ACT (Enhanced)MathematicsEasy
A civil engineer is calculating the stress on a support beam. The stress (S) is directly proportional to the applied load (L). If a load of 500 N produces a stress of 20 MPa, what stress will a load of 750 N produce?
- A25 MPa
- B30 MPa
- C35 MPa
- D15 MPa
Show answer & explanationAnswer & explanation
Correct answer: B. 30 MPa
Since stress is directly proportional to load, S = kL. First, find the constant of proportionality k using the given values (20 MPa = k * 500 N, so k = 20/500 = 0.04). Then, use k to find the new stress: S = 0.04 * 750 N = 30 MPa.
Why the other options are wrong
- A. Incorrect calculation, potentially from a misunderstanding of direct proportionality.
- C. Incorrect calculation.
- D. Incorrect calculation based on the proportionality constant.
Direct Proportionality
Two quantities are directly proportional if their ratio is constant. As one quantity increases, the other increases at a constant rate.
- Represented by y = kx, where k is the constant of proportionality.
- The graph is a straight line passing through the origin.
- If x doubles, y also doubles.
Memory trick: Direct means 'D'ivide and 'D'iscover the constant.