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698550
MECHANICS 1
Description
M1 maths AQA : Particle moving in a straight line, Kinematics, Dynamics, Statics, Moments, Vectors
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davidlouisshaw1750
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davidlouisshaw1750
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Resource summary
MECHANICS 1
Particle moving in a straight line
Kinematics (motion)
Graphs
Speed - time
Distance Travelled = area under graph
Trapezium rule: Area = average parallel sides x height
A = 1/2(a+b)h
Objects meet when they have the same distance travelled
Distance - time
Acceleration - time
Constant acceleraton
Acceleration = gradient of line
In free fall: Acceleration = g (9.8 ms-2)
Ignore air resistance
SUVAT
s=displacement u=initial velocity v = final velocity a=acceleration t=time
v=u+at s=(u+v)t/2 v^2=u^2+2as s=ut+1/2at^2 s=vt-1/2at^2
State which way is positive
Dynamics (motion of bodies under action of forces)
Momentum, p
= mass x velocity
Collisions
Conservation of momentum
Momentum before = momentum after
m1u1 + m2u2 = m1v1 + m1v1 + m2v2
Impulse, I
= force x time
Impulse = area under force - time graph
= final momentum - initial momentum
=mv-mu
Newtons 3rd Law: Objects exert equal and opposite forces (and so impulse) on eachother
Newtons 2nd Law: F = mass x acceleration
Statics (bodies at rest with forces in equilibrium)
Additional forces
Weight, W
= mass x g
Due to gravity acting on an abject vertically downwards
Tension, T
Being pulled along by a string
Strings
One string: Tension equal
Two separate strings: Tension different
In-extensible
Does not change length so accelerations and velocity of two particles attached are equal
Becomes slack
No tension so change in acceleration, must resolve again
Thrust, T
Being pushed along by a rod
Rods
Uniform
Weight acts at the centre of the rod
Light
Adds no weight to the system
Straight and does not bend, all forces remain perpendicular
Normal reaction, R
Perpendicular to the surface in contact with the object
Friction, F
F = uR
Annotations:
u is Mue
In limiting equilibrium (on the point of movement), otherwise equal to or less than
Opposes the motion between two rough surfaces
Smooth
No friction
u = coefficient of friction
0 < u <1
Balanced, no overall motion, equal and opposite in any direction
Resolving Forces
Resolve in the direction of the acceleration
Then resolve perpendicular to this
R(^): R - mg
R(>): ma - uR
If static
Resolve horizontal and vertical or up plane and perpendicular to plane
At an angle
Resolve to find the component of the force that acts in the direction of motion
Component of F = Fcos0
Annotations:
0 is Theta
Resultant Force
Resolve force in perpendicular directions and then apply pythagoras
Moments
Moment about a point = Force x distance
The sum of moments
State which way is positive (clockwise or anticlockwise)
Add up the moments about a point
M(P): clockwise moments - anticlockwise moments
In equilibrium
In equilibrium the sum of moments about any point is zero
M(P) clockwise moments = anticlockwise moments
Resultant force in any direction is zero
If tilting about a point, other point support force = 0
Vectors (quantity with both magnitude and direction)
i, j notation
i is a unit vector in the x-direction j is a unit vector in the y-direction
Add terms i and j seperately
i and j either bold or underlined
Adding vectors
Triangle law of addition
AC = AB + BC
Speed
Calculated using pythagoras for i and j
Magnitude of velocity vector
Length of line = magnitude
Arrow to show direction
Equal
Same magnitude and direction
Parrallel
Same direction
Vectors involving time
r = r0 + vt
r = Position vector at time t
r0 = Original position vector at time t=0
v = Velocity vector
Bearings
From north clockwise 3 significant figures before the decimal
Objects meet when they have the same position vector at the same time
Media attachments
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