Justin, with a mass of 30 kg, is going down an 8.0-m-high water s...

Question

Justin, with a mass of 30 kg, is going down an 8.0-m-high water slide. He starts at rest, and his speed at the bottom is 11 m/s. How much thermal energy is created by friction during his descent?

Accepted Answer

Hey, everyone in this problem, a car with a mass of 1200 kg is traveling at a speed of 25 m per second. On an inclined road, It stops at the ground level due to friction. After traveling a distance of 150 m, we're asked to determine the thermal energy generated by friction during its deceleration. They were told to consider the angle of inclination of the road with the vertical 70°. We're given four answer choices. Option A 228 kilojoules. Option B negative 228 kilojoules. Option C negative 978 kilojoules And option D 978 kilojoules. Now we're gonna draw a little picture of what we have here just to get an idea. So we have an incline And it makes a 70° angle with the vertical and we have a car, ok. Traveling down the incline until it reaches the bottom And where it has a final speed of 0m/s, it comes to a stop. We're told that its initial speed, it's initially moving at 25 m/s And it has a mass of 1200 kg. OK. This incline is 150 m long. The car travels 150 m before it comes to a stop on flat ground. And we're looking for thermal energy. Now, what's called the height of the car initially? H and let's use our work kinetic energy. The tells us that the total work work total is equal to the change in kinetic energy. OK. In this case, this change in kinetic energy, we have the initial speed, we have the final speed, we know the mass. So we can calculate the change in kinetic energy. But what makes up this total work? Well, we have to consider the work due to gravity. OK. This car starts at some height on this incline and then comes down to the level ground with no height. So there is work due to gravity happening there. And then we also have to worry about this thermal energy that is lost by friction. So our total work is actually gonna be the work due to gravity. No, that's acting the positive direction is doing positive work. It's helping bring that car down and then the work due to friction where that thermal energy. OK. That is decreasing. This the energy that we have left to transfer into kinetic energy. So we have the work data of gravity minus our thermal energy is equal to the changing kinetic energy. And recall that the changing kinetic energy is the final kinetic energy one half M V F squared minus the initial kinetic energy one half M V not squared. Now, what is the work due to gravity? Well, the work due to gravity is gonna be the mass times the gravitational acceleration times the height. Hm. So we get M G H minus the thermal energy Is equal to 1/ M V F squared minus one half M V not squared. Now, the mass of our car is 1200 kg. So we have 1200 kg gravitational acceleration 9.8 m per second squared multiplied by the height. Now, what is this height? We know that the hypo of the triangle that this incline makes is m. The angle with the vertical is 70 degrees. And so our height, OK. This is the adjacent side. So it's gonna be related to the cosine. So we have 150 m multiplied by cosine of 70 degrees. And that gives us that work due to gravity, we have minus the thermal energy is equal to what? While the final speed of our car is zero. So the first term goes to zero, we're gonna have minus one half the mass kg Multiplied by the initial velocity 25 m/s squared. So we're trying to find our thermal energy. We have everything else in this equation now. And so it's just a matter of simplifying and rearranging We simplify. On the left hand side, we get 603, .533, maybe a kilogram meter squared per second squared minus the thermal energy is equal to negative 375,000. And again, kilogram meter squared per second squared. Ok. If we isolate this thermal energy and we can move it to the right hand side by adding, We can add this 375,000 to the left hand side. We get that the thermal energy is equal to 900 in 323.533. And our unit is kilogram meter squared per second squared. Can recall that kilogram meter squared per second squared is a jewel. So we can write this as Times 10 to the three jewels. And if we're multiplying by 10 to the three, that's the killer prefix. And so this is equal to kilojoules. So that is the thermal energy we were looking for. If we go back up to our answer choices, OK. We found that the thermal energy generated due to friction was equal to 978 kilojoules which corresponds with answer choice. D Thanks everyone for watching. I hope this video helped see you in the next one.

Justin, with a mass of 30 kg, is going down an 8.0-m-high water slide. He starts at rest, and his speed at the bottom is 11 m/s. How much thermal energy is created by friction during his descent?

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