# Force to Vibration

## Remember Force

• a push or a pull, just what we usually mean.
• Units Newtons. 1 N = 1 kg m s-2. I.e. 1 N will give a mass of 1 kg an acceleration of 1Â m s-2 . 1N is a gentle push.
• Takes about 10N (9.8N) to hold up 1kg.
• Takes about 9N to hold up text book.
• Takes about 700N to lift up a 70kg student(that is about 164lbs).
• NOTE: you MASS 70kg, you WEIGH 700N. Weight is a force.
• (How do you tell the difference?)
• Newtonâ€™ s First Law says that unless there is a force then a body will stay still or move at constant velocity for ever.
• Forces needed to make air move and give us sound. We will need to consider where they come from!

## Force and Pressure

• â€¢Pressure: Force/area; 1Pa = 1N/m-2 or 1Nm-2.
• â€¢The air around us exerts ~100,000Pa or about same as supporting 15lbs of weight on each square inch of your body!
• â€¢You can actually suck nearly that much but only blow about 1/6 of that.
• â€¢Lying on floor pressure about 900Pa.
• On bed of nails each nail has about 1N!
• â€¢In sound, pressure changes about 0.1Pa.

## Force of a Spring

• Springs obey Hooke's Law (Robert Hooke, 1635-1703).
• F=-k x
• F is force that spring exerts
• x is the extension, stretch from rest
• k is Spring Constant-stiffness
• - sign means force opposes motion
• if you stretch (x>0) it tries to shrink back (F<0)
• If you compress it tries to expand.
• Plot of force against extension is a straight line so call this a Linear Force
• Spring Constant is slope of line.

## Sinusoidal Motion

• Amplitude is max excursion.
• Period is time to repeat = 1/Frequency.
• Thus Frequency=1/Period
• Units are Hertz: 1 Hertz is 1 period per second
• Phase is when wave goes through zero.

## Energy.

• Types of Energy
• Kinetic Energy, Potential Energy, Heat
• Electrical & Chemical (related to PE), Sound (bit of both)
• Heat is really a kind of localized kinetic energy but common enough to treat on its own.

## Kinetic Energy

• Energy of movement
• Name from a Greek word for motion
• Energy a body has simply because of its motion.
• Kinetic Energy =Â½ m v2
• The heavier it is the more energy it has.
• The faster it goes the more energy it has.
• Energy grows MUCH faster with speed than with mass!

## Potential Energy

• Energy that an object has because of its position or state. There but not apparent.
• E.g. Gravitational P.E. = m g h.
• E.g. Spring P.E. = k x2
• k is the spring constant
• x is the extension, the amount of stretch
• the stronger the spring the more energy it has
• the further you stretch it the more energy you store.

## Spring/Mass Energy

• K.E. Â½ m v2 greatest as mass goes through equilibrium where it is going fastest.
• K.E. minimum at ends where mass is still.
• P.E. Â½ k x2 greatest at ends where spring is stretched most.
• P.E. minimum at center, where spring is un-stretched from equilib.
• So total K.E. + P.E. = Constant.
• Total energy = Max. P.E. ∝ Amplitude2.

## Energy in a Sound Wave.

• Kinetic energy is in the movements of the air.
• Air is the mass and the velocity is the air moving from high to low pressure regions.
• Potential energy is stored in the springiness of the air.
• Air in the most compressed and most expanded regions has the most P.E.
• As the wave moves the energy is carried along at the speed of sound.

## First Law of Thermodynamics

• The First Law states that the total amount of energy in a closed system is a constant.
• A closed system is one where we are careful to include all the same particles before and after the experiment.
• This is an absolute law. In centuries of searching no errors have ever been found.
• In most systems it means that the sum of the kinetic and potential energies is constant.