Question

A body of mass 700 g hangs from the end of a long wire fixed to a high tree. A horizontal string attached to the body pulls it until the wire is 300 to the vertical. Find the tension in both the string and the wire.

Answer 1

To determine the tension in the string and wire with a body of mass 700g being pulled horizontally, we use static equilibrium principles and balance equations considering the vertical and horizontal components of the forces. The wire tension is calculated by balancing the vertical forces, and the string tension by balancing the horizontal components of the wire tension.

Step-by-step explanation:

To find the tension in both the string and the wire when a body of mass 700 g hangs from a wire and is pulled horizontally, we can apply principles of static equilibrium.

Since the body is at rest, the sum of forces in any direction must equal zero. In the vertical direction, the tension in the wire must balance the weight of the body, while in the horizontal direction, the tension in the string must balance the horizontal component of the wire tension.

Let Tw be the tension in the wire and Ts be the tension in the string. The body's weight (W) is the mass (700 g or 0.7 kg) times the acceleration due to gravity (g, approximately 9.8 m/s2).

For the vertical balance: Twcos(30°) = W,
which gives us Tw = W / cos(30°).

For the horizontal balance: Ts = Twsin(30°).

After finding Tw, it can be substituted into the second equation to find Ts.