Force, Mass, and Motion Lecture Notes

Definition of Force: A force is defined as either a push or a pull exerted upon an object.
Vector Nature: Force is a vector quantity, signifying that it possesses both magnitude (size) and a specific direction of action.
Measurement Units: The standard unit for measuring force is the Newton, abbreviated as $N$ .
Common Examples of Force:
- Weight: This is the downward pull exerted by gravity on a physical body.
- Tension: This is the force currently existing within a stretched rope, cable, or string.
- Friction: A force that acts to impede or stop the motion of objects.
- Air and Water Resistance: These are specific classifications or examples of the force of friction acting within fluids (gases or liquids).

Multiple Forces: In terrestrial environments, it is rare for an internal or external object to have only a single force acting upon it. Typically, at least two forces act through the same point simultaneously.
Definition of Resultant Force: When multiple forces act on a single point, they can be calculated and combined into a single vector known as the Resultant Force.
Calculative Examples:
- Opposing Forces (Different Magnitudes): If a force of $3\,N$ acts to the left and a force of $5\,N$ acts to the right, the resultant force is calculated as $(5 - 3) = 2\,N$ to the right.
- Additive Forces: If a force of $5\,N$ and a force of $2\,N$ both act toward the left, the resultant force is $(2 + 5) = 7\,N$ to the left.
- Balanced Opposing Forces: If a force of $4\,N$ acts in one direction and another force of $4\,N$ acts in the exact opposite direction, the resultant force is $(4 - 4) = 0\,N$ (Zero).

The Relationship: Newton’s second law establishes a fundamental link between force, mass, and acceleration.
Mathematical Formula:
- $\text{Force} = \text{mass} \times \text{acceleration}$
- $F = m \times a$
Mass ( $m$ ):
- Definition: The mass of an object describes the total amount of matter it contains.
- Invariance: Mass remains unchanged regardless of the object's location in the universe.
- Units: Mass is measured in kilograms ( $kg$ ).
Acceleration ( $a$ ):
- Definition: Acceleration is the rate of change of speed with respect to time.
- Units: Acceleration is measured in $m/s^2$ or $m\,s^{-2}$ .
- Calculation: Acceleration can be determined by the formula: $a = \frac{F}{m}$ .

Gravity: This is defined as the pull exerted by a large body (such as a planet) on a significantly smaller body.
Weight ( $W$ ):
- Definition: Weight is the specific pull acting on a body caused by the force of gravity.
- Variability: Unlike mass, the weight of an object depends entirely on its location in the universe and the local gravitational strength.
Gravitational Acceleration ( $g$ ): On Earth, the gravitational pull causes an acceleration denoted as $g$ , which is approximately $9.8\,m/s^2$ .
Weight Formula:
- $\text{Weight} = \text{mass} \times \text{acceleration due to gravity}$
- $W = m \times g$
Weight Measurement: Because weight is a force, its units are Newtons ( $N$ ).
Comparative Case Study (100kg Man):
- On Earth: Where gravity $g$ is approximately $10\,m/s^2$ (or $10\,N/kg$ ), the weight is calculated as $W = 100 \times 10 = 1000\,N$ .
- On the Moon: Where gravity $g$ is approximately $1.3\,m/s^2$ (or $1.3\,N/kg$ ), the weight is calculated as $W = 100 \times 1.3 = 130\,N$ .

Centre of Gravity (CoG): This is the specific point at which the entire weight of a body is considered to be acting. It is synonymous with the centre of mass and can be determined through experimental methods.
Types of Equilibrium:
- Stable Equilibrium: A body is in stable equilibrium if it returns to its original position after a small displacement. Low centres of gravity increase stability; for instance, the wide, low shape of a racing car reduces the chance of overbalancing or falling sideways.
- Neutral Equilibrium: A body in this state has no tendency to return to its original position nor move further away when displaced. An example is a can resting on its side; displacement does not change the height of the CoG, and the vertical line from the CoG always passes through the point of contact with the surface.
- Unstable Equilibrium: An object in this state will move further away from its original position when given a small displacement, such as a bottle balanced precariously on its narrow opening.

Origins: Sir Isaac Newton was the pioneer in describing the movement of objects in the absence of external forces.
Principles of the First Law:
- If an object is stationary and no force acts upon it, it will remain stationary indefinitely.
- If an object is already in motion and no force acts upon it, it will continue to move at a steady speed in a straight line.

Friction in Practice: On Earth, vehicles come to a rest quickly because they are slowed by the force of friction.
Definition: Friction is the resistance that must be overcome when one surface moves over another.
Direction and Work: Friction always acts in the opposite direction of the intended movement and consistently opposes any attempt to perform work.
Microscopic Surface Interaction: While surfaces may look smooth to the naked eye, they are microscopically rough, consisting of "hills and valleys."
Interlocking Forces: When two surfaces attempt to move past one another, these hills and valleys interlock. The forces required to break these interlocks cause friction.
Consequences of Friction:
- Thermal Energy: The sliding of objects across each other generates heat.
- Wear and Tear: Frictional forces cause the surfaces of objects to gradually wear away.

The information presented in these materials was compiled by T. Harding, A. Lovell & D. Whitehall.