Further Mechanics (Unit 4) Flashcards
Newton’s 1st Law
An object remains at rest or in uniform motion unless acted on by a force
Newton’s 2nd Law
The rate of change of momentum of an object is proportional to the resultant force on it
Newton’s 3rd Law
When two objects interact they exert equal and opposite forces on each other
Force (in terms of momentum change)
Force = rate of change of momentum. VECTOR
Units of momentum
kgms-1
Units of rate of change of momentum
kgms-2
Impulse, I
Force x time for which the force acts (F(delta)t)
Hence Impulse = change of momentum. VECTOR
Units of Impulse, I
Ns or kgms-1
Area under a graph of force against time
change in momentum ((delta)p) or Impulse I
Principle of conservation of linear momentum definition
In a collision (or explosion) the total momentum before equals the total momentum after, providing no external forces are acting.
Elastic collision definition
A collision where kinetic energy is conserved
Inelastic collision definition
A collision where kinetic energy is not conserved.
Note: Total Energy is still conserved.
Angular speed, w
angle turned through per second. SCALAR
Units of angular speed, w
rad s-1
Centripetal force
Resultant force acting towards the centre of the circular path
Conditions for shm (simple harmonic motion)
- acceleration is proportional to displacement
2. acceleration is in opposite direction to displacement OR acceleration always acts towards the equilibrium position.
Relating a= -(2(Pi)f)2 x, to definition of shm
- acceleration is proportional to displacement
a directly proportional to x and hence a = kx, where k is a constant (2(Pi)f)2. - acceleration is in opposite direction to displacement
minus sign indicates that acceleration, a, is in opposite direction to displacement, x.
Graph of acceleration against displacement.
Gradient = -(2(Pi)f)2
Gradient of displacement against time
Gradient of a displacement against time graph is velocity
Graphical representations linking x, v, a and t
Check Sheet
Conditions for the time period equation of a pendulum
Time Period equation for a pendulum is only true for oscillations with a small amplitude, that is, angular displacements less than 10 degrees.
Dependence of time period on amplitude of an oscillation
Time period of oscillation in SHM is independent of amplitude.
Variation of Ep and Ek with displacement
Check Sheet
Variation of Ep and Ek with time
Check Sheet
Resonance definition
When the driving frequency equals the natural frequency of an oscillating system, vibrations with large amplitude are produced
Free oscillation definition
oscillations with a constant amplitude because there are no frictional forces and hence no energy loss.
(Total energy of oscillating system remains constant).
Forced oscillation definition
oscillation due to external periodic driving force
Time Period
time taken for one complete oscillation
Frequency
number of oscillations per second
Amplitude
maximum displacement of a particle from its rest position
Damping definition
Damping is when frictional forces oppose motion, dissipating energy
(Total energy of oscillating system decreases)
Damping descriptions
Light damping : takes a long time for the amplitude to decrease to zero. System oscillates at natural frequency.
Critical damping : shortest time for amplitude to decrease to zero.
Heavy damping : takes a long time for amplitude to decrease to zero. No oscillating motion occurs.
Phase difference between driver and driven oscillations
Check Sheet
Resonance curve
Check Sheet
