When a vehicle is traveling at a constant velocity, the forceproduced by the engine must match the total resistive forcesof friction and drag to maintain a constant...

When an automobile moves with constant speed down a highway, most of the power developed by the engine is used to compensate for the energy transformations due to friction forces exerted on the car by the air and the road. If the power developed by an engine is 175 hp, estimate the total friction force acting on the car when it is moving at a speed of 29 $\mathrm{m} / \mathrm{s}$ . One horsepower equals 746 $\mathrm{W}$ .

We know that the force of the drag is equaling 1/2 times the density of the medium. Essentially time. See the dry coefficient times a the drag area times velocity squared. And so for party, we can say that the force of the drag this would be for the Toyota car. So it's a capital T at 70 kilometers per hour. This is equal in 1/2 times the density of air. 1.21 kilograms per cubic meter multiplied by the drag coefficient of 0.28 mode supplied by the area 0.70 meters squared. And then we're gonna multiply this by 70 kilometers per hour. We're gonna multiply this by 1000 meters per kilometer. We're gonna multiply this by one hour for every 3600 seconds, and we're going to square this entire term. This is equaling 44.8 Newtons. Now, for the 100 kilometer car, it's again still a Toyota. This would be again 1/2 times 1.21 times 0.28 times 0.70 And then we're gonna multiply this by ah 100 kilometers per hour multiplied by 1000 divided by 3600 and we're gonna square this entire term, and this is gonna equal 91.5 Newton's. So we have our two answers for the drag force for the 70 kilometer per hour Toyota car and the 100 kilometer per hour Toyota car. Now we have a Hummer H two. So Hummer H two has a greater drag area, so essentially 20.7 is gonna increase. And four part B, we have the force of the drag. This would be for the Hummer going 70 kilometers per hour. This is gonna be again 1/2 times 1.21 But now it's going to be the drag coefficient ist 0.64 and the drag area is 2.44 meters squared. And then again, we're gonna multiply this by 70 kilometers per hour, multiplied by 1000 divided by 3600. We're gonna square this entire term. This is equal in 357 Newtons and the force of the drag for the Hummer. For the 100 come on out of speed going 100 kilometers per hour. This is again 1/2 times 1.21 times 0.64 times, 2.44 meters squared and then here, times 100 kilometers per hour. We're gonna most play this by the 1000 divided by 3600 quantity squared. This is equaling. 729. Newton's thes would be our two answers for part B. That is the end of the solution. Thank you for watching.

The Drac forces, given by half role a three squared equals have times density. Off air is one point to do times. Area off the camera is 0.7 meters squared times the velocity squared. He's 70 kilometers per hour. 30 kilometer is 1000 Medard. But our is 3602nd. It's one of that. The draft force comes out to be 1 62 He knew them. Now, using 100 kilometer per hour, we find that that drag force at 100 either meter par our comes out to be 331. Milton. No area of the Hummer is given by 2.44 meter square. So force the drag force on the Harmer at 70 kilometers apart hours speed will be given by whatever it waas for the Camry at that speed multiplied by the area. Correction. 2.4 4/1 point. To do so that comes out to be exactly double no. Ah, the area for the camera. The war 0.7. So that comes out to be 5 65 milion and seven of the draft force on the Hummer at 100 kilometer per hour will be 3 31 new done times The area corrections, which is you live in. 53 new done

We know that power is given its He quit. Uh, and don't be. He is Don't go far. 00 equal to four years in tow. We lost the witches. Given less 27 meters per second. Solving this, we will get the force as it could be new. Done. This is very quiet force.

