stays stationary. If the resultant force on a moving object is zero, it continues moving at the same speed and in the same direction (constant velocity).
Newton's Second Law: The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to its mass. - $F = m \times a$ - Inertia is the tendency of objects to continue in their state of rest or uniform motion.
Newton's Third Law: Whenever two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction.

Stopping Distance and Safety

Stopping Distance = Thinking Distance + Braking Distance.
Thinking Distance: The distance the vehicle travels during the driver's reaction time. Factors include: - Speed: Higher speed means more distance traveled. - Reaction time: Affected by tiredness, drugs, alcohol, and distractions.
Braking Distance: The distance the vehicle travels once the brakes are applied. Factors include: - Speed: Higher speed increases braking distance significantly ( $d \propto v^2$ ). - Weather/Road conditions: Wet or icy roads reduce friction. - Vehicle condition: Worn brakes or tires reduce the ability to stop.
Reaction Times: Typical human reaction times range from $0.2\,s$ to $0.9\,s$ .

Momentum

Momentum is a property of all moving objects with mass.
The formula for momentum is: - $p = m \times v$ - Where: - $p$ is momentum ( $kg\,m/s$ ). - $m$ is mass ( $kg$ ). - $v$ is velocity ( $m/s$ ).
Conservation of Momentum: In a closed system, the total momentum before an event (such as a collision or explosion) is equal to the total momentum after the event.
Changes in Momentum: When a force acts on a moving object, it causes a change in momentum. - $F = \frac{m \times \Delta v}{\Delta t}$
Safety features (airbags, seat belts, crumple zones) work by increasing the time over which the change in momentum occurs, thereby reducing the rate of change of momentum and the force exerted on the passengers.