Further Mechanics Flashcards

1
Q

What is the equation for Hooke’s law?

A

T = λx / l

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2
Q

What is the equation for energy stored in a spring?

A

E = λx² / 2l

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3
Q

What are the units of modulus of elasticity?

A

N

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4
Q

What is the equation for the final velocity and angle of a particle with initial velocity U which collides with a wall at angle α, and coefficient of restitution e.

A

Vcosβ = Ucosα
Vsinβ = eUsinα

⇒ tanβ = etanα
⇒ V = U√(e²sin²α + cos²α)

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5
Q

How can you work out the angle of deflection?

A

cosθ = (U.V) / (|U||V|)

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6
Q

What are sin(90-x), cos(90-x) and tan(90-x)?

A

sin(90-x) = cosx
cos(90-x) = sinx
tan(90-x) = cotx

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7
Q

What’s the strategy for just finding the magnitude of an impulse in a collision with a wall?

A
  • Just look at the perpendicular components of velocity before and after.
  • Remember to multiply by mass.
  • You can do mUsinα (e+1)
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8
Q

What’s the strategy for impacts on a wall of an unknown angle?

A
  • Find a unit vector Î perpendicular to the wall, in the direction of the impulse.
  • Find a unit vector W^ parallel to the wall, in the general direction of U.
  • U = (I.U)I + (W.U)W, and same for V

https://www.youtube.com/watch?v=7iZ2USrIpuE

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9
Q

How do you find e given u and v?

A

e = ∆v.v / ∆v.u

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10
Q

What do you always get wrong about the line of centres?

A

The line of centres is of course the line containing both of the circles’ centres. You always seem to think this is the line tangent to both circles.

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11
Q

What should you remember when finding a range of values for e?

A

By default, 0 ≤ e ≤ 1

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12
Q

What are important exam techniques for the mechanics paper?

A
  • Make sure you’ve worked out what you are trying to find before you start working, so you know you’re on the right track.
  • Take time to organise your work: label your variables on the diagram (speeds: v, w), and lay everything out neatly so you can retrieve old information faster and correct mistakes more easily.
  • Always put a heading above your work with the principle you are using: law of restitution, conservation of momentum (in x, y), work-energy principle.
  • Don’t rush, or you end up making silly mistakes, such as wrong direction of velocity, formula written out wrong (a = F/m!!), forgetting to multiply by e, misreading the question, using the length rather than the extension, etc.
  • Sense check for silly mistakes, e.g. ∆EPE should always be in terms of A, second velocity should have a smaller magnitude than initial, the angle should be at least similar to what is shown on the diagram.
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