Mechanics: Forces and Force Diagrams for the ESAT

Understanding Types of Force

A force is the application of a push or a pull to an object by another object. Because forces have both magnitude and direction, they are vector quantities, measured in newtons ($N$). In physics, many different types of forces arise depending on the situation.

The following table summarises the primary types of force, their causes, and the factors determining their magnitude and direction:

Type of force	Cause	Magnitude depends on	Direction
weight	mass in a gravitational field	mass, gravitational field strength	downwards
normal contact	two solid objects in contact	physical properties of contact	normal to surface of contact
drag	movement through a fluid	speed, cross-sectional area	opposite to relative motion
friction	relative sliding between solids	nature of surfaces	opposite to relative motion
magnetic	magnets or current in field	field strength, current	attraction/repulsion
electrostatic	charges in an electric field	electric field strength	like charges repel, opposites attract
upthrust	solid immersed in a fluid	weight of fluid displaced	upwards
thrust	driving force from an engine	power of engine	direction of propulsion
lift	aerofoil moving through fluid	speed, fluid density, wing shape	normal to wing
tension	stretched spring, string, or wire	extension	along the string/spring/wire

Important Distinctions

1. Avoid the word reaction: While some texts refer to normal contact force as a reaction force, this is misleading and can cause confusion with Newton's third law. Use the term normal contact force instead.

2. Resistive Forces: Both drag (such as air resistance) and friction act to oppose motion. Drag occurs through fluids (liquids or gases), while friction occurs between solid surfaces. These are often grouped together as total resistive forces.

3. Non-contact vs. Contact Forces: Most forces require physical contact. However, weight (gravitational), magnetic, and electrostatic forces can be exerted over a distance without contact. These are known as field forces.

Worked Example: Force vs. Energy

Scenario: A student claims that a football kicked along the ground comes to rest because it has transferred its energy to friction.

Explanation: This is not a precise explanation because friction is a force, not a form of energy. A better explanation is that as the ball moves, a resultant friction force acts in the opposite direction. The ball does work ($force \times distance$) against this friction force, which transfers the kinetic energy of the ball into thermal energy in the surroundings.

Drawing and Interpreting Force Diagrams

Analysing the forces acting on an object is essential for solving equilibrium and motion problems. Every force on an object is exerted by another distinct object. When drawing force diagrams, follow these rules:

1. Every force is represented by an arrow starting at the point on the object where the force acts (or can be considered to act).
2. Arrows must point away from the object in the direction the force is applied.
3. Arrows should be labelled with the type of force, the object exerting it, and its magnitude.
4. Resultant force is never added as an extra arrow. It is the combination of the existing forces, not a separate physical force.

Example 1: Aircraft in Horizontal Flight

Four main forces act on an aircraft:

• Thrust: Exerted by engines, directed forwards.
• Drag: Exerted by air, directed backwards.
• Weight: Exerted by the Earth, acting at the centre of gravity, directed downwards.
• Lift: Exerted by air on the wings, directed upwards.

Example 2: Rock Resting on the Seabed

Three vertical forces act on the rock:

• Weight: Exerted by the Earth, directed downwards.
• Normal contact force: From the seabed, directed upwards.
• Upthrust: From displaced water, directed upwards.

Worked Example: Moored Boat

Question: Draw a free body diagram for a boat moored at rest on the sea and describe the forces.

Answer: $U$ is the upthrust from the seawater (due to displaced water). $W$ is the weight of the boat caused by Earth's gravity. Since the boat is at rest, the resultant force is zero, meaning the magnitudes of $U$ and $W$ are equal.

Resultant Force in One Dimension

The resultant force is the vector sum of all forces acting on an object. It is the single value that determines whether an object accelerates or deforms. To calculate it in one dimension, subtract the total force in one direction from the total force in the opposite direction.

• If the forces in opposing directions are equal, the resultant force is zero (the forces are balanced).
• If forces act in multiple dimensions, calculate the resultant for each dimension separately.

Worked Example: Aircraft Forces

Scenario: An aircraft has a thrust ($T$) of $200\text{ kN}$, weight ($W$) of $160\text{ kN}$, lift ($L$) of $160\text{ kN}$, and drag ($D$) of $140\text{ kN}$.

Calculation:

• Horizontally: Resultant = $200\text{ kN (forward)} - 140\text{ kN (backward)} = 60\text{ kN forwards}$.
• Vertically: Resultant = $160\text{ kN (up)} - 160\text{ kN (down)} = 0$. Since the vertical forces balance, the total resultant force is $60\text{ kN}$ forwards.

Worked Example: Rock on Seabed

Scenario: A rock has a weight ($W$) of $4000\text{ N}$ and upthrust ($U$) of $1500\text{ N}$. The resultant force is zero.

Calculation: For the resultant to be zero, total upwards force must equal the downwards force ($4000\text{ N}$). Total upwards force = $Upthrust + Normal\ contact$. Therefore, $Normal\ contact = 4000\text{ N} - 1500\text{ N} = 2500\text{ N}$.

Worked Example: Firework Launch

Question: A firework of mass $0.40\text{ kg}$ is launched vertically with a thrust of $7.2\text{ N}$. What is the resultant force at launch?

Calculation:

1. Calculate Weight: $W = mg = 0.40 \times 10 = 4.0\text{ N}$.
2. Calculate Resultant: $Thrust - Weight = 7.2\text{ N} - 4.0\text{ N} = 3.2\text{ N}$ vertically upwards.