Topic 2 - Mechanics

[!#important]# 2.1 - Motion

Definitions

• Displacement: a vector, the shortest distance from the initial point to the final point
• Distance: a scalar, the total length of path travelled to get to the final point (including reversals)
• Position: the location of an object at a certain time, relative to the origin
• Velocity: the rate of change of displacement over time ()
  • m/s
• Speed: the rate of change of distance over time
• Acceleration: rate of change of velocity over time ()
  • m/s

Graphing Motion

• Position-time
  • slope of tangent = instantaneous velocity
  • stationary object = horizontal line
  • constant velocity = linear graph
  • constant acceleration = parabolic curve
• Velocity-time
  • area under curve = acceleration
  • slope of tangent = instantaneous displacement
  • stationary object = horizontal line at 0
  • constant velocity = horizontal line
  • constant acceleration = linear graph
  • non-uniform acceleration = non-linear graph
• Acceleration-time (usually rare)

Uniformly accelerated linear motion

• definition: straight line motion with constant acceleration, producing constant change in velocity in equal time intervals
• doesn’t include:
  • motion varying in magnitude (ex. pendulums)
  • non-linear motion (ex. circular)
• examples:
  • a falling object
• solving equations:
  • 
  • s = displacement
  • u = initial velocity
  • v = final velocity
  • a = acceleration (the gradient)
  • t = time
  • equations to use:

Projectile Motion

• the motion of a projectile is a composite motion formed from horizontal and vertical motion
• the components of projectile motion (horizontal & vertical) are independent and do not affect each other

Checklist

• Distinguish between distance and displacement.
• Distinguish between velocity and speed.
• Understand the meaning of acceleration.
• Understand the distinction between instantaneous velocity and average velocity.
• Know how to sketch and interpret d–t and v–t graphs.
• Know how to get the speed from a d–t graph.
• Know how to get the acceleration from a v–t graph.
• Know how to get the distance travelled from a v–t graph.
• Know that bodies falling through a fluid will eventually reach a terminal velocity.
• Know how to sketch and graph a problem in order to help solve it.
• Know how to see a projectile problem from two perspectives.
• Know how to use a suvat equation. (s, u, v, a, t)

Formulas

• see uniformly accelerated linear motion :3

End of Section 2.1

[!#important]# 2.2 - Forces

Definition

• a force has:
  • magnitude and direction (ie. is a vector)
  • an object and location on the object it acts on
  • an object that exerts the force
  • a general type
  • a physical origin
  • units: newtons,

Graphing

• free body diagram
  • simplified version of object
  • forces as vector areas, to approximate scale
  • axes for coordinates
• drawing free body diagrams:
  • if an object is on something, there is a normal force R present, equal to the force of gravity on the object

Intro to Force Types

• gravitational
  • weight:
    • the gravitational force experienced by any object
    • affected by gravitational field strength (dependent on masses and distance)
    • the product of gravitational mass and field strength
  • when one object is on another, there is a reactional normal force ( that creates net zero with the force of gravity
  • , where is the mass and is gravity (9.81 N/kg)
• frictional
  • opposes motion
  • split into two types:
    • static, when an object is at rest
    • dynamic, when an object is in motion
      • is typically less than static friction
  • caused by:
    • microscopic roughness of surfaces
    • doesn’t depend on surface area
    • increased by normal force on the surface (as interlocking increases)
      • however not necessarily proportional (as surfaces can be deformed)
    • a constant friction coefficient
      • again not necessarily true and due to deformation
  • , where is the friction coefficient (between 0 and 1) and R is the normal force
• tension
  • directed along a rope, away from its ends
• fluid drag
  • acts on an object in fluid, opposing motion
    • caused by displacement of fluid particles
  • depends on:
    • fluid density
    • drag coefficient (how easily fluid flows around the shape of the object)
    • cross-sectional area of the object
    • speed of the object
  • magnitude:
    • proportional to velocity and low smooth flow rates
    • square of velocity at turbulent flow rates

End of Section 2.2

[!#important]# 2.3 - Work, Energy, and Power

End of Section 2.3

[!#important]# 2.4 - Momentum and Impulse

End of Section 2.4