A2 Forces and Momentum

Forces and Momentum

A2.1 Force, resultant, momentum basic

Force = push or pull causing acceleration of a body (change v/deform.(newtons: kg m s ^-2)
Adding vectors of force → resultant force
Momentum p=mv =mass x velocity,conserved

A2.2 Components of vectors

imagine you have θ and the magnitude: Fsinθ = F_x, Fcosθ = F_y

A2.3 (translational) Equilibrium

Resultant/Net force = 0, balanced → no acceleration

A2.4 Free body diagrams

Draw forces on centre of body. Body can be a block, even if it isnt. Force always attatched to something, usually considers one body at a time. Can define own x,y axes. Label forces

A2.5 Newtons first law of motion (Inertia)

A body is at rest/moving with constant velocity unless acted on by a resultant force.

A2.6. Contact vs non-contact forces

Contact require phys contact: friction, tension (spring and string) , drag, normal
Non contact: no contact: grav/electr/magnet

A2.7. Tension

taut = under tension.

the force that arises in any body when it is stretched - (pulled on from opposite sides)

Opposite to applied force. through string, rope, cable etc.

C2.8 Normal Force

Reaction force exerted by surface perp. to object resting on it: F_N = mg cosθ (θ angle of inclination). Counteracts vertical forces, needed in equilibrium/friction calculations. Always equal to “other” force.

C2.9 Weight (grav)

F_g :force due to gravity acting on objects mass: weight = W = mg (g=9.81 ms^-2).
Acts downwards to center of earth from middle of body. - non contact F

C2.10 Friction

F_f(s) Static: resists motion between stat. surfaces, matches applied force until motion starts. F_s < μ_sF_N

F_f(d) Dynamic: resists motion between moving surfaces, constant: F_d = μ_dF_N

μ_s>μ_d so F_s>F_d

A2.11 Electrostatic

Force between charged particles, can be attracting/repulsive, see later but know its NON—CONTACT

A2.12 Magnetic

exerted by magnetic field on moving charge/wire - non contact

A2.13 Buoyancy (Upthrust)

F_b = Upward force exerted by fluid on object in it; due to displacement of fluid; causes floating.

Archimedes: F_b = ρgV
(ρ=fluid density, V=displaced volume)

A2.14 Viscous Drag

Resistive force opposing motion through fluid. Increase with speed; leads to terminal velocity when F_net = 0.

Stokes law: F_d = 6πηvr

(η. =viscosity of fluid, r = radius of moving body, v = velocity of body)

When F_d = F_g ; terminal velocity.

A2.15 Elastic (restoring) force

Elastic material being stretched or compressed. F_H is opposing the applied force

F_H = kx
(k=spring constant, x=displacement from equilibrium)

A2.16 Newtons Third Law of Motion

If Body X exerts a force on body Y, body Y will exert an equal and opposite force on body X. F_ab = -F_ba.

A2.17 Newtons 2nd law of motion

F = ma = ^{change in momentum}/_t

kg m s^-2.

A2.18 Momentum and Impulse

Momentum =m x v (Ns)

Change in momentum = impulse = J

J = Ft, F = ^J/_t

A2.19 Conserving momentum

No external force = momentum always conserved.

A2.20 Collisions (→←)

Elastic: ← → (no change in E_k)
Inelastic: → —> (heaviest one directs)
Perfectly in.: → (both)

A2.21 UCM

Uniform circular motion. Always accelerating, velocity changes; speed is constant but directino is not. (centripetal) Force pointing inwards to centre of circle; cause centripetal acceleration. No work is done

A2.22 Quantities of UCM

Time period (one circle): T

Angular displacement (angle swept): θ rad

Angular velocity: ω = θ/t rad s^-1 = 2π/T = 2πf

Frequency: rev/time: f = ¹/_T

Speed: v = ωr

Arc length: s = θr

Centripetal acceleration: a = vω = v²/r - pointing to centre.

Centripetal force: F. =mv²/r = mω²r