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Numerade Educator

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Problem 7 Medium Difficulty

Jennifer lifts a 2.5 -kg carton of cat litter from the floor to a height of $0.75 \mathrm{m} .$ (a) How much total work is done on the carton during this operation? Jennifer then pours $1.2 \mathrm{kg}$ of the litter into the cat's litter box on the floor. (b) How much work is done by gravity on the $1.2 \mathrm{kg}$ of litter as it falls into the litter box?

Answer

(a) $18 \text{ J}$ (b) $8.8 \text{ J}$

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Video Transcript

this question asked us to calculate how much total work is done on a carton of cat litter when it is lifted up off the ground. So first things first. I've got my person. I've got my cat litter. I need to pull the relevant information from the question First piece of information I give us is that the mass of the Kent letter is 2.5 kilograms. Next piece of information is that the Bucks is raised off the ground by 0.75 meters. It's in order to calculate work. I'm going to start with the formula for work, which is work equals force times, displacement times, the co sine of the angle between the force and the displacement. You know, Let's, um, zoom in on the litter box here for a second. I'm just gonna drop down below here and read. The displacement of the box was up. It was lifted from the ground by 7.5 meters. The force applied on the box was also up. But we're not told explicitly what that force waas. We actually have to calculate what the force applied on the litter box was in order to finish our calculation for work. So we know that the mass of the box is 2.5 kilograms and our person is having to lift the box. And what I'm gonna call an applied for us. That's their force acting up. But my question is, what is the force that they're fighting against? Why do they have to apply a force to lift up the box? And it's because they're fighting against gravity, the gravitational force on the box also known as the weight of the box, which we calculate with a formula as M. G. So if we do that, we can figure out what is Theglobe Rotational force on the box 2.5 is the mass times acceleration due to gravity which is 9.1 meters per second squared. And if we calculate that we get 24 0.5 to 5 nudes. So this is the force that are person would have had to apply in orderto lift this box. So if we substitute that into our work formula over here for F, we can finish off this calculation nice and neatly. My force was 24 0.5 to 5. My displacement was 0.75 and I couldn't throw in close of zero. But because they're in the same direction. I know I don't have to worry about the coastline, um, the coastline term. So I'm just gonna compute what, 24.525 times 0.75 is to get our final answer oath 18 0.39375 And looking at the numbers given in the question, they all seem to be given to two significant digits. So I would record my final answer as 18 jewels. Now that's for party. In part b of the question are person dumps 1.2 kilograms of the letter back onto the floor? Or perhaps I'm assuming into the litter box. So looking at her litter box now, instead of lifting the litter box, were basically dumping 1.2 kilograms of this letter onto the floor. And the question is asking us specifically how much work is done by gravity as it falls. So, using my drawing of the litter box from before, I'm just gonna change its mass from the previous 2.5 toe, 1.2 kilograms. Again, it's displacement. A 0.75 But what direction is the falling litter going in this case down? Our letter is going down, and I My next question is what is the force that is pulling the litter down to the ground? In this case, it's the same as the force that was trying to keep the litter box on the ground in the first place. It's the force of gravity, which we can calculate in the same way that we did last time using mass times. The gravitation acceleration of 9.81 get 11 0.772 means as the gravitational force. So in this case, it's important to again keep track of who's doing the work and were what force that thing is applying because the question is asking for the work done by gravity. We're going to make sure we're using the gravitational force, which makes sense. Gravity is the only force acting on the letter as it falls anyways. It's not like our person who's throwing the objects down as they dump the litter onto the floor, probably into the letter box, so dumping our numbers back into the formula as before. In part A. We have a force of 11.772 We have a displacement of the 0.75 and luckily for us are forced and are displacements are in the same direction. So I can have to drop the coastline term or just safe the coastline of zero degrees, which is just gonna be one anyways, so I don't need to worry about it. But if you like to see it there for completion, by all means, go ahead and write it down. So shoving this into a calculator, we get a final answer of 8.8 to 9 jewels for the work or again rounding toe are too significant digits. We would just get eight 0.8 jewels of work done by gravity.