1) A flying pig (wings not shown) of mass m, supported from theceiling by a string, travels at speed v -- just the right speedthat it doesn't go up or down; it travels in a horizontal circle ina plane parallel to the ground. c) On the pig at right, draw a force diagram showing the two forcesacting on the pig. Donât draw the components yet. d) One force is diagonal and one force is vertical. Which do wechoose for an axis? We'll choose horizonal/vertical. Why not choosethe string and a line perpendicular to the string? e) Given that we're choosing the radius and up/down line for ouraxis, which force needs to be resolved into components? f) Using letters only, write the force equation for the up/downaxis in terms of FT, θ, m and g (Correct answer: FtCos(θ)=mg) g) Using letters only, write the force equation for the radius axisin terms of FT, θ, m,v and r. (Correct answer:Ftsin(θ)=(mv^2/r) h) Combine them into one equation using everybody's favorite trigidentity. (No, not sin(2θ) = 2sin(θ)cos(θ).) The equation shouldread: tan(θ) = v^2/rg
1) A flying pig (wings not shown) of mass m, supported from the ceiling by a string, travels at speed v -- just the right speed that it doesn^'t go up or down; it travels in a horizontal circle in a plane parallel to the ground. c) On the pig at right, draw a force diagram showing the two forces acting on the pig. Don^?t draw the components yet. d) One force is diagonal and one force is vertical. Which do we choose for an axis? We^'ll choose horizonal/vertical. Why not choose the string and a line perpendicular to the string? e) Given that we^'re choosing the radius and up/down line for our axis, which force needs to be resolved into components? f) Using letters only, write the force equation for the up/down axis in terms of FT, theta, m and g (Correct answer: FtCos(theta)=mg) g) Using letters only, write the force equation for the radius axis in terms of FT, theta, m,v and r. (Correct answer: Ftsin(theta)=(mv^2/r) h) Combine them into one equation using everybody^'s favorite trig identity. (No, not sin(2theta) = 2sin(theta)cos(theta).) The equation should read: tan(theta) = v^2/rg
