You have a 2.0-m chain lying on the floor alongside ten 0.15-kg cubical blocks, each 0.20 m on a side. Each block is resting on the floor, and the inertia of the chain is 1.5 kg.What amount of work is required for lifting one end of the chain so that the chain hangs vertically with the bottom link just touching the floor?Express your answer with the appropriate units.
Question
You have a 2.0-m chain lying on the floor alongside ten 0.15-kg cubical blocks, each 0.20 m on a side. Each block is resting on the floor, and the inertia of the chain is 1.5 kg.What amount of work is required for lifting one end of the chain so that the chain hangs vertically with the bottom link just touching the floor?Express your answer with the appropriate units.
Solution
To solve this problem, we need to calculate the work done in lifting the chain. The work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force is the weight of the chain, and the distance is the height to which the chain is lifted.
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First, calculate the weight of the chain. The weight (W) of an object is its mass (m) times the acceleration due to gravity (g). Here, the mass of the chain is given as 1.5 kg, and the acceleration due to gravity is approximately 9.8 m/s². So, W = m * g = 1.5 kg * 9.8 m/s² = 14.7 N.
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Next, calculate the height to which the chain is lifted. The chain is 2.0 m long, and when it is hanging vertically, one end is touching the floor. So, the height (h) to which the chain is lifted is half the length of the chain, or h = 2.0 m / 2 = 1.0 m.
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Finally, calculate the work done in lifting the chain. The work (W) done on an object is the force (F) applied to the object times the distance (d) over which the force is applied. So, W = F * d = 14.7 N * 1.0 m = 14.7 J.
Therefore, the work required to lift one end of the chain so that it hangs vertically with the bottom link just touching the floor is 14.7 Joules.
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