SI Units and Force Diagrams

The International System of Units (SI) is the standard for measuring physical quantities. Here are the most common SI units in mechanics:

• Length: metre (m)
• Mass: kilogram (kg)
• Time: second (s)
• Force: newton (N)
• Velocity: metres per second (m/s)
• Acceleration: metres per second squared (m/s²)

These units form the basis for most calculations in mechanics. For example, force is calculated using Newton's second law:

\[
F = ma
\]

Where \( F \) is the force in newtons (N), \( m \) is the mass in kilograms (kg), and \( a \) is the acceleration in metres per second squared (m/s²).

Force Diagrams

Force diagrams are used to show all the forces acting on an object. They help in solving problems by visualising forces, making it easier to apply Newton’s laws of motion.

Steps to Draw a Force Diagram

1. Represent the object as a simple shape, such as a box or dot.
2. Draw arrows to represent all the forces acting on the object. The length of the arrow should represent the magnitude of the force, and the direction of the arrow shows the direction of the force.
3. Label each force clearly, such as gravitational force (\( W = mg \)), tension, friction, or normal contact force.

Common Forces in Force Diagrams

• Weight (\( W \)): The force due to gravity, acting vertically downwards. It is calculated as \( W = mg \), where \( g \approx 9.8 \, \text{ms}^{-2} \).
• Normal Force: The support force exerted by a surface, acting perpendicular to the surface.
• Tension (\( T \)): The force transmitted through a string, rope, or wire when it is pulled tight by forces acting at each end.
• Friction (\( F_r \)): The force resisting the relative motion of two surfaces in contact, acting opposite to the direction of motion.

Example

For an object on a horizontal surface with friction, the forces acting on it may include:

• Weight acting vertically downwards: \( W = mg \)
• Normal reaction force acting vertically upwards
• Friction force opposing motion
• An applied force (e.g., a push or pull)

The sum of forces can be used to calculate the resulting motion using Newton's second law. For example, the horizontal net force \( F_{\text{net}} \) could be written as:

\[
F_{\text{net}} = F_{\text{applied}} - F_r
\]

This net force is then related to acceleration by:

\[
F_{\text{net}} = ma
\]

where \( a \) is the object's acceleration.