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Maths Y13 Mech
Maths Spring Y13
| Question | Answer |
|---|---|
| When integrating | Keep adding the +c and then removing it with proof at every stage e.g. v = something at t = 0 |
| v^2 = u^2 + 2as | Dont need in vector form - too complex to square vectors for single maths. Use the basic formulas and use i and j for simple algebra |
| Speed | Give magnitude |
| When integrating i and j coefficients | Make sure to add c1, c2, etc to both i and j at every stage, proving each of them into constants at each stage as per normal |
| r = xi + yj. What is r? | Position vector. Not the same thing as displacement. When calculating using suvat, add the displacement to the start point to get r. |
| Cartesian equations | Where r = xi + yj, where x and y are expressions in terms of t, can sometimes eliminate variable t to get a cartesian equation. 1. Find x and y equations 2. Rearrange easiest for t 3. Sub into the other equation 4. Simplify |
| Domain of x using cartesian | t can only be positive so shows what domain of x. e.g. x = t + 2, so x =< 2 |
| e.g. Find cartesian equation for path of particle r = (t^2 - 2)i + (t+1)j | x = t^2 - 2 y = t + 1 t = y - 1 x = (y-1)^2 - 2 x = y^2 - 2y - 1 |
| Range from projectile motion | The x displacement |
| Symmetry of projectile motion | Dont assume symmetry for e.g. landing angle. DRAW DIAGRAM. If starting at a weird point, add the vector position of its start point to the displacement |
| Phrasing for angle | '30 degrees above/below horizontal' |
| For v^2 suvat equation | No t, so is +- as multiple possible points can be there. Watch out for the +- |
| For force diagram questions | Give values if at all possible Add resistance, tension, etc if relevant - dont miss one Add acceleration value too if given |
| Resultant forces | Make sure they're *end-to-end* - rearrange if needed |
| When resolving perpendicular/parallel to slope | Make sure to add the perpendicular and parallel components of weight or other horizontal/vertical forces to the ones already in correct directions. Also make sure arrows going correct way to be end-to-end of resultant of weight |
| When given the bearing something is moving at and multiple times in your answer | To remove solutions, check to make sure that at both times it's moving in the correct bearing not the opposite direction. |
| Vector form of suvat | Don't need the squared one, but the rest can be done with simple algebra while keeping in vector form |
| Projectile motion not from ground reminders | Don't assume landing angle symmetry with start if it doesnt start on the ground. Add starting to displacement for max |
| Phrasing for direction | 30 degrees above/below horizontal |
| v^2 in suvat | Show as +- when relevant |
| Finding displacement between certain time when Q gives acceleration and displacement equations | Instead of integrating can just find displacement at points 3, 4, 5 seconds |
| Suvat | REQUIRES CONSTANT ACCELERATION FOR THE LOVE OF GOD |
| Reminders for maths mech | 9.8 g 3 s.f. |
| Friction | Fmax = mu*R. Mas when moving or about to start. mu = coefficient of friction mu determined by combination of surfaces. 2 rough has highest. Generally between 0 and 1. above 1 sometimes. Always above 0 |
| Reaction force | Remember affected by vertical components |
| Rods | Modelled with length+mass and are rigid. Weight only acts through centre if uniform |
| Lamina | Thin sheet where thickness small compared to other dimensions |
| Moments | Fd: d is the perpendicular distance of the point to the line of action (can extend line of action). Can pivot around any point but best to eliminate a variable i.e. on a support |
| 'On the point of tilting' when on two supports | Support not acting as pivot has 0 R |
| Forces acting at 3 points A, B, C (coords and force vectors given). Find total moment about C | For each of B and A, split forces into horizontal and vertical. For each of these, work out perpendicular distance of line of action to C and assign CW vs ACW |
| Careful when working out total displacement | Careful about initial velocity Also careful when working out acceleration and the mass is 0.5kg to double the force, not halve it |
| Trying to simplify down | Keep note of the end result, so you notice if it appears for substitution when working. Also don't skip the step of expanding (i.e. show before and after) to make sure you dont miss it |
| To get rid of an arccos when integrating | Can rearrange sometimes, cosing both sides, so you can then integrate for a dx/dy unlike normal. dx/dy result can then just be ^-1 for dy/dx |
| Careful if had initial velocity to add it | |
| Doing mech where sin of angle given and exact answer needed | Do the triangle to find exact cos and tan |
| Doing complex moments (do lots of practice) | Split into vertical/horizontal distance (tracing from pivot) for each point, then horizontal/vertical for each force |
| Check if Q wants it in terms of g so can keep it simpler | |
| Negative tension on rod | Compression |
| Weight of block Q | In newtons. Not mass. |
| Friction | F =< mu*R Keep sign the correct way around Make sure if moving up slope is acting down |
| Simple calculations to find free body diagram parts | Show calculations |
| Free body diagram reaction, friction, etc | Label with 1 and 2 |
Created by:
Pyrogearos2