Concept explainers
Law of the Lever A plank 30 ft long rests on top of a flat-roofed building, with 5 ft of the plank projecting over the edge, as shown in the figure. A worker weighing 240 lb sits on one end of the plank. What is the largest weight that can be hung on the projecting end of the plank if it is to remain in balance? (Use the law of the lever stated in Exercise 77.)
To find: The largest weight required to balance the plank.
Answer to Problem 76E
The largest weight required to balance the plank is 1200 lb.
Explanation of Solution
Given:
The length of plank is 30 ft with 5 ft of the plank projection over the edge.
The weight of worker is 240 lb sits at the end of the plank.
Formula used: Law of the lever
The product of the weight and its distance from the fulcrum must be same on each side,
Calculation:
Let the largest weight required to balance the plank be x.
Tabulate the given information into the language of algebra.
In words | In algebra |
Required weight | x |
Product of weight and distance | 5x |
Model the equation for the above information.
Simplify the above equation for x.
Thus, the largest weight required to balance the plank is 1200 lb.
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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