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Answer :
To solve this problem, we need to understand the concept of inverse variation. In this context, the amount of force [tex]F[/tex] needed to lift an object with a lever varies inversely with the length [tex]L[/tex] of the lever. The relationship can be expressed by the formula:
[tex]F \times L = k[/tex]
where [tex]k[/tex] is a constant.
First, we are given that when a 24-inch lever is used, a force of 240 pounds is needed. We can use this information to find the constant [tex]k[/tex]:
[tex]240 \times 24 = k[/tex]
[tex]k = 5760[/tex]
Now, we know that for any other length of the lever, the product of the force and the length must equal 5760.
We need to find the force [tex]F[/tex] required for a 36-inch lever:
[tex]F \times 36 = 5760[/tex]
To find [tex]F[/tex], divide both sides by 36:
[tex]F = \frac{5760}{36}[/tex]
[tex]F = 160[/tex]
Therefore, a force of 160 pounds is needed if a 36-inch lever is used. The correct answer is:
B. 160 pounds
This solution shows how the inverse relationship between force and lever length can be used to calculate the force required for different lever lengths.
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Answer:
B. 160 pounds
Explanation:
We can find the force with the formula:
[tex]\red{\boxed{\bf F=\dfrac{k}{L} }}[/tex]
- F = force
- k = constant of variation
- L = length
[tex]240=\dfrac{k}{24}[/tex]
[tex]k=240\times24[/tex]
[tex]\implies k=5760[/tex]
We find the force when L= 36 inches:
[tex]F=\dfrac{5760}{36}[/tex]
[tex]\implies\bf F= 160\:pounds[/tex]
