Question

A box of mass M = 10 000 grams rests on 35° inclined plane with the horizontal. A string is used to keep the box in equilibrium. The string makes an angle of 25° with the inclined plane. What steps are needed to find magnitude of tension in string?

Answer 1

To find the magnitude of the tension in the string, you can follow these steps:

1. Draw a diagram: Sketch a diagram of the inclined plane, the box, and the forces acting on it. Label the given angles (35° and 25°) and any other relevant information.

2. Analyze the forces: Break down the weight of the box (mg) into components parallel and perpendicular to the inclined plane. The perpendicular component (mgcosθ) will balance the normal force from the inclined plane, and the parallel component (mgsinθ) will be balanced by the tension in the string.

3. Resolve the tension: Decompose the tension force into components parallel and perpendicular to the inclined plane. The perpendicular component (Tcosα) will balance the weight's perpendicular component (mgcosθ), and the parallel component (Tsinα) will balance the weight's parallel component (mgsinθ).

4. Write equilibrium equations: Establish equilibrium in the perpendicular and parallel directions separately. In the perpendicular direction, set up the equation: mgcosθ = Tcosα. In the parallel direction, set up the equation: Tsinα = mgsinθ.

5. Solve the equations: Substitute the given values (mass m = 10,000 grams = 10 kg, θ = 35°, α = 25°, g = acceleration due to gravity) into the equilibrium equations. Then solve the equations simultaneously to find the magnitude of tension, T.

6. Calculate the tension: Once you solve the equations, you will obtain the values of Tcosα and Tsinα. Use these values to find the magnitude of the tension in the string, T.

By following these steps, you should be able to find the magnitude of the tension in the string.