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Automotive Power Driving Uphill How much power must an automobile engine expend E t0 move 1200-kg car up 1590 grade at 90 kmh (Figure 7.15)? Assume that - 25%0 of t...

Question

Automotive Power Driving Uphill How much power must an automobile engine expend E t0 move 1200-kg car up 1590 grade at 90 kmh (Figure 7.15)? Assume that - 25%0 of this power is dissipated overcoming air resistance and friction: 90 km/h1200 kg15% gradeFlgure 7.15 We want t0 calculate tlie power needed to move cai Up hill at colstant speed:"Instead of 15% grade use 15 degree incline"

Automotive Power Driving Uphill How much power must an automobile engine expend E t0 move 1200-kg car up 1590 grade at 90 kmh (Figure 7.15)? Assume that - 25%0 of this power is dissipated overcoming air resistance and friction: 90 km/h 1200 kg 15% grade Flgure 7.15 We want t0 calculate tlie power needed to move cai Up hill at colstant speed: "Instead of 15% grade use 15 degree incline"



Answers

While a $1700-\mathrm{kg}$ automobile is moving at a constant speed of $15 \mathrm{~m} / \mathrm{s}$, the motor supplies $16 \mathrm{~kW}$ of power to overcome friction, wind resistance, and so on. (a) What power must the motor supply if the car is to move up an $8.0 \%$ grade $(8.0 \mathrm{~m}$ vertically for each $100 \mathrm{~m}$ horizontally) at $15 \mathrm{~m} / \mathrm{s} ?$ (b) At what downgrade, expressed in percentage terms, would the car coast at $15 \mathrm{~m} / \mathrm{s}$ ?

So the situation is such that the guard is going up and inclination off theta equals 30 degree on the card travels from here to there. Off distance off l equals 100 meter and we're trying to find what is age the height update by the card. So we have guard and scientists are equals age. So age it waas In this 100 dives sign up 30 degree it was 7 30 is half so that 50 meter no power equals walk over 30. What is M. G h? Actually, that's just calling Delta H MG did the age off dead d massive. The Carty's either event 50 kilogram G 9.81 meters per second height rises 50 in to a second. So that comes out to be for the seven times 10 to the three. What? It was 47 either. What

Question number 99. Enough. A spike. The power in the friction case is Uranus. Eight hours forward. So it didn't do 746 words is equal to the force applied into will Osti off 60 kilometers per hour, which is 16 2000 m. They were there by 3600 seconds. Soldering this. We will get the force. Ethical duty will be it new done now, Sigurd. Part of the question In the second part, we have to find the power at 60 kilometer per hour on an incline. So what is, um G signed Pita in theory, plus the initial power off. It didn't do seven for six. What now We will get with that Rita by the great. Given the type of dough, then in words 0.1. This is a type of to five point 71 daily now substituting the values. It's a bit in the 9.8 induce I know five point 71 into velocity 60. In 2000, they were aided by 3600 less it in 27464 Solving this, we will get very quiet power. He's a weirdo. 35 219 What? And this is also equal. Do 47 point to one parts forward in the part C by word he's given us, um g sign Reda. In doing, they had the new angle. He, uh, is able to do 10 inwards one by one day on the ties it could do zero point 57 to 9 bigotry. Now stop shooting the values equal to 18 and it in June and born dead induce. I know. You know 0.57 nine big me in doing last er 60 in 2000. They were never 26 ended. Solving this, you will get the new power as 989 What? This is all safer too. He Why 94 horsepower. Now, in the last part of the question, we have to find that great. So now, equipping the power. It didn't go seven for nine. This is the power for the for posthaste. This is equal to it. Didn't one day in the 9.8 into sign off. He, uh, in the velocity. 60 in 2000, we were dead by 3600. Solving this, you'll get science data. People do 0.0. Do zero nine. This means he does people too. One point 16 gigi and does the greatest 2.3 for seven days.

Friends. This is the problem based on power delivered by the angel. Here it is, given Barbara often automobile is HP that is 5968 work. It is putting the car off muss Internet education at a constant speed off 60 kilometer per over. That is 16.67 m per hour. Sorry, 16.67 m per second on the level road. In the first part, we have to calculate Ned registered force acting on the car. In second part, we have toe calculate power required toe derive the car up 10% grade. Hit it rising 10 m vertically for 100 m origin. Tal distance in C part, we have to calculate power required toe Derive the car at 60 kilometer para ver down up 1% grade head and deep part We have to calculate Don't what percent graded book the car. Mhm cost out 60 kilometer Perata. Let us start solving first part Power is to find us forced into velocity so this to force will be power upon various three substitute develop. Father is 5968 on velocity is 16.67 So it is to be 3 58 Newton. So all that is to post having the value 3 58 Newton now. Beeper. Yeah. Yeah. Cobb engine has to pull the car up around that. Quite plain having inclination. Oh, beautiful. Yeah. And had five movie 10 of 100. That is one by 10. So it's where a city can be resolved in the two components designer for and we cause help. Sorry. We cause Alpi original direction. This is given to you. 100 m. This is given 10 m. So work done against gravity or power to revert against gravity will be mg into be signing. So it is 1802 9.8 and to 16.6. Sign off 5.71 Because from here, l probably 5.71 degrees. So it is. Story 21 Time Tau and Tau 10 to the power forwards. So total power required. 5968 plus 292 00 Yeah, that is 68 one. Both. It is to be 35 I'm 16 Said what? Or in horse horsepower. It can be written as Yeah, 39.1 hp. Okay. Wow, Whoa! Super! The power required by the engine. No. Introduced by the rate at which grave he does positive part during downward motion. Notice you. It will be MGB signed off. Alpo here, Al. Page 10 in Worse off. Why did you level? Which is equal to yeah, 0.57 to 93. Moss is 1800 9.8. Spirit is 16.7. Sign up 157 to 9. So it is Toby equal toe right. 2.94 tend to keep our three vote. Andi, if we convert in HP, it is 3.94 hp. So powered required eight hp minus 3.94 That is 4.6 hp. Well, no large part That is D. We have to calculate No power is required if gravity eaters yes, worked at a rate off HB that is 5968 water. So create required between m g v. Sign off, Alfa. So from here, sign off, Alfa, You gonna get substituting the value I'm solving value off and you will damage Sign Universal. Brian Jiro 20 How Right. But from here, sign Alfa, you will get 0.2030 that is Alfa is 1.1 C three degrees. So 10 off family week turn off 1.163 That is, why am 0 to 03? That is 2.3 grade. Be required that so thanks for watching it.

