Two squirrels are sitting on a rope as shown. The tension in segment BD is TBD = 6.3 lb at an angle of ϕ = 47 degrees. The tension in segment AB is TAB = 5.229 lb. Find the weight of the squirrel at B and the angle α.
To solve this problem, we need to draw a free body diagram and use the equations of equilibrium.
First, let's draw a diagram to clarify the situation. We have two squirrels sitting on a rope, with segment AB above and segment BD below. The weight of the squirrel at B is acting downwards, and the tension in segment AB is acting upwards.
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Now, let's apply the equations of equilibrium. In the vertical direction, the sum of the forces must equal zero. We have two forces in the vertical direction: the tension in segment AB and the weight of the squirrel at B.
Tension in AB (TAB) is acting upwards, so it is positive.
Weight of squirrel at B is acting downwards, so it is negative.
Thus, the equation for the vertical equilibrium is:
TAB - Squirrel's weight = 0
Now, let's find the weight of the squirrel at B.
From the equation of equilibrium, we can say:
TAB = Squirrel's weight
Given that TAB = 5.229 lb, we can conclude that the weight of the squirrel at B is also 5.229 lb.
Now, let's find the angle α.
The angle α is formed between segment AB and the horizontal direction. We can find this angle using trigonometry.
TBD is the tension in segment BD, and ϕ is the angle between segment BD and the horizontal direction. From the given information, TBD = 6.3 lb and ϕ = 47 degrees.
We can use the equation of equilibrium in the horizontal direction:
TBD * cos(ϕ) - TBD * sin(ϕ) - TAB = 0
Substituting the given values, we get:
6.3 * cos(47) - 6.3 * sin(47) - 5.229 = 0
Now, solve this equation for α to find the angle.
Therefore, to summarize:
- The weight of the squirrel at B is 5.229 lb.
- Solve the equation 6.3 * cos(47) - 6.3 * sin(47) - 5.229 = 0 to find the angle α.