QuestionA chain 63 meters long whose mass is 27 kilograms is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the top 5 meters of the chain to the top of the building? Use that the acceleration due to gravity is 9.8 meters per second squared. Your answer must include the correct units.
Work =
Studdy Solution
STEP 1
1. The chain is uniform, meaning its mass is evenly distributed along its length.
2. The total length of the chain is meters.
3. The total mass of the chain is kilograms.
4. The acceleration due to gravity is .
5. We need to lift the top meters of the chain.
STEP 2
1. Calculate the linear mass density of the chain.
2. Determine the mass of the top meters of the chain.
3. Calculate the work done to lift the top meters of the chain.
STEP 3
Calculate the linear mass density of the chain:
STEP 4
Determine the mass of the top meters of the chain:
STEP 5
Calculate the work done to lift the top meters of the chain:
The work done to lift a small segment of the chain is given by .
The force required to lift the chain is equal to the weight of the chain segment, which is .
The work required to lift the top meters of the chain is:
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