Physics

A force of 16 N is required to stretch a spring a distance of 40 cm from its rest position. What force (in Newtons) is required to stretch the same spring ... a. ... twice the distance? b. ... three times the distance? c. ... one-half the distance?

32, 48, 8 As the extension, so the force. Force and stretch are proportional to one another such that if you double the force, the amount of stretch will double. If you triple the force, the amount of stretch will triple. If you half the force, the amount of stretch will halve.

Inertia

Tendency for mass to oppose acceleration

Newton's Second Law

This is the principle of Newton's Second Law: a force F on a mass m produces an acceleration a F = ma

Sound is what kind of wave?

Traveling ressure wave in the air

Relationship between frequency and period:

f = 1/T.

normal modes

overtones

Stiff Spring

A stiff spring would have a high spring constant. This is to say that it would take a relatively large amount of force to cause a little displacement.

Applied Force

An applied force is a force that is applied to an object by a person or another object. If a person is pushing a desk across the room, then there is an applied force acting upon the object. The applied force is the force exerted on the desk by the person.

Gravity

An intrinsic attractive force between any two objects that depends on the masses of the objects and the distance between them.

Forces

Applied Force, Magnetic Force, Gravitational Force, Resistance Force, Friction Force, Normal Force, Spring Force, Tension Force

Which of the following mass-spring systems will have the highest frequency of vibration? Case A: A spring with a k=300 N/m and a mass of 200 g suspended from it. Case B: A spring with a k=400 N/m and a mass of 200 g suspended from it.

Case B has the highest frequency. Frequency and period are inversely related. The highest frequency will have the shortest (smallest) period. Both springs have the same mass; only the spring constant (k) is different. A spring with a higher spring constant will have a shorter period. This is consistent with the equation for period.

ke + pe = j

Energy is conserved. So the total amount of KE + PE must be the same for each location

What is the restoring force for a pendulum?

Gravity

fundamental frequency

Lowest frequency a standing wave can support, given by f = nv/2L for strings fixed at both ends, f = nv/4L for pipes open at one end, n = 1 when pipes are closed at one end; first harmonic.

Referring to the previous question. If Mr. H wishes to have his bird feeder (and attached squirrel) vibrate with the highest possible frequency, should he use a spring with a large spring constant or a small spring constant?

Mr. H should use a spring with a large spring constant (k). Using a large spring constant (k) will cause the period to be small. A small period corresponds to a high frequency. Get them squirrels, Mr. H!

Perpetually disturbed by the habit of the backyard squirrels to raid his bird feeders, Mr. H decides to use a little physics for better living. His current plot involves equipping his bird feeder with a spring system that stretches and oscillates when the mass of a squirrel lands on the feeder. He wishes to have the highest amplitude of vibration that is possible. Should he use a spring with a large spring constant or a small spring constant?

Mr. H should use a spring with a low spring constant (k). The spring constant (k in the Hooke's law equation) is the ratio of the F/x. If this ratio is low, then there will be a relatively large displacement for any given F value. Being displaced furthest from the equilibrium position will set the spring into a relatively high amplitude vibrational motion.

Weightlessness/Orbit

Now imagine repeating the elevator exercise with the elevator descending with a continuous acceleration of g. The elevator would be falling, and you would be falling with it. Since you and the elevator have the same acceleration, there would be no force between you; you would feel no weight, everything around you would appear to be floating. You would be "weightless". But this is not the absence of mass or gravity. Gravity is still there, pulling on you and the elevator, but in this state of free fall there is no weight because the floor of the elevator is not pushing back against you. This is the situation with astronauts in orbit around the earth. The orbit is simply the ship falling toward the earth as it moves forward. The amount it falls in a given time is compensated by the curve of the earth, so it stays at the same height even though it is falling. And since everything in it is falling at the same rate, the astronauts experience weightlessness.

resonance

Occurs when the frequency of forced vibrations on an object matches the object's natural frequency, and a dramatic increase in amplitude results.

