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How much work is done when a hoist lifts a 200-kg rock to a height of 3 m?
$$5880 \mathrm{J}$$
Calculus 2 / BC
Chapter 6
Applications of Integration
Section 4
Work
Oregon State University
Baylor University
University of Michigan - Ann Arbor
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All right, so in this question, were asked how much work is done on a rock that is lifted two hundred kilogram rock that has lifted three meters. Solis, draw this out. We have a object here. That's, uh, two hundred kilograms, and what we're going to be doing is lifting it up three meters. So to answer this question, we use a simple force equation for work which states that work this just force times distance work. He goes force times, distance. And we use this doing calculus by saying that work is going to be equal to the force. Heinz, this is Delta DX right Right here. And what this d X refers to where these incremental, marginal distances that is being that is, moving this thiss object. Okay, so force is actually quite easy. We didn't get the force by looking at this object right here. And we know that the equation for force for ah project that doesn't undergo acceleration, custom velocities, is going to be force equals mg. And that's gonna give us two hundred kilograms times nine point eight years per second squared. And that is going to give us nineteen sixty Newtons. Okay, So let's just put that in here. And now we still have our VX term. Let me write this and blue corresponds distance over here and where we're moving, this thiss object is going to be from zero leaders the three meters. So now we have the bounds for a miracle like this. Now all we need to do is integrate this equation. So nineteen, sixty the X When we integrate, that is going to be nineteen. Sixty. Thanks. Found it. Zero to three and then we just solve that pretty simply nineteen, sixty times three. And remember that we shouldn't forgot mutants here, minus zero, he falls five thousand hate hundred and baby Whoops together. Eunice here is well, three leaders, right, Newton meters, which is going to eat? All right, Ever hear five thousand eight hundred and eighty? Jules, that is our answer.
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