Kinematics (graphs and equations of motions) and Mechanical energy. Work/Energy Notes

explaining terminology

  • distance

    • obvious

  • displacement

    • direction and movement. Think vectors

      • definition → the length and direction of the straight line joining the start and end point of an objects motion

  • vectors → past section

  • speed

    • object in motion covers certain distance in given time. → how fast

  • Average speed

    • varies

    • average speed = total distance covered/time taken

    • m.s-1

  • instantaneous speed

    • speed at specific moment

    • average speed for a short time interval

  • velocity

    • speed is a scalar, velocity is a vector

    • velocities in pos. direction = positive

    • velocities in neg. direction = negative

    • you choose which direction is pos and neg

  • average velocity and instantaneous velocity

    • distinction, same as speed

    • when its just speed or velocity, its assumed instantaneous unless stated otherwise

  • acceleration

    • vector

    • speed and direction changes change velocity

    • motion with changing velocity = acceleration

      • def → rate of change in velocity

    • acceleration = change in velocity/time taken

    • m.s-2

    • either negative or positive

skipping ticker timer stuff, cba

Graphs of Motion

Displacement/Time (non vector would be distance/time/ All that changes is vectors become scalars)

gradient/m = velocity (think of formula)

area = nothing

v = Δx / Δt

  • v → velocity

  • x → change in displacement

  • t → change in time

increase in displacement (x) → v = + (right)

decrease in displacement (x) → v = - (left)

displacement = 0 → v = 0 (rest, direction change)

  • if acceleration is concave down its negative and vice versa (same as maths)

1) Constant velocity

2) positive acceleration

3) negative acceleration

Velocity/time (non vector is speed/time)

  • gradient/m = acceleration (think of formula)

  • area under = displacement

a = v/t = 0m.s-2

a = acceleration (m.s-2)

v = velocity (m/s)

t = time (s)

1) constant velocity

2) positive acceleration

3) negative acceleration

Acceleration time

  • gradient/m = jerk (not doing this, ignore it)

  • area under = change in velocity (vf - vi)

    • a.t = (change) v

    • vf = vi + a.t

Equations of motion

points to note

1) only apply to recticilinear motion (motion in a straight line)

2) always state a direction which is positive as all quantaties apart from time are vectors. First movement direction usually the positive

3) starting from rest or brought to rest means v = 0 m.s-1

4) velocity increasing = a is pos, velocity decreasing = a is negative

5) most problems want you to use what variables you know to find unknown

  • list known variables (i do this mentally)

  • decide on equation

  • remember to write the equation b4 substitution

  • rearrange to make unkown subject

questions

1) a body is travelling at 30 m/s is decelerated by 3 m/s. calc.

a) distance travelled

take the forward direction as positive

x = 30.8 + 1/2(-3)(8)²

= 144 m

Gravity and Mechanical energy

gravitional force

  • all options have force between them → gravity

  • size of mass and distance

  • earths surface → 10N.kg-1

acceleration due to gravity

  • speed determined by air resistance if force is same (on earth)

  • both would fall with the same downward acceleration of 9,8m.s-2 if no air resistance

    • for each second they fall, increase by 9,8m.s-2

  • therefore g → gravitional field strength (10N.kg-1) and acceleration due to gravity

weight

  • earths gravity on an object

  • Newtons

  • 1kg → 9,8N

  • greater mass = greater weight

  • mass is a measure of how many particles there are in your body, it does not change based on location

  • weight is pull of gravity on body, depends on planet

  • w = mg

    • weight = mass x g

equations of motion applied to free fall

  • expercience accelerated motion, following formulas apply

  • things to note

    • time taken to rise = time taken to fall

    • at any height, measured from point of project, upward velocity = downward velocity

    • if object falls from rest, vi = 0m/s

    • choose motion of direction as positive

      • upwards, everything is positive aprt from g which is negative

      • downward motions, all positive

work/energy notes

gravitational potential energy

  • energy stored in an object based on its vertical position

  • dependent on

    • mass of object

    • height

  • more massive = greater

  • higher = greater

equation

  • gravitational potential energy (J) = mass (m) x gravity (10 m.s-2) x height (m)

  • Ep = mgh

  • energy is measure in joules

    • scalar quantity

Kinetic energy

  • energy it has due to motion

  • all moving objects have kinetic energy (because they are moving)

  • the prerequisite is that it need to have mass and velocity for the following formulas to apply

    • kinetic energy = ½.m.v2

    • Ek = ½.m.v2

Mechanical energy

  • mechanical energy → able to do work

    • enables an object to apply force to another

  • it can be kinetic, potential (including gravitional potential) or a combination of the two

Conservation of mechanical energy

  • energy changed form → transformed. during, tot energy stays same

  • the law of conservation of energy → energy cannot be created or destroyed; it may be transformed from one form to another.

  • abscence of friction only thing considered is potential and kinetic

  • kinetic + potential = the same always (total mechanical energy)

    • total mechanical energy never exceed potential energy maximum or kinetic energy at point of impact (maximum energy)

    • you have to do calculation at top and bottom for some