If the angle decreases what will happen to the tension? Please explain why.
When the angle between the two sides of an object or system decreases, the tension in the system will increase. This can be explained by considering the equilibrium of forces acting on the object.
When an object is in equilibrium, the sum of the forces acting on it is zero. When a string or rope is used to support an object, it exerts tension forces on the object in opposite directions along the string. These tension forces are equal in magnitude when the object is at rest or in equilibrium.
Now, let's imagine a simple system where an object is connected to a string that makes an angle with the horizontal. When the angle decreases, it means that the vertical component of the tension force increases. This is because the vertical component of the force that counters the gravitational force acting on the object must also increase to maintain equilibrium.
Mathematically, we can express the relationship between the angle and the tension force using trigonometry. Consider a mass 'm' connected to a string, making an angle 'θ' with the vertical. The vertical component of the tension force is given by T * cos(θ), where T represents the total tension force in the string.
As the angle θ decreases, the value of cos(θ) increases. Since the total tension force T remains constant (assuming there are no external forces involved), the vertical component of the tension force T * cos(θ) increases. As a result, the tension in the string increases.
In summary, when the angle between the two sides of an object or system decreases, the tension in the system increases because the vertical component of the tension force increases to maintain equilibrium.
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