Flashcards · H556 · Topic 3

Forces and motion flashcards

43 cards on Topic 3, subtopics 3.1 to 3.5. Pick a subtopic or study them all.

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3.1 Motion

Displacement, velocity and acceleration: Displacement: straight-line distance from the start in a stated direction. Velocity: rate of change of displacement. Acceleration: rate of change of velocity, a = Δv/Δt. All are vectors.
What do the gradient and area give on s–t, v–t and a–t graphs?: s–t gradient: velocity. v–t gradient: acceleration; area: displacement. a–t area: change in velocity.
The four constant-acceleration equations: v = u + at s = ½(u + v)t s = ut + ½at² v² = u² + 2as Only for constant acceleration in a straight line.
A train slows from 30 m s⁻¹ to 12 m s⁻¹ in 360 m. Find its acceleration.: v² = u² + 2as: a = (12² − 30²) ÷ (2 × 360) = −756 ÷ 720 = −1.05 m s⁻².
Measuring g with an electromagnet and trapdoor: h = ½gt², so plot h against t²: gradient = g/2 and g = 2 × gradient. A late release from residual magnetism is a possible systematic error.
Thinking distance vs braking distance: Thinking distance = speed × reaction time, so ∝ speed. Braking distance = v²/(2a) for constant deceleration, so ∝ speed². Stopping distance = thinking + braking.
Projectile: what is constant horizontally and vertically?: Horizontal velocity is constant (no horizontal force). Vertical acceleration is g downwards. Only the time is shared between the two directions.
A ball is launched at 20 m s⁻¹ at 30° above level ground. Find its time of flight and range.: vₓ = 17.3 m s⁻¹, vᵧ = 10.0 m s⁻¹. T = 2vᵧ/g = 2 × 10.0 ÷ 9.81 = 2.04 s. Range = 17.3 × 2.04 ≈ 35 m.

3.2 Forces in action

Define the newton: The net force that gives a 1 kg mass an acceleration of 1 m s⁻². 1 N = 1 kg m s⁻².
Direction of the normal contact force, friction and upthrust: Normal contact force: perpendicular to the surface (not vertical on a slope). Friction: parallel to the surface, against the relative motion. Upthrust: upwards, from the fluid.
Explain how a falling object reaches terminal velocity in air: Weight acts down, drag up. As speed increases, drag increases, so the net force and the acceleration decrease. When drag equals weight the net force is zero and the velocity is constant.
Condition for terminal velocity in a liquid: Weight = drag + upthrust.
Moment of a force, and torque of a couple: Moment = force × perpendicular distance from the pivot to the line of action of the force. Couple: two equal, opposite, parallel forces; torque = one force × perpendicular separation of the lines.
The two conditions for equilibrium: Resultant force zero and resultant moment zero (about any point).
Three coplanar forces in equilibrium: Their lines of action meet at a point, and the force vectors form a closed triangle when drawn head to tail.
Finding the centre of gravity of an irregular lamina: Hang it freely from a pin through one hole, hang a plumb line from the same pin and draw the vertical. Repeat from a second hole. The centre of gravity is where the lines cross; a third hole is a check.
Pressure, and pressure due to a liquid: Pressure = normal force per unit area, p = F/A (Pa). In a liquid, p = hρg with h the vertical depth; add atmospheric pressure for the total.
Archimedes' principle: The upthrust on an object in a fluid equals the weight of fluid it displaces: U = ρgV.
Ice (density 920 kg m⁻³) floats in sea water (1030 kg m⁻³). What fraction is submerged?: Floating: upthrust = weight, so V_displaced/V = ρ_object/ρ_fluid = 920/1030 = 0.89, about 89%.

