A man plans to use a 2-meter crowbar to lift a rock by placing a pivot 0.8 meters from the rock. One end of the crowbar will be under the rock, and he will push down on the other end with a force of 400 N. The mass of the rock is 50 kg.
1. Will the man be able to move the rock? Show how you worked out your answer.
2. The man’s daughter says that she can move the rock although her force on the other end is only 200 N. Explain how this is possible.
Answer (3)
1. The man will be able to move the rock. See diagram. Moment of Man's force : 400 N * 1.2 meter = 480 N-m Rock's Weight = 50 Kg * 9.8 m/sec² = 490 Newtons Moment of Rock's weight : 490 N * 0.80 meters = 392 N-m Moment of Man's Force is MORE : 480 N-m > 392 N-m So man will be able to lift the rock.
Let is look at the diagram - second one. Let us assume that the fulcrum (Pivot) is placed at X meters from the rock. So moment of Girl's force about Pivot = 200 N * (2 - X) meters = 400 - 200 X Moment of Rock's weight = 490 N * X = 490 X
As the Girl is able to lift the rock, 400 - 200 X > 490 X Hence 400 > 200 X + 490 X 400 > 690 X X < 400/690 = 0.58 meters *** If the Pivot is placed closer than 0.58 meters or 58 cm to the Rock, then she can lift the rock.***
The answer is 0.58 meters. I agree with the working shown below. I did the same on paper, and it is the right answer.
The man can lift the rock since the torque from his force (480 N-m) exceeds the torque from the rock's weight (392 N-m). His daughter can also lift the rock by applying her force from a position that's closer to the pivot, utilizing leverage, provided it's within the calculated distance. Therefore, the placement of the pivot is crucial for both of them to successfully lift the rock.
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