Additional notes Flashcards
Vector triangles in Circular Motion
A vector triangle can be drawn with existing velocities, to determine change in velocity represented by completing the vector triangle
Textbook figure 16.9
Newton’s thought experiment
In order to get an object into orbit it must be fired at just the correct speed else it will either go out of orbit or be pulled down by gravity
Textbook figure 16.10
Maximum displacement from equilibrium position
amplitude x₀
Displacement time graph for s.h.m
Shows period (T) and amplitude (x₀)
Velocity can be determined by gradient of graph
Textbook figure 18.7
Phase difference for waves with different frequencies
Waves with different frequencies have continuously changing phase differences
Requirements for s.h.m (3)
The three requirements for s.h.m. of a mechanical system are:
- a mass that oscillates
2. a position where the mass is in equilibrium
3. a restoring force that acts to return the mass to its equilibrium position; the restoring force F is directly proportional to the displacement x of the mass from its equilibrium position and is directed towards that point
Velocity time graph for s.h.m
where displacement is zero velocity is at a maximum (could be positive or negative)
acceleration can be determined from gradient of graph
Acceleration time graph for s.h.m
acceleration is proportional to the negative displacement which is a key idea
a ∝ - x
Acceleration displacement graph for s.h.m
gradient is -ω²
Textbook figure 18.20
Gradient and amplitude relationship for s.h.m
The gradient is independent of the amplitude of the motion. This means that the frequency for the period T of the oscillator is independent of the amplitude and so a simple harmonic oscillator keeps steady time.
Key idea behind a = -ω²x
We say that the equation a = -ω²x defines simple harmonic motion-it tells us what is required if
a body is to perform s.h.m.
The equation x = x₀ sin ωt is then described as a solution to the
equation, since it tells us how the displacement of the body varies with time
Kinetic and potential energy of an oscillator
The kinetic and potential energy of an oscillator vary periodically but the total energy remains constant if the system is undamped
Textbook figure 18.22
Kinetic and potential energy graph for s.h.m
Kinetic energy is max when displacement x = 0
Potential energy is max when displacement x = ±x₀
Total energy = Ek + Ep
(total energy is the same at any point on the graph)
Textbook figure 18.23
Amplitude and driving frequency graph
Maximum amplitude is achieved when the driving frequency equals the natural frequency of oscillation
Textbook figure 18.32
Types of damping
Damping reduces the amplitude of resonant vibrations, the heavier the damping the smaller the amplitude
Textbook figure 18.34
Critical damping is just enough to ensure that a damped system returns to equilibrium without oscillating
Textbook figure 18.35
Temperature against time graph for heating water/ice at a steady rate
The regions where the temperature does not change represent where all the energy is being used to change the state of the ice/water into water/gas (breaking bonds) and no energy is being used to change the temperature, hence the temperature stays constant
During change of state:
temperature does not change, molecules are breaking free of one another and potential energy in increasing
Between change of state:
input energy raises temperature of substance, molecules move faster and kinetic energy is increasing
Note:
takes longer or more energy to go from water to gas than from ice to water
Textbook figure 19.4
Potential energy and separation graph for atoms
The electric potential energy of atoms is negative and increases as they get further apart
Textbook figure 19.5
Changing internal energy
To increase the internal energy of a gas you can heat or compress it
Likewise its internal energy can decrease if it loses heat to its surroundings or does work on its surroundings by expanding
First law of thermodynamics; Rules and positive and negative values
Positive:
(U) internal energy increases
(q) heat added to system
(w) work done on the system
Negative:
(U) internal energy decreases
(q) heat taken away from the system
(w) work done by system
At constant volume:
No work is done ∴ ∆U = q
Not allowing heat to leave or enter system:
No heat is added or lost ∴ ∆U = W
Constant temperature:
∆U constant ∴ U = 0 ∴ q + w = 0
Key idea around thermal energy transfer
Thermal energy is transferred from a region of higher temperature to a region of lower temperature
Key idea about thermodynamic temperature scale
Thermodynamic temperatures do not depend on the property of any particular substance
Resistance thermometer (thermistor and resistance wire) and thermocouple thermometer comparison
Features:
robustness
range
size
sensitivity
linearity
remote operation
Textbook table 19.2
Graphs of Boyle’s law (2)
p ∝ 1/V
Textbook figure 20.5
Relationship between volume and temperature of gas
The volume of a gas decreases as its temperature decreases
Textbook figure 20.6