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Flashcards · YPH11 · Topic 1

Mechanics and Materials flashcards

29 cards on Topic 1, subtopics 1.3 to 1.4. Pick a subtopic or study them all.

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1.3 Mechanics

The four equations of uniformly accelerated motion, and when they apply
v = u + at s = ut + ½at² v² = u² + 2as s = (u + v)t / 2 Only for uniform (constant) acceleration.
What do the gradient and the area of a velocity–time graph give?
Gradient: acceleration. Area under the line: displacement. (Gradient of a displacement–time graph: velocity.)
How do you solve a projectile problem?
Treat horizontal and vertical motion independently. Horizontal: constant velocity (no drag). Vertical: acceleration g = 9.81 m s⁻² downwards. Time links the two: find it from the vertical motion.
Velocity of a projectile at its maximum height
The vertical component is zero, but the horizontal component is unchanged, so the velocity is not zero.
Newton’s second law in its general form
Resultant force = rate of change of momentum, F = Δp/Δt. For constant mass this reduces to F = ma.
Newton’s third law
If body A exerts a force on body B, B exerts a force on A that is equal in size, opposite in direction and of the same type.
Explain how an object falling through air reaches terminal velocity
As its speed rises, drag increases until it equals the weight. The resultant force, and so the acceleration, is then zero, and the velocity is constant.
Moment of a force, and the principle of moments
Moment = F × x, where x is the perpendicular distance from the line of action of the force to the axis. In equilibrium, the sum of clockwise moments about any point = the sum of anticlockwise moments.
60 N hangs 0.8 m left of a central pivot. Where must 40 N hang on the right to balance?
40 × d = 60 × 0.8 = 48, so d = 1.2 m
Momentum, and where impulse fits
p = mv, a vector in kg m s⁻¹. Unit 1 uses conservation of linear momentum in one dimension. Impulse = FΔt = Δp (the area under a force–time graph) is Unit 4 topic 4.3.
What is conserved in elastic and in inelastic collisions?
Momentum is conserved in all collisions (no external force). Kinetic energy is conserved only in elastic collisions; in inelastic ones some becomes thermal energy, sound and deformation.
Work done by a force at an angle θ to the displacement
W = Fs cos θ. Only the component along the displacement does work, so a force perpendicular to the motion does no work.
Two expressions for power
P = W/t, and P = Fv for a force F moving its point of application at velocity v.
Core Practical 1
Determine the acceleration of a freely-falling object (g), using light gates or strobe/video photography.

1.4 Materials

Density, and upthrust
ρ = m/V. Upthrust = weight of fluid displaced = ρgV (ρ the fluid’s density, V the volume displaced).
Stokes’ law, and when it applies
F = 6πηrv, the viscous drag on a small sphere of radius r moving at speed v. Only for small spheres at low speed in laminar flow.
Forces on a sphere falling at terminal velocity in a liquid
Weight = upthrust + viscous drag (three forces). Leaving out upthrust is the usual error.
How does viscosity change with temperature?
For liquids it decreases as temperature rises. For gases it increases.
Hooke’s law
F = kΔx: extension is proportional to the applied force, up to the limit of proportionality.
Elastic vs plastic deformation
Elastic: the material returns to its original shape when the force is removed. Plastic: the deformation is permanent.
Stress, strain and the Young modulus
stress = F/A (Pa) strain = Δx/x (no unit) E = stress/strain = Fx/(AΔx) E is a property of the material, not of the specimen.
A 2.00 m wire (area 1.5 × 10⁻⁷ m²) extends 3.0 mm under 45 N. Young modulus?
stress = 45 ÷ 1.5 × 10⁻⁷ = 3.0 × 10⁸ Pa strain = 0.0030 ÷ 2.00 = 1.5 × 10⁻³ E = 2.0 × 10¹¹ Pa
Core Practical 3: why is a long, thin wire used to find the Young modulus?
Long, so the extension is large enough to measure. Thin, so a modest load gives a large stress. Measure the diameter at several points with a micrometer.
Elastic strain energy
The area under the force–extension graph. In the linear region, E = ½FΔx.
Strong
Has a high breaking stress.
Stiff
Has a high Young modulus.
Tough
Absorbs a lot of energy before it fractures.
Brittle
Breaks with no plastic deformation (glass, for example).
Ductile
Can undergo large plastic deformation, so it can be drawn into a wire (copper, for example).

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