02 mechanics by hei man kwok. 2.1 kinematics definitions displacement: distance moved in a...
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02 Mechanics
BY HEI MAN KWOK
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2.1 KINEMATICS
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Definitions
• Displacement: distance moved in a particular direction – vector; SL Unit: m; Symbol: s
• Velocity: rate of change of displacement (has a direction) – vector; SL Unit: ms¯¹; Symbol: v or u
• Speed: rate of change of distance – scalar; SL Unit: ms¯¹; Symbol: v or u
• Acceleration: rate of change of velocity (change of direction or velocity) – vector; SL Unit: ms¯²; Symbol: a
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Instantaneous vs Average
• Instantaneous: at a particular point in time • Average: taken over a period of time
Average Instanteous
Speed
Velocity
Acceleration Doesn’t exist
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Conditions of SUVAT/ Uniformly Accelerated Motion
• Acceleration must be uniform/ constant • Acceleration, velocity and displacement are all
in the same plane (same direction or opposite)
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Free-fall
• Acceleration of a body in a vacuum near the Earth’s surface has an acceleration of of free-fall
• Air resistance increases as an object free falls as the velocity increases until the force of air resistance is equal to the weight where the object reaches terminal velocity
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Sketch + label, calculate and interpret
• Distance - time • Displacement – time • Velocity – time • Acceleration – time
• Eg. Bouncing ball and free-fall
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Relative Velocity in 1D and 2D
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9.1 PROJECTILE MOTION
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2.2 FORCES AND DYNAMICS
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Weight (a type of force)
• Weight = mass x gravity • W = mg • W = mass x 9.81
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Forces
Force in Newtons (N); a vector quantity
1. Tension 2. Contact (Normal if at 90 degrees)3. Weight 4. Friction 5. Upthrust 6. Air resistance
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Determining Resultant Force
• Use sin cos tan and phytagorous if needed • Make sure the forces are only in opposite
directions before final calculation
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Newton’s First Law of Motion
• A body will remain at rest or moving with constant velocity unless acted upon by an unbalanced force
• Eg. Mass on a string, parachutist,
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Translational Equilibrium
• All forces are balanced • Center of force will not move however the
mass can rotate around the center
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Newton’s Second Law of Motion
Acceleration of a body is proportional to the force applied and inversely proportional to its mass
Rate of change of momentum of a body is directly proportional to the unbalanced force acting on the body and takes place in the same direction
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Linear Momentum and Impulse
Linear Momentum = mass x velocity ; vector quantity
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Force-time graph
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Law of Conservation of Linear Momentum
• Linear momentum is conserved (always the same) for a system of isolated bodies without any external forces acting upon the two objects
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Newton’s Third Law of Motion
If body A exerts a force on body B, then body B will be exert an equal and opposite force on body A Eg. Falling body, box at rest Gun recoiling, water cannon
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2.3 WORK, ENERGY AND POWER
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Work
• Work done = force x distance moved in the direction of the force
• If displacement is not in the direction of the force – change one of them
• Interpret a force – displacement graph
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Energy and Principle of Conversation of Energy
• Energy is the quantity that enables body A to do work on body B
• When body A does work on body B, energy is transferred from body A to body B
• (be able to describe energy transformation)• Principle of Conversation of Energy – Energy
cannot be created nor destroyed – it can only be changed and transferred from one form to another
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Kinetic Energy and Gravitational Potential Energy Kinetic Energy = energy a body has due to its movement
Gravitational Potential Energy = energy a body has due to its position above the earth
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Elastic and Inelastic Collisions
• Elastic Collisions: KE and mv (p) are conserved • Inelastic Collisions: two bodies stick tgt and
according to the law of energy conservation; wd squashing the balls = energy lost as KE
• Eg. Explosion – energy to initiate an explosion comes from the chemical energy contained in the explosive = energy gained in KE of the ball
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Power and Efficiency
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2.4 UNIFORM CIRCULAR MOTION