DYNAMICS Dynamics is the study of things that move, ….. And why they move.

OVERVIEW OF DYNAMICS Motion Forces Work and Energy Conservation Laws Conservation of Energy Conservation of Momentum

MOTION

Describing motion Motion can be described using Words Numbers Graphs Equations Vector diagrams

Equations V = d/t Only used for constant speed Use kinematic equations for constant acceleration v f = v i + at d = v i t + ½ at 2 V f 2 = v i 2 + 2ad d = v i +v f t 2

Vectors Displacement, velocity and acceleration are vectors quantities – have size and direction Use vector diagrams to add/subtract vector quantities – join vectors head to tail Solve using scale drawing or pythagorus and SOCATOH

A B A + B A -B A - B

Vector components Vectors can be split into vertical and horizontal components θ V V cos θ V sin θ

Relative motion The motion may have a different appearance as viewed from a different reference frame, Relative velocities are used to describe the motion of an airplane in the wind or a boat in a current.

Example V boat rel water V water rel graound V boat rel ground Boat is traveling at 4 ms -1, river is flowing at 3 ms -1 ; Calculate speed of boat relative to ground

FORCES A force is a push or pull A force affects the motion of an object It is a vector quantity Measured in Newtons

Types of Forces Non-contactContact GravityFriction ElectricSupport magnetictension

Friction A friction force tries to prevent two surfaces from moving past each other It depends on the roughness of the surfaces Moving things need a force to keep them moving because friction slows them down i.e. Work must be done to overcome friction When work is done against friction, energy is converted to heat

More Friction Friction is also needed to make something move E.g. if you wear smooth shoes on ice you will slip – friction between your foot and the ground provides the force that accelerates you forwards

Support Support force stops something falling It always acts perpendicular to the surface

Tension When something is stretched or compressed it produces tension forces

Hookes Law The more you pull something, the more it stretches Hookes Law F = -kx

Mass and Weight The mass of an object is fixed. The weight of an object is the force of gravity on the object F = m x g Since weight is a force, its SI unit is the newton e.g. Sam has a mass of 60 kg; her weight is 60 N

Adding Forces There are usually multiple forces acting on an object Use vector diagram to find the combined effect of several forces acting on an object Weight force Support force Friction force Sum of forces = 0 N i.e. forces are balanced so block does not accelerate FsFs FgFg FfFf

Newton’s Laws

Newton’s First Law An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It is a statement about inertia - objects will remain in their state of motion unless a force acts to change the motion.

Newton’s 2 nd Law A change in motion involves an acceleration Larger force  greater acceleration Larger mass  smaller acceleration

Newton’s 3 rd Law Forces always come in pairs. For every external force that acts on an object there is a force of equal magnitude but opposite direction which acts back on the object.

Torque A force can cause an object to accelerate If it does not act through the centre of mass, it can cause an object to rotate Torque is the turning effect of a force Torque = force x distance (perpendicular)

Example

Equilibrium

Momentum p = m x v Momentum is a vector quantity. The momentum of a system is the vector sum of the momenta of the objects in the system. In the absence of external forces, momentum is conserved

Collisions

When objects collide, their individual momentum will change Total momentum before the collision equals total momentum after the collision (if outside forces = 0)

Elastic Collisions Momentum and KE are conserved The car and truck collide, the car rebounds at –40 ms -1 and the truck is stationary Is this collision elastic?

Inelastic Collisions Momentum is conserved, but KE is not (i.e. some energy is converted to heat) After the car and truck collide, the car rebounds at –10ms -1 and the truck continues at –30ms -1. Is this collision elastic?

Explosions Occur when two objects move apart Forces exerted by objects are equal and opposite, so momentum is conserved Both objects are initially stationary, so initial total momentum and final total momentum are zero

Impulse Impulse = FΔt But F = ma = mΔv/Δt Thus FΔt = mΔv = change in momentum i.e. the change in momentum equals the impulse of the force Impulse is used to study the average force during collisions - mass and change in velocity are easily measured, but the force during the collision is not.

Minimising impact force If an impact stops a moving object, then the change in momentum is fixed Since FΔt = mΔv, if Δt increases, F will decrease E.g. If you jump to the ground, you bend your knees, extending the time of collision and lessening the impact force. A boxer moves away from a punch, extending the time of impact and lessening the force. Cars are made to collapse on impact, extending the time of collision and lessening the impact force.

WORK AND ENERGY Energy Work Capacity to do work Conservation of energy Types of energy Energy changes to another form/object KineticPotential e.g. gravtitational, elastic

Work Work is done when a force moves an object in the direction of the force W = F x d // (Unit: Joule) A force of 20 N pushing an object 5 m in the direction of the force does 100 joules of work.

Energy If something has energy, it can do work - it can push something and make it move. Work done on an object equals energy gained by the object e.g. If you lift a 5 kg object 2 m W = F x d = 50 x 2 = 100 J. It gains 100 J of gravitational potential energy

Types of Energy Mechanical EnergyRadiant ActiveStored SoundGravitational HeatElastic kineticChemical electrical

Energy Conservation Energy cannot be created or destroyed Energy changes from one form to another but total energy is constant

Power Power is the rate at which work is done or the rate of using energy. P = W/t(Units: Watt) If you do 100 joules of work in one second (using 100 joules of energy), the power is 100 watts

Projectile Motion A projectile is an object in free fall (i.e. the only force acting on it is gravity) If we ignore air resistance, all objects fall at the same rate of 10 ms -1 The path followed by a projectile is its trajectory

Trajectory

Projectile calculations You must separate the horizontal and vertical motion No forces act on the projectile in the horizontal direction => it travels at a constant horizontal velocity Horizontal distance travelled d H = v H x t

Calcs (cont’d) It travels with a constant acceleration vertically (+10 ms -2 down; -10 ms -2 up) If it is travelling upwards, its final vertical velocity is 0 ms -1 It is accelerating so we use the kinematic equations for vertical motion

Example A ball is thrown upwards with an initial velocity of 5 ms -1 at an angle of 30˚ to the horizontal. a) What height does the ball reach b) How long does it take to reach the highest point? c) What horizontal distance does it cover?

Circular Motion If a constant force acts on an object at right angles to its direction of motion, the object will move in a circular path e.g. swinging a mass on a string Because the direction is changing, the object’s velocity is changing i.e. it is accelerating The acceleration is towards the centre of the circle The force causing the acceleration is the centripetal force

Centripetal Acceleration The faster the object moves, the faster it changes direction => greater centripetal acceleration The smaller the radius, the faster it changes direction => greater centripetal acceleration a = v 2 /r

Centripetal Force F = m x a => F c = mv 2 /r Examples As a car turns, friction acting on the wheels of the car provides centripetal force required for circular motion.

As a bucket of water tied to a string is spun in a circle, tension in the string provides the centripetal force

As the moon orbits the Earth, the force of gravity acting upon the moon provides the centripetal force required for circular motion.