a boy of mass 40 kg hanging from the horizontal branch of a tree .the tension in his arms is minimum when the angle between the arms?
Can you plz explain how it will be 0° bcz still I m Unable to understand....
To find the angle at which the tension in the arms is minimum when a boy of mass 40 kg is hanging from a horizontal branch of a tree, we need to analyze the forces acting on the boy.
When the boy is hanging, two forces are acting on him: the tension in his arms and the gravitational force pulling him downward.
We can break down the forces acting on the boy as follows:
1. Tension in the arms: This force acts vertically upward due to the arms pulling on the boy to counteract his weight.
2. Weight (gravitational force): This force acts vertically downward and is equal to the product of the boy's mass (40 kg) and the acceleration due to gravity (9.8 m/s²).
Now, let's consider the equilibrium condition. When the boy is at rest and not accelerating, the sum of the horizontal and vertical forces acting on him must be zero:
Vertical forces: Tension in the arms - Weight = 0
Since the tension in the arms is minimum when the angle between the arms is considered, we need to analyze the vertical component of the tension.
To find the vertical component, we need to resolve the weight force into its horizontal and vertical components. The vertical component of the weight force is given by:
Vertical component of the weight = Weight * sin(θ)
Where θ is the angle between the arms.
Now, let's equate the vertical component of the tension to the vertical component of the weight:
Vertical component of the tension - Vertical component of the weight = 0
Since the tension in the arms and weight have opposite directions, we need to subtract the vertical component of the weight from the vertical component of the tension to get zero:
Vertical component of the tension - (Weight * sin(θ)) = 0
Simplifying this equation, we get:
Vertical component of the tension = Weight * sin(θ)
We want to find the angle θ at which the tension in the arms is minimum. To find this angle, we need to determine when the vertical component of the tension is minimum.
Since the weight remains constant, to minimize the tension, we need to minimize the sin(θ) component. This occurs when sin(θ) is zero.
Therefore, the tension in the boy's arms is minimum when the angle between the arms is 0 degrees or 180 degrees.