mechanics for M1 and phy unit 1 notes

# mechanics for M1 and phy unit 1 notes - Modelling In...

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Modelling In mechanics, it is necessary to take a real life problem and put it in mathematical language. This process is known as modelling. Terminology When modelling, we often make assumptions to make the mathematics simpler. A particle is a body whose entire weight acts through a single point. A particle doesn’t suffer from air resistance. A lamina is a two dimensional body, it is the 2-dimensional equivalent of a particle. All of the weight acts through one plane. A body is said to be uniform if it has constant density. A body is non-uniform if the density varies throughout. A smooth surface is one which has no friction. A rough surface is one upon which friction acts. We say an object is light if it has no mass. So no weight acts on a light body. An inextensible string is a string which has a fixed length- it is impossible to stretch. A rigid body is a body which is not a point and whose shape is fixed. Acceleration The “suvat” Equations Acceleration is the rate of change of velocity of an object. where a is acceleration, v is the final velocity of the object, u is the initial velocity of the object and t is the time that has elapsed. This equation can be rearranged to give: v = u + at If s represents the displacement of the object, then: s = ½ (u + v)t

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s = ut + ½ at 2 v 2 = u 2 + 2as These equations are true if the acceleration of the body in question is constant (i.e. it doesn’t change over the time period). The units used must be consistent, and the standard units are: Acceleration: ms -2 (or m/s 2 ) Velocity: ms -1 (or m/s) Displacement: m Time: s The equation which you will need to use depends upon the question. The Acceleration due to Gravity If a body is dropped from a height, it will accelerate because of gravity. The acceleration caused by gravity is written as “g”, and is usually taken to be 9.8 ms -2 . Example A ball is dropped from the leaning tower of Pisa, at a height of 50m from the ground. The ball is dropped from rest and falls freely under gravity. How long will it be before the ball hits the ground? We know: s = 50, a = 9.8, u = 0 and we want to find t. The equation connecting these four is s = ut + ½ at 2 So 50 = 0 + ½ × 9.8 × t 2 Rearranging: t 2 = 10.20408 t = 3.19… the time taken is 3.19s (3sf) Newton's Laws of Motion Forces A force is "an influence tending to cause the motion of a body" (OED). Forces are usually represented diagrammatically as an arrow, pointing in the direction the force. For example:
Force is measured in newtons (symbol N). Newton's First Law Newton's First Law of Motion states that a body will remain at rest or will continue to move at a constant velocity, unless an external force is applied. This means that in order for the acceleration of a body to change, there must be a net

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## This note was uploaded on 04/04/2012 for the course PHY 170 taught by Professor Law during the Spring '12 term at HKU.

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mechanics for M1 and phy unit 1 notes - Modelling In...

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