The force (in pound-force) needed to keep a car from skidding on a curve…
2023
The force (in pound-force) needed to keep a car from skidding on a curve varies directly with the weight of the car (in pounds) and the square of its speed (in miles per hour [mph]) and inversely with the radius (in feet) of the curve. Suppose 6125 pound-force is required to keep a 2750 pound car, travelling at a speed of 35 mph, from skidding on a curve of radius 550 feet. How much pound-force is then required to keep a 3600 pound car, travelling at a speed of 50 mph, from skidding on a curve of radius 750 feet?
Answer: D. 12000 — ConceptWhen a quantity varies directly with some variables and inversely with another, it equals a constant of proportionality times the direct factors…
- A.
11960
- B.
12150
- C.
12240
- D.
12000
Attempted by 78 students.
Show answer & explanation
Correct answer: D
Concept
When a quantity varies directly with some variables and inversely with another, it equals a constant of proportionality times the direct factors divided by the inverse factor. Here, if force is F, weight is W, speed is v, and radius is r, then F = kWv2/r.
Application
Use the first car to determine k: 6125 = k × 2750 × 352 / 550.
Since 352 = 1225 and (2750 × 1225) / 550 = 6125, we obtain k = 1.
Apply the same relationship to the second car: F = 1 × 3600 × 502 / 750.
Compute 502 = 2500, so F = (3600 × 2500) / 750 = 12000 pound-force.
Cross-check
Using ratios gives F2/F1 = (3600/2750) × (50/35)2 × (550/750). Multiplying this ratio by 6125 also gives 12000 pound-force, confirming the result.