Physics: Vectors, Scalars, and Forces

Vectors and Scalars

• Vectors have magnitude and direction.
• Scalars have only magnitude.
  • Examples of vector quantities include displacement, velocity, and acceleration.
  • Examples of scalar quantities include distance, speed, and time.
  • Displacement and distance are related, as velocity and speed are related, because removing direction from velocity leaves speed, and removing direction from displacement leaves distance.

Forces

• Contact forces are forces that need to be in contact with the object to have an effect.
  • Examples of contact forces are friction, air resistance, and the normal contact force.
• Non-contact forces do not require contact.
  • Examples of non-contact forces are magnetic, gravitational, and electrostatic forces.

Key Equations

• Weight is a force that acts on a mass due to gravity.
  • Weight (N) = Mass (kg) x Gravity (N/kg).
• Acceleration is the rate of change of velocity over time.
  • Acceleration (m/s²) = (Final velocity (m/s) - Initial velocity (m/s)) / Time (s).
• Work Done is the amount of energy transferred when a force causes a displacement.
  • Work Done (Nm) = Force (N) x Displacement (m)
• Momentum is the product of its mass and velocity.
  • Momentum (kg m/s) = Mass (kg) x Velocity (m/s)

Resultant Forces

• Free body diagrams are used to show all the forces acting on an object.
• Newton's Third Law states that every force has an equal and opposite force.
• The resultant force is the overall force acting on an object.
  • It is found by combining all individual forces acting on an object.
  • To find the resultant force, subtract the forces acting in opposite directions.

Elasticity

• Force versus extension graphs show the relationship between the force applied to a material and its extension.
• The limit of proportionality is the point on the graph where the material no longer obeys Hooke’s Law, and the extension is no longer proportional to the force applied.
• Materials are elastic if they return to their original shape after the force is removed.
• Materials are inelastic or plastic if they are permanently deformed.
• Force (N) = Spring constant (N/m) x Extension (m)
  • The spring constant is the gradient of the straight line on a force versus extension graph.

Distance and Velocity Time Graphs

• Distance-time graphs and velocity-time graphs are used to describe the motion of an object.
• The gradient of a distance-time graph is the speed of the object.
• The area under a velocity-time graph represents the distance traveled by an object.
• The gradient of a velocity-time graph represents the acceleration of the object.

Newton's Laws of Motion

• Newton's First Law states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity, unless acted upon by a net force.
• Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object's mass.
• Newton's Third Law states that for every action, there is an equal and opposite reaction.

Explore the fundamental concepts of vectors and scalars in physics, including their definitions, examples, and relationships. Additionally, discover the difference between contact and non-contact forces, along with key equations related to weight and acceleration.