Mechanics

• Motion Equations and Graphs

• Combining and Resolving Vectors

• Force and Acceleration

• Gravity and Free-Body Diagrams

• Projectile Motion

• Work and Power

• Energy and Energy Conservation

Equations of Motion

For uniform accelerated motion in one dimesion

v = u + at

s = ut + ½at2

v2 = u2 + 2as

Displacement-Time Graphs

Velocity-Time Graphs

Projectile Motion• Independence of vertical and horizontal motion

of a projectile moving freely under gravity.– Vertical Force: Gravity acting downwards– Horizontal Force: Air resistance is usually neglected

Vectors and Scalars

• Scalars only have a magnitude (size)– Mass– Speed– Length– Distance– Energy

• Vectors have a magnitude and a direction– Force– Velocity– Acceleration– Displacement– Field strength

Changing the Subject of a Formula

SOH CAH TOA

Pythagoras Theorem

Resolving Vectors• Resolve a vector into two components at

right angles to each other by drawing and by calculation.

Combining Vectors• Combine two coplanar vectors at any

angle to each other by drawing, and at right angles to each other by calculation

Free-Body Force Diagrams• Draw and interpret free-body diagrams to

represent forces on a particle or on an extended but rigid body, using the concept of centre of gravity of an extended body

Centre of Gravity• The centre of gravity of an object is the

single point that you can consider the whole weight to act through

Newton’s First Law of Motion

– A body will either stay at rest or move with constant velocity unless acted upon by an external force.

Newton’s Second Law of Motion

• F=ma

• The more force the more acceleration

• The more mass, the less acceleration

• Force is directly proportional to acceleration

• Mass is inversely proportional to acceleration

Gravitational Field Strength

• Use the expressions for gravitational field strength g=F/m and weight W=mg

• Gravitational field strength has the units N/kg. On the Earth’s surface this value is 9.8 N/kg which is the same as acceleration due to gravity near the Earth’s surface

Newton’s Third Law of Motion• If an object A exerts a force on object B, then

object B exerts an equal but opposite force on object A

• If you push against a wall, the wall will push back against you, just as hard.

Newton’s Third Law of Motion• Identify pair of forces constituting an

interaction between two bodies.

Kinetic Energy (KE)• The Energy an object has when it’s moving.

Gravitational Potential Energy (GPE)

• The Energy something gains if you lift it up

Conservation of Energy• Work is done to lift an object up. This gives the object

gravitational potential energy. When the object falls back to earth the GPE gets converted almost completely to KE.

Work• W=Fs• Be able to do calculations when the force

is not along the line of motion

Power• Calculate power from the rate at which

work is done or energy transferred.

Applications of Mechanics

• Understand some applications of mechanics, for example to safety or to sports