In sector size. We have a car that is coasting in neutral, meaning that no power is being given by the engine to the car at a speed of 20 m per second and down a hill that has an inkling on inflammation off two degrees with the horizontal, the car has a mask off 1500 kg in question. A. We have to suppose that the car is now moving in a level road and we want to completely, What is the power that the engine must give to the car such that it travels at the same speed of 20 m per second? Well, first of all, uh, what we need to consider in this exercise is that when the car is closing down the road, the forces that act upon it are that traditional floors that causes an acceleration parallel to the inclined plane off MG science data and and we have also have and their resistance force, that I'm gonna call f air the points of works. Now if the car is moving with a constant speed, that is, the car reached a terminal speed, then the some of the forces must be zero. So you know that f air, the force, The force of the answers over the car minus mg sign data is equal to zero. So from here we can obtain that the force of the air exterior toe over the car is mg time Science data and theatre here is just to okay Now when the car is moving at the left in level road, we also have the force off air the air resistance we do not have the The Tarallo judicial component of the gravitational force against force is just pointing downwards and not causing an ex exploration on the car. This means that the force that is making the car go forward is the force that the the the engine of the car is providing it. And if the car is moving with a constant speed of 20 m per second, then the force that the car the engine of the car exerts over the car is equal to it was our mind is a force of the force of resistance of air is equal to zero. This means that the forced the engine exerts is equal to the force that the characters and as we saw before this is equal to mg. Time to sign of to no. Now if we want to calculate what is the average power that's given by the the engine? And we know that the power is equal to Theo. Energy that's given divided by the time of the energy is just the work that the the engine does. And this is equal to the force of the engine times the distance, the divided by t. Now I noticed that the cars movie under at a constant speed, so D divided by t is just the speed. So we have the force of the engine times this Pete, this is N g sign, afraid of times the speed V so I can calculated explicitly. M is 48 kg g is 9.8 m per second square. Then we have multiplied by sine of two degrees men by 20 m percent. So the power is equal to 10 to the fourth lots or 10 kilowatts. This is the power that must be provided by the engine in question be We have to suppose that the power that the engine gives to the car it's even which of 40 kilowatts and with this information. We want to know what is the steepest incline. So this means that we want to calculate the angle data that the car can climb up at a constant speed of 20 meters per second. For this case you have again here inclined Twain. We want to complete this data here we have the car that subject to the following forces. Actually, the cars moving imports. I'm going okay with us. Um car subject to the falling forces. There is the gravitational force Tangential component MG science. Later, there is the force of the engine experience over the car moving pointing upwards. So this is the force of the engine and we also have the the force of the of the air resistance. So that's pointing upwards because of the car is moving. Actually the force of the air resistance pointing downwards because the car is moving upwards and for the car to move other at a constant speed of 20 m per second. Then all the forces must sum to zero. So have that the force of the engine most the force of the air minus MGI Sign of fada is equal to zero Now. What is the force of the engine gives to the car. As we saw before the power, he is equal to the force of the engine times V. Now the power is 10 is for 40 times into the third. This is equal to a of the force of the engine times 20 everything years in the international system of units. So he gets that the force of the engine is 2000 uniqueness. And we know how much. Uh, but we know what is the force of the air? Ah, for the for 20 m per second. So it can substitute everything here. So you have the force of the engine. Mine is the force of the air which, as we saw a Zen G times the south to then miners mg times a sign of data. It is what we want to find out now. F off the engine is 2000 unions. They have to subtract 15,015 1500 times of course times 9.8 m per second squared times sign of to and this is equal to I m g 10 sign of thieving. So this is 2000 new homes minus five 100 Newtons divided by M G, which is 1500 kilograms times 9.8 m for seven square Mrs Sign of Fada. So Fada is the arc sine of 1500. Newton's divided by 1500 kg. Time is 9.8 m per second square is the ark sign of 1/9 0.8, which is equal to 5.8 the police and this concludes there exercise.


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