Further Mechanics Flashcards
What is a cyclotron and how does it work?
A type of particle accelerator where particles start off in the centre of the accelerator, and electric and magnetic fields cause them to move in circles of increasing size
If a car is moving in a circle, which was is its velocity and acceleration directed?
- Velocity directed at a tangent to the circle
- Acceleration directed towards the centre of the circle
When a car is moving in a circle, what remains constant and what constantly changes?
- Magnitude of linear velocity remains constant
- Linear velocity constantly changes
Define Centripetal Force
The collective name for any resultant force directed towards the centre of the circle which makes an object move in a circle, often gravity or friction
Define simple harmonic motion
Acceleration is proportional to displacement in the opposite direction
Define resonance
When the driving frequency matches the natural frequency in a system, there is a rapid increase in amplitude of the wave
Define damping
The decrease in amplitude of a oscillating object over time , caused by energy lost as heat by friction
Define free oscillation
An oscillation with no external, resultant driving force
Define forced oscillation
An oscillation with an external, resultant driving force
Define potential energy
Energy that is stored, such as elastic strain energy
What are simple harmonic oscillators?
Systems which oscillate with simple harmonic motion
Give the 2 common types of SHO
- Masses on springs
- Pendulums
Describe how a mass on a spring works
- When the mass is pushed or pulled either side of the equilibrium position, there is a restoring force that is exerted on it.
- The size and direction of this force are given by Hooke’s Law.
In a mass-spring system, what is the relationship that the time period squared has with: mass, spring constant and amplitude?
- Time period squared is proportional to the mass
- Time period squared is proportional to the inverse of the spring constant
- Time period is not affected by amplitude
Derive the simple pendulum formula
- F = ma
- acceleration is component of weight in the direction of the bob’s motion, so F = mgsinθ
-F = ma = -mgsinθ - a = -gsinθ
- Arc length(s) = rθ, so θ = s/r where r = length of string(l)
- Small angle approximation so a = -gsinθ becomes a = -gθ
- a = -gs/l
- Centripetal acceleration: a = -ω²x = -(2πf)²x , so a/x = -(2πf)²
- -a/x = -a/s = (2πf)² = g/l
- T = 2π x √l/g
In a simple pendulum, what is the relationship that the time period squared has with the: mass, length of string and amplitude
- Time period is not affected by mass
- Time period squared is proportional to the length of string
- Time period is not affected by amplitude
How does a U-tube work?
- The U- shaped tube contains water which at equilibrium, is at the same level on either side.
- When water is pushed down on one side, the other side raises the same amount
- When the pressure is released, each side water levels rise and fall
- As the water oscillates, it will exchange kinetic energy and potential energy
- At the equilibrium position, the kinetic energy is at a maximum and the potential energy will be zero
What is the equation for time period of a U-tube?
T = 2π x √L/2g
State the U-tube equation
T = 2π√L/2g
Define driving frequency
The frequency of a periodic external force which can force a system to vibrate
Give 3 examples of resonance
- A radio being tuned so that the electric circuit resonates at the same frequency as the radio station
- Glass resonating when driven by a sound wave of the right frequency
- A swing resonates if it’s driven by someone pushing at its natural frequency
What is a synonym for damping forces?
Dissipative forces
Describe the difference between light and heavy damping
- Lightly damped systems take a long time to stop oscillating, and their amplitude reduces a small amount per period
- Heavily damped systems take less time to stop oscillating, and their amplitudes get reduce a greater amount per period
Define critical damping
The amplitude is reduced in the shortest possible time
Define Overdamping
Damping which takes longer to return to equilibrium than a critically damped system
Describe the difference between the resonance peaks of light and heavy damping
- Light damping has sharp resonance peak
- Amplitude only increases dramatically when driving frequency is close to natural frequency
- Heavy damping has a flatter response
- Amplitude doesn’t increase much near the natural frequency and they aren’t as sensitive to the driving frequency
What is the condition under which the equation for the simple harmonic motion for a simple pendulum applies?
Oscillations must be of small amplitude
How do you calculate the number of oscillations needed for two pendulums with different time periods to be next in phase?
- Divide the smaller time period by the larger time period
- Multiply the answer by 100
