02 Mechanics

BY HEI MAN KWOK

2.1 KINEMATICS

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

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

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)

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

Sketch + label, calculate and interpret

• Distance - time • Displacement – time • Velocity – time • Acceleration – time

• Eg. Bouncing ball and free-fall

Relative Velocity in 1D and 2D

9.1 PROJECTILE MOTION

2.2 FORCES AND DYNAMICS

Weight (a type of force)

• Weight = mass x gravity • W = mg • W = mass x 9.81

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

Determining Resultant Force

• Use sin cos tan and phytagorous if needed • Make sure the forces are only in opposite

directions before final calculation

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,

Translational Equilibrium

• All forces are balanced • Center of force will not move however the

mass can rotate around the center

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

Linear Momentum and Impulse

Linear Momentum = mass x velocity ; vector quantity

Force-time graph

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

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

2.3 WORK, ENERGY AND POWER

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

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

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

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

Power and Efficiency

2.4 UNIFORM CIRCULAR MOTION