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TOPIC 2— MECHANICS FOUNDATIONS:

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Displacement— A measured distance in a given direction— tells us not only the distance of an object from a particular reference point, but also the direction from the reference point— is a vector.

Velocity— Is speed in a given direction, and is also a vector. Acceleration— is the rate of change of velocity in a given direction (velocity/time). The unit in SI is metres per second per second, or ms-2. Is also a vector.

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Motion can be ‘relative’, ie. taken from a different reference point. The determination of speed, and also velocity and acceleration depends on what it is measured to.

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Speed and velocity can be both ‘instantaneous’ and ‘average’ Average is the speed taken over a certain time period, but Instantaneous is the speed taken at a certain point: ∆s

vav =

∆t

The instantaneous speed is given as the limit of this, or the derivative.

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Both displacement-time and velocity-time can be graphed— the area under a velocitytime graph is the displacement (when both positive and negative areas are graphed).

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Linear Motion with Constant Acceleration:

There are 4 equations for this type of momentum:

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v = u + at — The definitions of accleration. If a body starts from rest then its speed after time t will be given by v = at. If its initial speed is u then this equation applies.

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s = ut + at2 — The distance travelled is the area under the speed-time graph 2

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and the body starts from rest, then s = vt2. But if the body starts from speed 2

u then we must add the area ut.

v2 = u2 + 2as

— We can eliminate the time from the last equation by

v–u

. We eventually end up with this equation.

substituting in t =

a

(u + v)

s=

t

2

Acceleration due to free fall is called the acceleration due to gravity. It is denoted g in SI, and is usually given the value 9.8 ms-2.

NOTES BY JAMES ROBERTSON, 2001

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Force and Mass:

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A force in physics is recognised by the effect or effect that it produces. It is some that can caused and object to:

• deform, ie. change its shape.

• speed up

• slow down

• change direction.

Force is a vector. A force produces an acceleration.

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Mass and Weight— weight is the gravitational force , and depends on the acceleration due to gravity.

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Newton’s First Law of Motion:

‘every object continues on a state of rest or uniform motion in a straight line unless acted upon by an external net force.’

Equilibrium follows from Newton’s First Law— that the sum of the forces is zero, which is expressed as ∑F = 0.

Static Equilibrium is like a book resting on a table, the weight of the book (due to gravity) W, is equal to the normal force the table exerts on the book, N. Dynamic Equilibrium is like a book being pulled along a table with constant velocity, gravity and the normal reaction still act, but there is now also a frictional force Ffr acting which is equal in magnitude but opposite in direction to an applied force FA.

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Newton’s Second Law of Motion:

‘The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the directio of the net force acting on the object.’ This can be summarised by the equation F = ma.

The SI unit of force is the Newton, which is the force which produces an acceleration of 1 ms-2 for a mass of 1 kg.

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Newton’s Third Law of Motion:

‘When a force acts on a particle an equal and opposite force acts on another particle somewhere in the universe.’

eg. a book on a table— table force equal to book force.

NOTES BY JAMES ROBERTSON, 2001

THIS FILE DOWNLOADED FROM THE IB NOTES SITE:

http://ibnotes.tripod.com/

Types of Forces:

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Gravitational Force— the force that gives rise to the...