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Mechanics 1 ­ Revision notes

1. Kinematics in one and two dimensions

EQUATIONS FOR CONSTANT ACCELERATION ARE NOT GIVEN ­ Learn Them!

1 2 1 2
v = u + at s = ut + at s = vt ­ at
2 2
1 2 2 s : displacement…

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FREE FALL UNDER GRAVITY
Acceleration due
Assumptions
to gravity
- the body is a point mass
- air resistance can be ignored
- the motion of a body is in a vertical line
9.8 ms-2
- the acceleration due to gravity is constant Unless given in the
question
EXAMPLE…

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Vector equations ­ for constant acceleration the 5 equations involving, displacement,
velocity etc can be used
· If asked to write an equation in terms of t for displacement/ velocity etc ­ simplify
your equation as far as possible by collecting the i terms and j terms

e.g u…

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For questions involving river
Method 2 ­ Lami's theorem
crossings and current you may
need to use the cosine rule as
T1 T2 12g well as the sine rule to calculate
= =
sin 128 sin 117 sin 115 missing lengths and angles

T1 = 102 N Cosine Rule…

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Tension / Thrust ­ pulling or pushing force on the body

Friction
· Always ­ acts in a direction opposite to that in which the object is moving or
tending to move
· Smooth contact ­ friction is small enough to be ignored
· Maximum Friction (limiting friction) -…

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2nd Law F = ma Net Force = mass x acceleration

· Always work out and state Net force clearly before equating to ma
· Check - if acceleration is positive ­ net force should also be positive

Example : A taut cable 25m long is fixed at 35º…

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Finding the acceleration
Coefficient of friction = 0.2 2g ­ T = 2a Friction = 0.2R
T ­ F = 6a R = 6g so F = 11.76 N

2kg 2g ­ T = 2a
T ­ 11.76 = 6a a = 0.98 ms-2
Force on the pulley
Resultant…

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Displacement (r) : r = ut+ ½at2
2
r = Ut cosqi + (Ut sinq ­½9·8t )j



Horizontal dispalcement Height ( vertical dispalcement)
after t seconds after t seconds

To find the range

Height component = 0
Solve 2
Ut sinq ­½9·8t = 0
To find t


Substitute into…

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Modelling Assumptions

Common Terms and Meanings

Term Applies to What is disregarded
Inextensible Strings, rods Stretching
Thin Strings, rods Diameter, thickness
Light Strings, springs, rods Mass
Particle Object of negligible size Rotational motion, size
Rigid Rods Bending
Small Object of negligible size Rotational motion
Smooth Surfaces, pulleys Friction

Assumptions…

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