Revision Notes For Mechanics

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1
Motion at a constant acceleration
Learn these formulae:
2
2
2
2
S = ut + ½ at
v = u + at
v
= u
+ 2as
s = ½ (u + v)t
s = vt – ½ at
For each question, write down what you want and what you’ve got then choose which
formula to use.
Pulleys
To find the acceleration, resolve using f=ma for each object separately then solve the 2
equations simultaneously. Decide which way you think the objects will move and resolve in
that direction e.g.
so you get T - mg for one object and mg - T for the other.
For vehicles towing, same process applies so either resolve (f=ma) for each object and
solve simultaneously or look at the whole system as one.
Variable Acceleration
If the question has an expression for the displacement, velocity or acceleration, then need
to differentiate or integrate to move between the 3 measurements.
Differentiate
S
V
A
Remember the constant when integrating and you
Integrate
will have enough information to find it.
Objects on a Slope
Resolve parallel and perpendicular to the slope using F=MA and F=µR if friction present.
Remember if it is on the point of moving, it is limiting friction so friction is a maximum and
the forces are balanced. This means you can find µ as friction is at a maximum.
N
Remember if an extra horizontal force is
applied, the normal contact force will
Wcos
change as the new force is pushing into the
slope as well so friction will change.
Wsin
Weight
Momentum
Decide which direction you are taking as positive and stick to it.
Then find momentum before = momentum after. (momentum is conserved)
mu = mv
Remember to apply frictional force if there is one.
Projectiles
Use equations of constant acceleration from above as acceleration is only due to gravity.
Decide which way is positive and stick to it. Usually use the direction it is projected in at
first.
S = displacement so if it goes up and then comes down, s=0 on 2 occasions (e.g t=0 and
2
when it comes back down.) You will probably use s=ut + ½ at
and solve for t.
Graphs
For displacement against time:
Gradient = velocity
For velocity against time:
Gradient = acceleration
Area = displacement
To find the area can use the area of a trapezium: (Sum of the parallel sides) x height.
2
Forces from a Point
Either: 1)
Resolve vertically and horizontally then use Pythagoras to find the magnitude
of the resultant and trig for the angle.
2)
Use triangle law to combine 2 forces and find the resultant.

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