An artist designs a mobile of light horizontal rods connected by vertical strings and supporting various shaped weights (see figure below). Find the magnitudes w2, w3, and w4 if w1 = 4.92 units of weight. The numerical values given in the figure all have units of length.
2 answers
hmmmmm. You have been given a tricky one I don't know good luck
I don't see the figure and the distances associated with it. So you will have to use the distances provided by your problem, but the problem can be solved using the steps below.
w1= 4.92
In Static equilibrium equations: ∑τ= 0 So… w1+w2=0; using τ= F(distance) we get
W1 *(d1) - w2*(d2)= 0. Plug in your w1 value and solve for w2¬.
(w3+w4)(d3) – (w1+w2)(d3)=0; The d3 will cancel naturally, and you will find that (w3+w4)=(w1+w2).
Next part requires substitution method. So… ∑τ=0 or w3 - w4= 0. Using τ= F(distance) we get w3(d4) - w4(d5).
Solve for w3 and get an expression like w3= w4(d5)/(d4). Plug this expression into (w3+w4) = (w1+w2) for w3.
Then solve for w4. Once you have w4, you can easily solve for w3.
w1= 4.92
In Static equilibrium equations: ∑τ= 0 So… w1+w2=0; using τ= F(distance) we get
W1 *(d1) - w2*(d2)= 0. Plug in your w1 value and solve for w2¬.
(w3+w4)(d3) – (w1+w2)(d3)=0; The d3 will cancel naturally, and you will find that (w3+w4)=(w1+w2).
Next part requires substitution method. So… ∑τ=0 or w3 - w4= 0. Using τ= F(distance) we get w3(d4) - w4(d5).
Solve for w3 and get an expression like w3= w4(d5)/(d4). Plug this expression into (w3+w4) = (w1+w2) for w3.
Then solve for w4. Once you have w4, you can easily solve for w3.