A 29 kg sign is supported by a vertical chain at each end. A strong wind blows and the chains make a 30 degree angle with the vertical. What force does each chain exert?
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To find the force exerted by each chain, we need to consider the forces acting on the sign. There are two forces involved: the weight of the sign acting downward and the tension in the chain acting upward.
Let's start by breaking down the weight of the sign into its vertical and horizontal components. The weight of the sign can be calculated by using the formula:
Weight = mass * gravity
Given that the mass of the sign is 29 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the sign:
Weight = 29 kg * 9.8 m/s^2 = 284.2 N
Now, we can calculate the vertical component of the weight by using trigonometry. The vertical component is given by:
Vertical component = Weight * sin(angle)
Angle is the angle made by the chains with the vertical, which is 30 degrees.
Vertical component = 284.2 N * sin(30°) = 142.1 N
Since the sign is in equilibrium (not accelerating in the vertical direction), the tension in each chain must be equal to the vertical component of the weight. Therefore, each chain exerts a force of 142.1 N.