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Maths Y12 Mechanics
Maths Autumn Y12
| Question | Answer |
|---|---|
| Value of g | 9.8 in maths |
| Velocity (and other vectors) can be expressed as | Vectors |
| Variable acceleration graph on vt | Not straight line |
| Speeding up or slowing down | Getting faster backwards even if acceleration negative |
| Straight line on vt graph diagonally down through x axis. What happens at point where it crosses? | Stationary X At rest X Changing direction YES Instantaneously at rest YES |
| Stationary/at rest on vt graph | Extended time on v = 0 |
| If it takes a lower time to drive back to the start, what is the velocity? | Higher X Greater magnitude YES (or more negative) |
| Displacement time graph of train acceleration then deceleration to stop | Same gradient at end of acceleration and period of velocity after. Doesn't go negative if not going backwards. Negative acceleration has curve too. |
| How to find average speed or velocity for complex vt graph | Find the total distance (easy from area) and divide by total time. Find total displacement (positive area - negative area) and divide by total time |
| A and B 30m apart. A from rest accelerates 2ms^2 and B constant 1ms^1. Find time until collision | Draw line with A at one end and B at the other. A will have travelled x distance by the time they meet. B will have travelled 30 - x. Then use SUVAT. |
| Car accelerates at constant rate from stationary to 16ms. Maintains for T. Then decelerates at constant rate to rest. Total distance 980m and total time 72s. Find T. | Draw graph and use area of trapezium |
| 2 cars on level road. A at 20ms^-1. 60m behind, B at 4ms^-1 accelerating 2ms^-2. When level? | By the time they level, B will have travelled x, while A must have travelled an extra 60m, so x + 60 |
| (A crosses B at times 6 seconds and 10 seconds). How far ill B have travelled when it first draws level with A? | First level at t = 6 |
| If ball starts in the air and finding its max height | Add how much it's in the air |
| A project up at 25ms. B 3s later at same speed from same point. How long A in air when meet? | Answer is 4 seconds The data for the 2 suvats is identical except one has T and one has T + 3. Both have x displacement |
| How to turn velocity into acceleration | Differentiate, saying dv/dt = a = ..... |
| When integrating to go to position/velocity | The +c for position is what it is when t = 0 (initially), so is not needed for displacement just position |
| Displacement integration | Just integrate whole thing |
| Distance integration | Have to split into positive negative absoluteing each |
| Displacement | From start point not origin |
| What forces can strings/ropes exert | Only tension |
| What forces can rods exert | Both tension and thrust |
| When asked to find force/velocity/acceleration | Should give in vector form unless asked for magnitude specifically. Especially important if you were given any in vector/component form to start with |
| For every question pretty much what is the first part of working | Draw a diagram then work out the forces acting |
| How to connect newton's second and SUVAT | acceleration |
| All of SUVAT's parts except time | Are all vectors so has +ve and -ve. Don't take magnitude unless specifically asked. GIVE COLUMN VECTOR |
| Scalar form of the A of SUVAT | Magnitude of the acceleration (same style thing for force) |
| When looking at direction of movement what type of vector | You care about velocity not position |
| When can you treat separate objects as a closed system | If travelling same direction |
| Quick trick for simul equations to eliminate annoying thing like tension | Try to just add them together |
| Two pulleys attached to block on table. How to label tensions | Need diff variables: T1 and T2 etc works |
| Force not in direction of motion | Deceleration |
| 3 requirements for pulley | Light, inextensible, smooth |
| Light (rope/tow bar) meaning | Tension is the same either side of pulley |
| Inextensible meaning | Acceleration is the same for each particle |
| Smooth (pulley) | Tension is the same either side of pulley |
| 'Force between floor and man's feet' | Find reaction force acting on man counteracting weight (and accounting for acceleration) |
| Weights on pulley so one hits the ground. Find max height of the other one | Will have v when other hits ground. SUVAT. |
| What force can a tow bar exert | Thrust |
| Contact force | Combined vector of NRF and friction |
| Resistive force | Friction is one type but there are others (e.g. air res) |
| Remember with body between 2 pulleys | Still accelerating so friction acts - dont assume equilibrium |
| For avg speed and velocity, what graph? | Not vt graph - that would give acceleration |
Created by:
Pyrogearos2