Question

select the correct answer. the amount of force, f, needed to lift an object using a lever varies inversely as the length, l, of the lever. when a 24 - inch lever is used a force of 240 pounds is needed. how much force is needed if a 36 - inch long lever is used? a. 120 pounds b. 160 pounds c. 252 pounds d. 360 pounds

Explanation:

Step1: Write the inverse - variation formula

Since \(F\) varies inversely as \(l\), the formula is \(F=\frac{k}{l}\), where \(k\) is the constant of variation.
When \(F = 240\) and \(l=24\), we substitute into the formula: \(240=\frac{k}{24}\).

Step2: Solve for \(k\)

Multiply both sides by \(24\): \(k = 240\times24=5760\).

Step3: Find \(F\) when \(l = 36\)

Substitute \(k = 5760\) and \(l = 36\) into \(F=\frac{k}{l}\), so \(F=\frac{5760}{36}\).
Calculate \(\frac{5760}{36}=160\).

Answer:

B. 160 pounds