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.

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.

To solve this problem, we'll need to use the principles of equilibrium for a system of weights and strings. We'll start by analyzing the forces acting on each weight and rod.

Let's denote the tension in each vertical string as T1, T2, T3, and T4, where T1 is the tension in the string supporting w1, and so on. Since the weights are in equilibrium, the sum of the vertical forces acting on each weight must be zero.

1. For weight w1:
The only vertical force acting on w1 is T1, which is equal to the weight of w1: T1 = w1 = 4.92 units of weight.

2. For weight w2:
There are two vertical forces acting on w2 — T2 pulling upwards and T3 pulling downwards. The sum of these forces must be zero: T2 - T3 = 0.
But we know that T2 is equal to w1: T2 = w1 = 4.92 units of weight.
Substituting this value into the equation above, we get: 4.92 - T3 = 0. Therefore, T3 = 4.92 units of weight. Hence, w2 = T3 = 4.92 units of weight.

3. For weight w3:
Similarly, the vertical forces acting on w3 are T3 pulling upwards and T4 pulling downwards. The sum of these forces must be zero: T3 - T4 = 0.
But we already know that T3 = 4.92 units of weight.
Substituting this value into the equation above, we get: 4.92 - T4 = 0. Therefore, T4 = 4.92 units of weight. Hence, w3 = T4 = 4.92 units of weight.

4. For weight w4:
The only vertical force acting on w4 is T4, which is equal to the weight of w4: T4 = w4.
Since T4 = 4.92 units of weight, we can conclude that w4 = 4.92 units of weight.

So, to summarize:
w1 = 4.92 units of weight
w2 = 4.92 units of weight
w3 = 4.92 units of weight
w4 = 4.92 units of weight