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(III) A 3.0 -m-long steel chain is stretched out along the top level of a horizontal scaffold at a construction site, in such a way that 2.0$\mathrm { m }$ of the chain remains on the top level and 1.0$\mathrm { m }$ hangs vertically, Fig. $26 .$ At this point, the force on the hanging segment is sufficient to pull the entire chain over the edge. Once the chain is moving, the kinetic friction is so small that it can be neglected. How much work is performed on the chain by the force of gravity as the chain falls from the point where 2.0$\mathrm { m }$ remains on the scaffold to the point where the entire chain has left the scaffold? (Assume that the chain has a linear weight density of 18$\mathrm { N } / \mathrm { m } . )$

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$72 \mathrm{J}$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

University of Washington

Hope College

University of Sheffield

University of Winnipeg

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

03:47

In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

02:50

49. (III) A 3.0-m-long ste…

50-m-long chain hangs vert…

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A 30 -m-long chain hangs v…

03:05

Winding a chain A 30 -m-lo…

04:29

A 3 -m chain with linear m…

06:12

$\mathrm{A} 3$ -m chain wi…

07:14

A small mass $m$ hangs at …

7.49. So we have a chain. The total length of three meters is sort of stretched, uh, two meters of it horizontally off some scaffolding and a construction site. One meter is hanging down and we're told that this point is where the weight of the hanging segment is sufficient to start the chain moving and that the kinetic friction will be negligible. So you want to know how much work the force of gravity does, and dragging the remaining two meters of this chain off the edge of the scaffolding. We were told that what we'll call lamb to hear the wait for you at length is 18 per meter. So we call why the amount of chain hanging off the edge, then the forced from gravity is going to be lamb. Do the wait for unit length of chain times, the amount of chain that's being dragged down by gravity. And so this is the weight at a given point. Why, Okay, so no, the work. Why one being one meter and why to being three meters integral of Lambda? Why d why the forest is pulling downwards and the displacements air also downwards. So We have a coastline of zero degrees in here. So this is 1/2 Lambda Y squared from one meters, three meters, which is 72 jewels.

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