Tension in a cable and pulley ``` Tension, two unequal weights m₁ and m₂ with m₁>m₂ and pulley T is tension in rope for m₁, F = m₁g – T m₁a = m₁g – T for m₂, F = T – m₂g m₂a = T – m₂g adding, g(m₁ – m₂) = a(m₁ + m₂) accel: a = g(m₁ – m₂)/(m₁ + m₂) substituting: T – m₂g = m₂a T – m₂g = m₂g(m₁ – m₂)/(m₁ + m₂) T = m₂g(m₁ – m₂)/(m₁ + m₂) + m₂g T = 2gm₁m₂/(m₁ + m₂) tension in rope from pulley to ceiling: net force is tension and is sum of two weights minus F=ma where a is net acceleeration of masses T₁ = (m₁ + m₂)g – g(m₁ + m₂)(m₁ – m₂)/(m₁ + m₂) T₁ = (m₁ + m₂)g – g(m₁ – m₂) T₁ = 2gm₂ Angled rope pulling an a box. Rope is angled θ degrees above horizontal, Friction force is F, µ is coef of friction. T = Fcosθ T = mgµcosθ Tension, two equal weights m and pulley acceleration is zero tension T = 2mg tension T₁ = 2mg Tension, one weight, m, supported by two angled ropes. rope 1 makes angle θ with vertical rope 2 makes angle φ with vertical horizontal: T₁sinθ = T₂sinφ vertical: T₁cosθ + T₂cosφ = mg (two eq in 2 unknowns, use example to solve numerically) example, θ=5º, φ=5º, mg = 100 N T₁sinθ = T₂sinφ T₁cosθ + T₂cosφ = mg T₁0.087 = T₂0.996 T₁0.996 + T₂0.087 = 100 T₁ = T₂ = 1018 N ``` Home Area, Volume Atomic Mass Black Body Radiation Boolean Algebra Calculus Capacitor Center of Mass Carnot Cycle Charge Chemistry   Elements   Reactions Circuits Complex numbers Constants Curves, lines deciBell Density Electronics Elements Flow in fluids Fourier's Law Gases Gravitation Greek Alphabet Horizon Distance Interest Magnetics Math   Trig Math, complex Maxwell's Eq's Motion Newton's Laws Octal/Hex Codes Orbital Mechanics Particles Parts, Analog IC   Digital IC   Discrete Pendulum Planets Pressure Prime Numbers Questions Radiation Refraction Relativistic Motion Resistance, Resistivity Rotation Series SI (metric) prefixes Skin Effect Specific Heat Springs Stellar magnitude Thermal Thermal Conductivity Thermal Expansion Thermodynamics Trigonometry Units, Conversions Vectors Volume, Area Water Wave Motion Wire, Cu   Al   metric Young's Modulus