Final answer:
The Principle of the Triangle of Forces states that the vector sum of two or more forces in a closed system is equal to zero. The force board experiment is a demonstration of this principle. In the given scenario, the tensions in the string and the wire can be calculated using trigonometry. Therefore, the correct answer is option a) (T_textstring = 6.4 , textN, , T_textwire = 3.2 , textN)
Step-by-step explanation:
The Principle of the Triangle of Forces states that the vector sum of two or more forces in a closed system is equal to zero. In other words, if three forces are acting on an object at equilibrium, the magnitudes and directions of the forces can be represented by the sides of a triangle.
The force board experiment is a demonstration of this principle.
In the given scenario, the body hanging from the wire is in equilibrium, which means that the net force acting on it is zero. To find the tensions in the string and the wire, we can analyze the forces involved.
The weight of the body can be split into two components: the vertical component (mg) and the horizontal component (mg tanθ), where θ is the angle between the wire and the vertical.
The tension in the string balances the vertical component of the weight, and the tension in the wire balances the horizontal component.
Using trigonometry, we can calculate the tensions as follows:
Tstring = mg cosθ = 700 g cos30°
Twire = mg sinθ = 700 g sin30°
Calculating the values, Tstring is approximately 6.4 N and Twire is approximately 3.2 N.
Therefore, the correct answer is option a) (T_textstring = 6.4 , textN, , T_textwire = 3.2 , textN)