further mechanics

• What are the conditions for circular motion? Force at 90º to the objects velocity AND Acting the force is always acting towards the centre of the circle
• Why does the force always have to act towards the centre for an object moving with circular motion and constant tangential velocity? If any component of the force was in line with the velocity it would increase - as it is not there's no increase in the magnitude of velocity ONLY direction
• For a car going round a banked track what force acts as the centrapetal force? The frictional force which MUST be === to the component of the weight paralell to the slope
• For a satellite orbiting earth what is = to the centrapetal force? What is = to the radius? The weight (Field strength x by the mass) is = to the centrapetal force
• What are the conditions for simple harmonic motion? The acceleration is proportional to the displacement The acceleration is in the opposite direction to the displacement
• What is meant by one oscillation? Left to right back to left again
• What is frequency when it comes to SHM? The number of oscilations per second.
• What is the time period when it comes to SHM? The time it takes to complete 1 full oscilation
• When is acceleration at a max for an object undergoing SHM? What is the 'sign' in relation to displacement? When displacement is at a max - It's opposing displacement so it's the other sign. Max right hand side (+) displacement = max acceleration but (-)
• How do you find displacement at a time t? x = ACos(2πft) Basically, Displacement is a fraction of the maximum displacement A
• How do you find Vmax and when is this so? V is max when displacement is 0 (equilibrium) So Vmax = 2πf(A)
• How do you find v at a point? V = +-(2πf)√A2-x
• Draw the grid of displacement velocity acceleration and force showing how they compare
• How would you find max displacement, A given ∆h of a simple pendulum or spring mass system? Equate mgh to 1/2mv2 at the point where there is no mgh and all Ke the V will be at a max we know that Vmax = A(2πf) so easy to find A
• How would you find total energy in a system? Find max velocity, at this point all e is Ke, so use other numbers get your answer
• How do you find tension at any point? You ADD the centrapetal force to the tension due to mg and get a nice number
• What conclusions can we draw about how amplitude relates to time period for SHM spring mass and simple pendulum systems? A is independedt of mass and length and g and k
• What is the froce that keeps an object going in a circle? A centrapetal force - always directed to the centre of a circle
• Is an object with constant speed accelerating if it's moving in a circle? YES - the object is changing direction with time hence velocity is changing with time so yes
• What is x as a function of w and t? x = Asin(wt)
• What is light damping? Damping that will decrease the amplitude but not the time period. Graph like this:
• Sketch a heavy damping give its defining features. NO oscillations Amplitude decreases slowly.
• What is critical damping? Stopping an oscilation in as short time as possible. Blue line
• What is resonance? What frequency does it have? The opposite of a resistive force - a driving force IN THE DIRECTION OF VELOCITY The same f as the natural frequency 90º out of phase with restoring force
• What is required for resonance to occour with regards to the driving force? The f of the driving force to be ≈ to natural OR a multiple of it