3.3 Work, energy and power

Define the joule: The work done when a force of 1 N moves its point of application 1 m along the line of the force.
Work done by a force at an angle: W = Fx cos θ, where θ is the angle between the force and the displacement. At 90° no work is done.
Derive Ek = ½mv²: From rest under force F: v² = 2ax, so x = v²/2a. W = Fx = ma × v²/2a = ½mv², and the work done equals the kinetic energy gained.
Derive P = Fv: P = W/t = Fx/t, and at constant speed x/t = v, so P = Fv.
A ball falls 3.0 m from rest with no air resistance. Find its speed. Does mass matter?: mgh = ½mv², so v = √(2gh) = √(2 × 9.81 × 3.0) = 7.7 m s⁻¹. The mass cancels, so no.
Efficiency, and two machines of 70% and 50% in series: Efficiency = useful output energy ÷ total input energy × 100% (never more than 100%). In series: 0.70 × 0.50 = 0.35, so 35%.
Principle of conservation of energy: The total energy of an isolated system is constant: energy is only transferred between forms. Energy against resistive forces is dissipated as thermal energy, not destroyed.

3.4 Materials

Hooke's law and the force constant: Below the limit of proportionality, F = kx: extension is proportional to force. k is force per unit extension (N m⁻¹).
Elastic vs plastic deformation: Elastic: returns to its original size and shape when the force is removed. Plastic: a permanent change in size or shape remains.
Limit of proportionality vs elastic limit: Limit of proportionality: where the force–extension graph stops being a straight line through the origin. Elastic limit: beyond it, the object no longer returns to its original size.
Tensile stress, tensile strain and ultimate tensile strength: Stress σ = F/A (Pa). Strain ε = x/L (no unit). UTS: the maximum tensile stress a material can withstand before breaking.
Young modulus: E = stress/strain = FL/(Ax), within the limit of proportionality. It is the gradient of the straight part of the stress–strain graph.
Energy stored in a stretched spring: Area under the force–extension graph. For a straight line through the origin: E = ½Fx = ½kx².
Young modulus practical: extension is plotted against force. How is E found?: The gradient is L/(EA), so E = L ÷ (A × gradient), with A = πd²/4 from the mean micrometer diameter. The diameter dominates the uncertainty: 2% in d gives 4% in A.
Stress–strain behaviour: ductile, brittle and rubber: Ductile (copper): straight, then large plastic deformation before breaking. Brittle (glass): straight almost to the end, then sudden fracture. Rubber: curved; loading and unloading curves differ; the loop is energy dissipated as heat.
Stiffness k vs Young modulus E: k depends on the sample's size; E depends only on the material. k = EA/L.

3.5 Newton's laws of motion and momentum

Newton's three laws of motion: 1. With no resultant force, a body's velocity does not change. 2. Resultant force = rate of change of momentum, in the direction of the change. 3. Forces between two bodies are equal, opposite and of the same type, acting on different bodies.
Why is F = ma a special case of Newton's second law?: F = Δp/Δt. Only for constant mass does Δp = mΔv, giving F = ma. If the mass changes, only F = Δp/Δt works.
Impulse: Force × time for which it acts, FΔt. It equals the change in momentum and the area under a force–time graph. Unit N s.
Principle of conservation of momentum: The total momentum of a system is constant provided no resultant external force acts on it.
Perfectly elastic vs inelastic collision: Perfectly elastic: total kinetic energy unchanged. Inelastic: total kinetic energy decreases. Momentum is conserved in both (closed system), and total energy is always conserved.
A 12 000 kg truck at 1.5 m s⁻¹ couples with a stationary 8000 kg truck. Common speed?: (12 000 × 1.5) ÷ 20 000 = 0.90 m s⁻¹. Kinetic energy falls from 13 500 J to 8100 J, so the collision is inelastic.
Why are the weight of a book and the push of the table not a Newton's third law pair?: They act on the same body and are different types of force. The partner of the book's weight is the book's gravitational pull on the Earth.
How do air bags and crumple zones reduce injury?: They lengthen the stopping time. The change in momentum is the same, so the average force (Δp/Δt) is smaller.