A 737-800 jet airliner has twin engines, each with 105 kN thrust. A 78,000 kg jet reaches a takeoff speed of 70 m/s in a distance of 1100 m. (b) What is the increase in thermal energy due to rolling friction and air drag?

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Hi everyone in this practice problem, we wanna be able to calculate the increase in the thermal energy caused by the rolling friction where we'll have a train starting from rest with a mass of 500,000 kg, attaining a speed of 30 m per second at a distance of 1500 m. The train experiences a thrust with 90 kg Newton from each of its three engines. And we're being asked to calculate the increase in the thermal energy caused by the rolling friction. The options given are a 1.8 times 10 to the power of eight Jules b 1.8 times 10 to the power of seven Jules C four point oh five times 10 to the power of eight Jules and D four point oh five times 10 to the power of seven Joles. So in this practice problem, the force acting on the train is going to be constant. And therefore because of that by the definition of work, the trust work or w trust is then going to equals to three times the force trust multiplied by the distance the tree is coming from the fact that we have three different engines each experiencing or each exerting a trust of 90 kg Newton. So we then wanna calculate our W trust value. So w trust or the work from the trust will then be equals to three multiplied by 90 kg Newton will equals to nine multiplied by 10 to the power of three Newton. And the delta X is going to be the distance which is going to be 1500 m both given in the problem statement. So then that will actually give us W thrust to then equals to four point oh five times 10 to the power of eight chill. However, that is not our final answer because what we are being asked to calculate is to increase in the thermal energy caused by the rolling friction. And the way we want to calculate that is by um calculating W trust to be equals to the change in the kinetic energy plus the change in the thermal energy. So that will be delta K plus delta E P H. So the W trust is going to change the speed of the train from rest to the final speed. And using that fact, we will be then able to calculate our delta E T H. So rearranging this, then our delta E T H well then equals to W trust minus delta K. Uh our delta K will actually equals to half M V F squared minus half M V I squared just like usual. And we know that the train startss from rest, which is given in our problem statement right here. So the right side or the V I is going to equals to zero. So our delta K will then just equals to half M V F squared. Delta K equals half M V F squared. So we want to substitute that into our delta E T H equation. Delta E T H will then equals to W trust minus half M V F squared. And we want to actually substitute all of the known information given. So W trust is the one that we just calculated, which is four point oh five times 10 to the power of a jules minus half M mass is going to be 500,000 kg which is given in the problem statement. And the V F squared is also given which is 30 m per second squared just like. So OK, so then uh calculating all of this, that will give us delta E T H which will then be equals to 1.80 times 10 to the power of eight. So the increase in the thermal energy caused by the rolling friction of the, the three different engines giving each 90 kilometer rust is going to be 1.80 times 10 to the power of eight tools which will correspond to option A in our answer choices. So answer A is going to be the answer to this particular practice problem. And that will be all for this video. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topics and that'll be all for this one. Thank you.

A 737-800 jet airliner has twin engines, each with 105 kN thrust. A 78,000 kg jet reaches a takeoff speed of 70 m/s in a distance of 1100 m. (b) What is the increase in thermal energy due to rolling friction and air drag?

Verified Solution

Key Concepts

Thrust and Drag Forces

Work-Energy Principle

Kinetic Energy and Thermal Energy