A body of weight 150N is supported by a thin cord attached to a point in the ceiling .another cord is attached to the weight and pulled horizontally until the supporting cord makes an angle of 30° with the vertical . Draw the diagram of the arrangement and calculate the tension in each string
Tc ceiling string, Th horizontal string
vertical components
up down
Tc cos 30 = 150
horizontal
Th = Tc sin 30
so
Tc = 150 / .866
Th =half of that
Physics
To draw the diagram of the arrangement, we can use simple known symbols. Let's represent the weight as a rectangle pointing downwards, the supporting cord as a vertical line attached to the weight, and the pulling cord as a horizontal line attached to the weight. The point where the supporting cord is attached to the ceiling can be represented as a dot above the weight.
Here's a simple diagram of the arrangement:
|
|
|
----------
| |
| 150N |
| |
| |
----------------------- <- Ceiling
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|
|
|
Now, let's calculate the tension in each string. To do this, we'll need to resolve the forces acting on the weight.
1. Resolution of forces along the vertical axis:
First, let's find the vertical component of the tension in the supporting cord. Since the weight is being supported by this cord, its vertical component should balance the weight.
Tension in the supporting cord (vertical component) = Weight
Tension in the supporting cord (vertical component) = 150N
2. Resolution of forces along the horizontal axis:
Next, let's find the horizontal component of the tension in the supporting cord. This component can be determined using trigonometry. The angle between the supporting cord and the vertical is given as 30°.
Horizontal component of the tension in the supporting cord = Tension in the supporting cord * cos(angle)
Horizontal component of the tension in the supporting cord = 150N * cos(30°)
Horizontal component of the tension in the supporting cord ≈ 129.9N
Since the horizontal component of the tension in the supporting cord should be equal to the tension in the pulling cord, we can conclude:
Tension in the supporting cord = 129.9N
Tension in the pulling cord = 129.9N
Therefore, the tension in the supporting cord is 150N (vertical component) and 129.9N (horizontal component), while the tension in the pulling cord is 129.9N.