Physics
Physics
Problem
A small crate weighing 150 N is suspended from the ceiling by two identical light ropes that are attached to the crate’s top corners and meet the ceiling so that each rope makes an angle of 30° with the vertical. The crate is motionless. (a) Determine the magnitude of the tension in each rope. (b) If the crate’s weight is increased to 200 N while all other conditions remain the same, calculate the new tension in each rope and state whether the tension increases linearly with the weight. Explain your reasoning briefly.Intuitive explanation
The key is recognizing this as a static equilibrium problem where you must balance forces in both vertical and horizontal directions. Since the crate isn't accelerating, the upward components of tension from both ropes must sum to support the full weight, while the horizontal components must cancel each other out. Draw a clear free-body diagram and use the geometry of the 30° angles to set up your force equations—this geometry directly determines how much of each rope's tension goes toward lifting versus pulling sideways.
Intuitive explanation
The key is recognizing this as a static equilibrium problem where you must balance forces in both vertical and horizontal directions. Since the crate isn't accelerating, the upward components of tension from both ropes must sum to support the full weight, while the horizontal components must cancel each other out. Draw a clear free-body diagram and use the geometry of the 30° angles to set up your force equations—this geometry directly determines how much of each rope's tension goes toward lifting versus pulling sideways.