Section 7 - Further Mechanics Flashcards
What kind of force is required to keep an object moving in a circle at constant speed?
A constant centripetal force (a force applied always towards the centre of that circle)
Is an object moving in a circle at a cosntant speed accelerating and why?
Yes - the direction is always changing hence the velocity is always changing, and acceleration is defined as the rate of change in velocity
What is a radian?
The angle of a circle sector such that the radius is equal to the arc length - written in terms of π
What are the conditions for SHM?
- Acceleration must be proportional to its displacement from the equilibrium point
- It must act towards the equilibrium point
What is the small angle approximation for sinx?
sinx≈x
What is the small angle approximation for cosx?
cosx≈1-x^2/2
What does the graph for potential energy and kinetic energy against displacement for a SHM system look like?
- Potential energy - x^2 graph
- Kinetic energy - -x^2 graph
- Where the peak and trough line up
What is the definition for free vibrations?
The frequency of a system tends to vibrate at in a free vibration is called the natural frequency
What is the definition for forced vibrations?
- A driving force causes the system to vibrate at a different frequency
Define damping and explain the different types
Damping - occurs when an opposing force dissipates energy to the surroundings
* Critical damping - reduces the amplitude to zero in the quickest time
* Overdamping - when the damping force is too strong and it returns to equilibrium slowly without oscillation
* Underdamping - when the damping force is too weak and it oscillates with exponentially decreasing amplitude
What happens to a vibration with greater damping?
- The amplitude is lower at all frequencies due to greater energy losses from the system
- The resonant peak is also broader because of the damping
What are some implications of resonance in real life?
- Soldiers must break stop when crossing bridges
- Vehicles must be designed so there are no unwanted vibrations
What is the defintion of angular speed?
The angle an object has rotated through per unit time - rads^-1
What is the frequency of circular motion?
The number of complete revolutions per second (revs^-1 or Hz)
What is the time period of circular motion?
The time taken for a complete revolution
What is the restoring force in SHM?
- The force pulling or pushing the object back towards the midpoint
When does resonance happen?
When the driving frequency = the resonant frequency
What does the displacement time graph look like in SHM?
x, varies as a cosine with a maximum value, A (the amplitude)
What does a velocity time graph look like in SHM?
Reflection of sin graph in x
What does an acceleration-time graph look like in SHM?
Reflection of the cos graph in x
