further mechanics Flashcards
what’s simple harmonic motion?
an oscillation in which the acceleration of an object is directly proportional to its displacement from its equilibrium position, and is directed towards the equilibrium
how would we draw the graphs for displacement, acceleration and velocity against time for SHM?
displacement- cosine or sine wave with a maximum value of A (amplitude)
velocity- maximum of wA, when the gradient of the displacement time graph is 0 velocity is 0
acceleration- maximum is w^2(A), when gradient of velocity time graph is a maximum, acceleration is maximum, opposite to displacement graph, inversed.
whats phase difference?
how much one wave lags behind another
what’s the phase difference for two waves in phase?
2pi radians or 0
whats the phase difference between a velocity-time graph and a displacement time graph for SHM?
1/2 pi radians
what’s the amplitude of an oscillation for SHM?
the maximum magnitude of the displacement
what happens to the type of energy in all different stages of SHM?
as the object moves towards the equilibrium position, potential energy goes to kinetic
when the object is moving away from the equilibrium position, kinetics energy transfers back to potential
at equilibrium position, potential energy is 0 and kinetic is a maximum
at maximum displacement, kinetic energy is 0 and potential energy is at a maximum
what is mechanical energy?
the sum of potential and kinetic energy
what are simple harmonic oscillators?
systems that oscillate with simple harmonic motion
what are the two types of simple harmonic oscillators that we need to know?
masses on springs and pendulums
how is a mass on a string a simple harmonic oscillator?
when the mass is pushed or pulled either side of the equilibrium position, there is a restoring force exerted on it
how can you work out the restoring force on a mass on a spring?
hooke’s law F=k x extension
or F= -k x displacement
whats the equation to work out the frequency of a mass oscillating on a spring?
f= (1/(2pi)) x squareroot (m/k)
whats the equation to work out the time period of a mass oscillating on a spring?
T= 2pi x squareroot (m/k)
investigating the mass-spring system RP7- process
attach a trolley to a spring, pull it to one side by a certain amount then let it go
the trolley will oscillate back and forth as the spring pulls and pushes it in each direction
you can measure the time period by getting a computer to plot a displacement-time graph from a data logger connected to a position sensor
what are the three variables you can investigate by using a mass-spring system?
mass, spring content, amplitude
mass-spring system with variable as mass experiment RP7
change the mass by loading the trolley with masses
T^2 against mass graph as they should be directly proportional
mass-spring system with variable as spring content experiment RP7
change the spring constant by using different combinations of springs
plot a graph T^2 against 1/k as they should be directly proportional
mass-spring system with variable as amplitude experiment RP7
change the amplitude by pulling the trolley across by different amounts
plot T against A, T should remain constant as A increases
what’s the equation to work out the acceleration for a simple pendulum?
a= -g x ø (in radians)
a= -g x (arc length/ radius)
simple pendulum experiment RP7
attach a simple pendulum to an angle sensor and computer
use to computer to plot a displacement time graph and read off time period from this
you can change one variable at a time and see what happens
should show T^2 directly proportional to length
OR
hang the pendulum from a clamp and timing the oscillations using a stopwatch, use a fiducial marker
what are other examples of demonstrating SHO other then mass-spring systems and simple pendulums?
U-tube containing some water
when at equilibrium, the levels of the water on either side of the tube are equal. when the pressure is then released, water undergoes SHO
how does a U-tube show SHO for water?
to start the SHO water is displaced at maximum displacement
period of oscillation can be found through consideration of energy
as the mater oscillated, it will exchange KE and PE
at the equilibrium position, the KE will be at a maximum and PE will be 0
what are free vibrations?
they involve no energy transfer to or from the surroundings
if free vibrations occur, what type of frequency will a mass on a spring oscillate at?
its resonance frequency/ natural frequency
what are forced vibrations?
they happen when there’s an external driving force
what is the driving frequency?
the frequency of the periodic external force that causes a system to be forced to vibrate
what happens if the driving frequency is much less than the natural frequency?
then the two waves are in phase
what happens if the driving frequency is much greater than the natural frequency?
the oscillator won’t be able to keep up- the driver will be completely out of phase with the oscillator
when is the mass-spring system resonating?
when the driving force approaches the natural frequency, the system gains more energy from the driving force and so vibrates with a rapidly increasing amplitude
at resonance, what is the phase difference between the driver and the oscillator?
90 degrees
how can you investigate the relationship between amplitude and driving frequency?
use a vibration generator to oscillate a mass-spring system, signal generator sets driving frequency, mass oscillates with very large amplitude at resonant frequency
draw a graph amplitude-driving frequency
amplitude is highest at natural frequency
what are some examples of resonance?
radio is tuned so the electric circuit resonates at the same frequency as the radio station you want to listen to
glass resonates when driven by a sound wave at the right frequency
the column of air resonates in an organ pipe, driven by the motion of air at the base. this creates a stationary wave in the pipe
a swing resonates if its driven by someone pushing it at its natural frequency
what are damping forces?
forces that dissipate the energy of the oscillator to its surroundings eg. frictional forces like air resistance
how does damping effect amplitude of oscillations?
damping reduces the amplitude of the oscillation over time, the heavier the damping the quicker the amplitude is reduced to zero (not including over damping)
what is critical damping?
reducing the amplitude in the shortest possible time
example of critical damping
car suspension systems are critically damped so they don’t oscillate but return to equilibrium as quickly as possible
what is overdamping?
they take longer to return to equilibrium than a critically damped system
what’s an example of overdamping?
some heavy doors that close down slowly, giving people time to walk through
what also effects the amplitude of oscillations in the same way as damping?
plastic deformation of ductile materials
how does the degree of damping effect the sharpness of the peak in amplitude?
lightly damped systems have a sharper peak in amplitude
what experiment can you use to demonstrate effects of damping on the resonance of a spring-mass system?
attach a flat disc to the spring mass set up with a signal and vibration generator
as the mass oscillates, air resistance on the disc acts as a damping force, reducing the amplitude of the oscillation. the larger the disc, the larger the damping force and the smaller the amplitude of oscillation of the system at resonance
what is angular speed?
the angle an object rotates through per second
how can you work out arc length with radians?
radius x angle
