A body of weight 150N is supported by a thin cord attached to a point in the ceiling. Another cord is attachedto the weight and pulled horizontally until the supporting cords makes an angle of 30 degree with the vertical. Draw the diagram of the arrangement and calculate the tension in each string
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To solve this problem, we can start by drawing a diagram of the arrangement. Let's assume that the weight is represented by a rectangle and the cords are represented by lines. The weight is supported by a vertical cord attached to the ceiling, and there is another horizontal cord pulling the weight. The angle between the supporting cord and the vertical is 30 degrees.
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W (150N)--------/-----|
(Ceiling)|
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In the diagram, 'W' represents the weight of 150N, and the vertical line represents the supporting cord. The angle between the supporting cord and the vertical is 30 degrees.
Now, let's calculate the tension in each string. We'll label the tension in the supporting cord as T1 and the tension in the horizontal cord as T2.
To find the tension in the supporting cord (T1), we need to resolve the weight into its vertical and horizontal components. The vertical component of the weight is given by:
W_vertical = W * cos(angle)
Substituting the values:
W_vertical = 150N * cos(30°) = 150N * 0.866 = 129.9N
Since the weight is balanced by the tension in the supporting cord, T1 must be equal to the vertical component of the weight:
T1 = 129.9N
To find the tension in the horizontal cord (T2), we need to use the horizontal component of the weight:
W_horizontal = W * sin(angle)
Substituting the values:
W_horizontal = 150N * sin(30°) = 150N * 0.5 = 75N
Since the tension in the horizontal cord balances the horizontal component of the weight, T2 must be equal to the horizontal component of the weight:
T2 = 75N
Therefore, the tension in the supporting cord (T1) is 129.9N, and the tension in the horizontal cord (T2) is 75N.
To draw the diagram, you need to visualize the arrangement of the weight and the cords. Here is a description to help you draw it:
1. Start by drawing a vertical line to represent the ceiling or support point.
2. At the bottom of the line, draw a small circle to represent the weight. Label it as "150N."
3. From the top of the line, draw a cord slanting downwards at an angle of 30 degrees with the vertical. This will represent the first supporting cord.
4. At the end of the slanted line, draw a small circle to represent the attachment point of the first cord to the weight.
5. From the attachment point, draw a second cord horizontally towards the right side. Label this cord as "T2."
6. At the end of the horizontal line, draw a small circle to represent the attachment point of the second cord to the weight.
Now, let's calculate the tension in each string. To do this, we'll use the principles of equilibrium. The vertical component of the tension in the first cord will balance the weight, and the horizontal component of the tension in the second cord will oppose the tension in the first cord.
Given information:
Weight of the body (W) = 150N
Angle with the vertical (θ) = 30 degrees
To calculate the tension in each string, we can resolve the forces:
1. Resolve the tension in the first cord (T1):
Since the vertical component of T1 balances the weight, we have:
T1 * cos(30 degrees) = 150N
T1 = 150N / cos(30 degrees)
2. Resolve the tension in the second cord (T2):
Since the horizontal component of T1 is equal to the tension in T2, we have:
T2 = T1 * sin(30 degrees)
Now, you can substitute the value of T1 in the equation for T2 and calculate the numerical values.
Fv=150
sinTheta=fh/tensioncord
tanTheta=fh/fv