In this question. We have a create of fruit of mass, 35 kg and a specific heat of 3650 sliding down a ramp inclined at 36.9 degrees. The ramp is 8 m long and were asked to calculate how much work is done on the Great by friction if it slides down from rest and has a final speed of 2.5 m per second. And then we are asked to calculate the temperature change. If the work done by friction, uh, is equal to an amount of heat that is transferred into the Great. So the idea behind this question is that the crate slides down the incline. Um, the speed increases, but there is a force of friction. S o The speed is not increasing as much as it would have if it was just sliding down this ramp without friction. Friction is taking out some energy from the crate as it slides down the ramp. So since friction is taking energy out, um, one of the forms of energy that that could be converted into is heat. So this question is asking us to suppose that all of that work done by friction. All that energy taken out of the crate, Uh, in terms of its kinetic energy or it's mechanical energy. Ah is converted completely into, um, heat energy. So that's the basic premise of this question. Let's go ahead and jump into the calculations. So in the first part were asked to calculate the work done on the crate by friction. Now there's a couple different ways that you can calculate work so we can calculate work using force and displacement. Or we can calculate work using three overall change in energy. So, um, I'm going to use the second way today. Both are options here, but I just think that calculating the change in energy here is just a bit easier. So the work done by non conservative forces or a K A friction is going to be equal to three overall change and energy, and that's going to be composed of the change in kinetic energy, plus the change in potential energy. So the change input in kinetic energy is going to be one half MV F squared, minus one half MV I squared. But of course, this thing is starting from rest so this term is going to be zero and then the change in potential energy can be written as M G. Delta H. Now, we're not given Delta H specifically in the question, but the ramp is 8 m long and the angle is 36.9 degrees. So we can easily find the heights by calculating the height of this triangle. Um, so it will be Delta H. So the Delta H here is going to be sign 36 0.9 times eight. Just the hype oddness. Okay, so now we can go ahead and plug everything in. We've got a mass of 35 kg. The final speed is 2.5 m per second is going to be squared plus 35 times g times the height, which if we solve this, we get a height change in height off four points. 8 m. Now, we do want to consider the change in height as being negative, because as this great slides down the ramp, we're experiencing a negative change in potential energy, meaning the potential energy is decreasing. So we need to consider the height as negative. So we get that change in potential energy to be negative as well. So once we go ahead and plug all of those numbers in, we're going to get in overall amount of work. Negative 1.54 times 10 to the three jewels. So the change in the total mechanical energy here is 1.54 times 10 to the three jewels. The negative indicates that we're losing that energy. And so that is the work done by friction. That's the work, um, or the energy taken out by friction. Okay, for the second parts, um, were asked to calculate the heat if all of that work done by friction. Um, sorry. We're asked to calculate the temperature change if all of that work done by friction goes into heat. So we've got a formula that relates heat and temperature change, and so we can easily rearrange this to find Delta T. So that's going to be cute over EMC. And for Q, we're going to use that amount of work that we just found. So that's gonna be 1.54 times 10 to the three jewels, and then the rest is just found in the question. So 35 kg and then we can go ahead and fill in that specific heat. And once you put that into a calculator, you get about 1.2 times 10 to the minus two degrees Calvin or degrees Celsius. So the overall change in temperature that would be experienced by the great here if all of the work done by friction goes into heat is actually very, very small. So this is the final answer, Thio Part B and then the final answer to party.