PERLS104 Lecture Notes - Order Of Merit, X-Forwarded-For, If And Only If

Force F = (4.0 N)i + (-3.0 N)k acts on a pebble with positionvector r = (0.40 m)j + (-0.8k m)k , relative to the origin. What isthe resulting torque acting on the pebble about a point withcoordinates (-8.0 m, 8.0 m, -2.0 m)? Answer as a vector. I know τ =r - r₁ x F.

A newly planted tree is supported against the wind by a rope tiedtoa stake in the ground, as shown in the figure below. The forceofthe wind, though distributed over the tree, is equivalent toasingle force F, as shown in the figure. Findthetension in the rope. Assume that neither the tree's weight northeforce of the ground on the tree's roots produces anysignificanttorque about point O. (Let F = 113 N,D = 2.10 mand d = 1.12 m.)
1 N

A steel wire in a piano has a length of 0.6000 m and a mass of5.100*10^-3 kg. To what tension must this wire be stretched inorder that the fundamental vibration correspond to middle C (fC =261.6 Hz on the chromatic musical scale)?

F=?, L=0.6000 m, m=5.100*10^-3 kg, n=0.50031N whereg=9.81m/s², f_c=261.6 Hz

I honestly can not figure out where to begin. I believe this isa standing waves problem so I'm almost positive that it should usethe following equation, but I can not figure out a properderivative or manipulation of the equation to find a seeminglycorrect answer.

f_n= (n/2L)*√(F/μ) where n=the number of harmonic(1,2,3...)