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Answer :
Final answer:
To determine how much spring A is stretched, one must calculate the vertical force each spring exerts due to the weight of the object, and then use Hooke's law to find the stretch. The process involves trigonometry to find the force and Hooke's law to convert that force into the spring's stretch length.
Explanation:
The student is asking how much each spring is stretched to support the weight of an object in a static equilibrium scenario involving two springs at an angle. To solve for the stretch in spring a, we must first consider the vertical component of the force that each spring must exert to balance the weight of the object.
Since the springs are identical and the object is in equilibrium, each spring will exert half of the object's weight in the vertical direction.First, we calculate the force exerted by each spring in the vertical direction using trigonometry: F = (w/2) / cos(θ). Then, we use Hooke's law, which states that F = kx, to find the stretch (x) in spring A: x = F/k. Let's solve this step by step:
Calculate the force exerted by each spring:
F = (14.4 N / 2) / cos(19.1°) = 7.2 N / cos(19.1°).
Determine the stretch in spring A using Hooke's law:
x = F/k = 7.2 N / cos(19.1°) / 39.4 N/m.
The value of cos(19.1°) needs to be computed [(approx. cos(19.1°) = 0.945)] and then the division can be done to find the stretch (x).
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