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: Define inverse variation

Since force \( F \) varies inversely with length \( l \), we use the formula \( F = \frac{k}{l} \), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

We know that when \( l = 24 \) inches, \( F = 240 \) pounds. Substitute these values into the formula: \( 240=\frac{k}{24} \). Solve for \( k \) by multiplying both sides by 24: \( k = 240\times24 = 5760 \).

Step3: Calculate force for \( l = 36 \) inches

Now, use the formula \( F=\frac{k}{l} \) with \( k = 5760 \) and \( l = 36 \). So, \( F=\frac{5760}{36}=160 \) pounds.

Answer:

B. 160 pounds