Oscillator

Restoring forces are at the root of all vibrations and oscillations. Consider a weight on a spring. If you pull the weight down, the spring pulls back but overshoots and goes into compression. Then it pushes it down but overshoots into extension, starting the whole process over again. This is a simple oscillator.

Gravitational Force

The force of gravity is the force with which the earth, moon, or other massively large object attracts another object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity that is directed "downward" towards the center of the earth. The force of gravity on earth is always equal to the weight of the object as found by the equation: Fgrav = m * g where g = 9.8 N/kg (on Earth) and m = mass (in kg)

Mass on a Spring

The mass hangs at a resting position. If the mass is pulled down, the spring is stretched. Once the mass is released, it begins to vibrate. It does the back and forth, vibrating about a fixed position. Pulling the mass to the right of its resting position stretches the spring. When released, the mass is pulled back to the left, heading towards its resting position. After passing by its resting position, the spring begins to compress. The compressions of the coiled spring result in a restoring force that again pushes rightward on the leftward moving mass.

Normal Force

The normal force is the support force exerted upon an object that is in contact with another stable object. For example, if a book is resting upon a surface, then the surface is exerting an upward force upon the book in order to support the weight of the book. On occasions, a normal force is exerted horizontally between two objects that are in contact with each other. For instance, if a person leans against a wall, the wall pushes horizontally on the person.

Restoring Force

The restoring force acts upon the vibrating object to move it back to its original equilibrium position.

Spring Force

The spring force is the force exerted by a compressed or stretched spring upon any object that is attached to it. An object that compresses or stretches a spring is always acted upon by a force that restores the object to its rest or equilibrium position. For most springs (specifically, for those that are said to obey "Hooke's Law"), the magnitude of the force is directly proportional to the amount of stretch or compression of the spring.

Atoms as Springs

Think of all the atoms bound in the floor as if they are connected to each other by small springs. Your chair is pressing on the atoms, compressing all those springs, and they are pushing back with a restoring force that balances your weight, so that the net force is zero and you do not accelerate.

Bathroom scale

We can measure the weight of a thing by measuring this force required to hold it up. This is the principle of the bathroom scale. The scale platform sits on a stiff spring. When you step on the platform, your force of gravity compresses the spring until the force is balanced. The scale measures the (small) change in the length of the spring, which from Hooke's Law is proportional to the force.

Weightlessness/Elevator

When the elevator is at rest, the scale will read your usual weight, W = mg, where m is your mass. When the elevator rises with an acceleration of g, you will be distressed to read that your weight is now m(g + g) = 2mg. If the elevator cable is cut so that the elevator falls freely with an acceleration of -g, then your weight will be m(g - g) = 0.

damping

a decrease in the amplitude of an oscillation as a result of energy being drained from the system to overcome frictional or other resistive forces.

wind instruments are based on air oscillations that:

fit between the ends of the pipe

The velocity of a wave is the product of:

frequency (wavelength)

natural frequency

fundamental frequency

overtone frequencies

harmonics

"frequency is characteristic of the oscillator" because

it depends only on the intrinsic properties of the oscillator itself, in this case the mass m of the object and the constant k of the spring. THE NATURAL FREQUENCY

In a vibrating string, amplitude determines:

loudness

periodic motion

motion that is regular and repeating

A car is coasting to the right and slowing down. Neglect air resistance. A free-body diagram for this situation looks like this:

normal, friction, gravity

timbre

particular arrangement of overtone frequencies

In a vibrating string frequency determines:

pitch

Hooke's law

the amount that the spring extends is proportional to the amount of force with which it pulls. Fspring = -k•x where Fspring is the force exerted upon the spring, x is the amount that the spring stretches relative to its relaxed position, and k is the proportionality constant, often referred to as the spring constant.

frequency

the number of oscillation per second

Standing Wave

the oscillation moves up and down in the middle, but does not move along the string

amplitude

the size of the extension

period

time of one oscillation

This standing wave has a fixed wavelength:

twice the length of the string, λ = 2L.