Yeah, for this problem, we are given the total power of the engine. So total power is 28 kilowatt. Let's convert this kilowatt as the unit of what? And we know that one kilowatt is 1000 what? So 28 kg what? One kilowatt is equivalent to 1000 what? Sir, kilowatt and kilowatt will cancel. And then we will lift up with 20,000 what? And w is the unique for what? And then the constant velocity of the truck is given us 60 kilometer or our again kilometer per hour have to be expressed in metric unit. So for metric unit, one kilometer is 1000 m and then one hour is 60 minutes. And we know that in one minute we have 60 seconds. So 60 times 60 is 3600 2nd. Alright, So 60 kilometer par our All right. And then one hour half, 3600 2nd, and then one kilometer is equivalent to 1000 m. So kilometer and kilometer will cancel. Our and our will cancel. We will left of it meet up our second. So 60 times 1000 divided by 3600 years equivalent to Uh huh. 16.67 m/s. All I'm doing is is writing down what is provided on the problem and then expressing a in metric unit. All right. And then we are given the force due to air friction is directly proportional to square of the velocity. So what is given an equation is force due to here friction. Let it be denoted as F forced you to a friction is directly proportional to the square of the velocity of these develop city. And we all know that proposal sign is always replaced with a proportional consent for the scarce. Let it be denoted by. Okay, Okay. Now, if A is equivalent to k B square. All right. Now, the first part of the problem is we have to find the power of the engine. All right, So, what is the power of the engine? So, power is defined as the force times. Speak. Okay, now, over here, we don't know what is the total resistive force. Okay, we know speed. We are given power. So let's figure out what is the force. Actually? This is the resistive force. All right, Power is 28,000. We don't know what is the resistive force of the truck. Right? And then we just calculate speed as 16.67. All right now, we have to find resistive force and get rid of 16.671 method is dividing both sides of the equation by 16.67 so that our right hand side will left await resistive force. Okay? So, if you do matter over here, this too will be canceled. All right. This will give us resistive force is equivalent to 28,000 divided by 16.67 is equivalent to 168 year old newton. So, this is the first part of the problem. All right. Now, for a second part, What we are keeping is now 65% is of the resistive forces due to rolling friction. Okay, so now here's a step force due to rolling friction Is equivalent to 65% off resistive force. So 65% infraction is 65 over 100 with us 0.65 And our resistive force is 1680 Which we calculate on first part. Right? So the resistive force to to rolling friction happened to be. If you do this matt, then that would be equivalent to 109 to newton. Okay, So resistive force to to ruling friction. All right, this is another part. All right. So, and it says the rest is because of air friction. So out of 100%, is rolling friction. Right then, 65, -65 will be 35%. So, that means 35 percent off registered force is due to air friction. So, that means due to air friction will be 35% off 168 year olds. A 35% is 0.35. Alright. 1 680. And if we do mats over here, then that will be equivalent to 587.99 The unit of forces Newton. All right. So that will be equivalent to 587.99 Newton. So, this is the legislative forced to to air friction and then due to rolling friction is €1.9 to newton. Let's recall the equation that is given as if he is key The square we know velocity. Now we got the value of resisting forced into a friction. Then by plugging on this value on this equation, then we can calculate the value of kids. So if a is 587.99 K. Is the proportional constant. Our velocity was 60 kilometers per hour, which is 16.66 m per second. All right now, let's solve for K. K. Is dividing both sides by 16.67 587.99 divided by 16.67 whole square. And if we do match over here, this will give us the value of K. S 2.116 And it's a constant. Right? So, okay, is it devaluing too? 2.116. Okay, the second part of the problem, we have to find the power of the truck if the velocity is 30 km/h. So initial, initially the velocity was 60 km/h right now, at speed 30 kilometer per hour. What is the power of the truck? That's what we have to figure out now for 30 kilometer per hour. Right. That is 30 kilometer per hour hour. Now, you must be comfortable to convert kilometer to meet her by multiplying by 1000 and then convert one over our as 36 years zero second. And if we do match at 30 kilometers per hour, will be equivalent to 8.33 major per second. Now, let's see what is the power At 8.33 m/s, velocity. And power is force times speed. Right? So let's find out what is the total resistive force. Okay, let's recall the idea. Total resistive force is register forced you to rolling friction, which is not going to chance. But the register forced due to air friction depends on K and V. Square. When velocity chance then the value will chance. All right, let's figure out what is it? 1092 The value of key with this constant one chance 2.116. Our new velocity is 8.33 whole square. Okay, and when we do this mad then total resistive force will be equivalent to 123, 8-7. Newton. Okay, we got force and we know the velocity. Now let's find out what is the power. So therefore power is force times speed. Now our new forces 1238.8 to 7 newton. And then our new speed is 8.33 So if we do maths over here we will be give Alan too. If you multiply these 21 Do you know three? 19.4 to what? But we have to express the unit of power in kilowatts. So in at the first step we convert from kilowatt to what? By multiplying multiplying by 1000. Now we have to convert from water kilowatts. So this reverse. So to convert from one particular what we have to divide by 1000. Okay, so the power of the engine, if you divide this then that will be 10.319 You can just round it up as 10.32 kg. What? Also we are X. To express the power in horsepower. The Conversing Unit is one. Horse. Power is 746. What? Okay, so again Power is 10319.42 Okay, divided by 746 hearse. Power. Okay? And if you divide 12319 .42 divided by 746, then we will lift up with 13.8 hers power. So the power of the engine in terms of hers power is 13.8. Okay, so the last part of the problem is we did for 60 kilometers per hour. We did for 30 kilometer per hour. Now we have defined for vehicles 1 20 kilometer for our what is the power in terms of speed? 1 20 kilometer part our So let's convert it into meter or 2nd. So this is a gravelly in two 33.33 m per second. Our new speed is 33.33 m per second. Now let's follow the similar procedure and same state state. So total resistive force. Yes resistive force due to ruling friction which is not going to chance. And then the resistive force due to air friction is KV square. Since we have new velocity right? Our key is 2.116 And then our new velocity is 33 point 33 square. And if we do this map the in total resistive force will be covalin 23442.9. Newton. Now power is fourth times speed. Our new power is 3442.9. And then our new speed is 33.33 If you do maths of the hill, that will give us 114751 What? Right again, we have to convert it into kilowatt. So divided by 1000 right 751 divided by 1000 in kilowatts. Soapy is equivalent to 11 four point 75 kill, oh, what, and then another two expressed it in horsepower, right, He is equivalent to 114751 over, divide by 746. Then that will give us the power is equivalent to 154 horse power. So these are the power in terms of 60 km/h for the first part, And then for second part, we have velocity 30 km/h, and then for velocity 120 km/h in terms of kilowatt and hearst power.