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.)
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.)
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.)
Expert Solution & Answer
To determine
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,
w1x1=w2x2
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.
w1x1=w2x2x×5=240×25
Simplify the above equation for x.
5x=6000x=60005x=1200
Thus, the largest weight required to balance the plank is 1200 lb.
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