a-cars-engine-must-exert-a-force-of-2000-mathrmn-to-maintain-a-speed-of-30-mathrmm-mathrms-up-an-inc

Question

A car's engine must exert a force of $2,000 \mathrm{N}$ to maintain a speed of 30 $\mathrm{m} / \mathrm{s}$ up an incline. What is the power provided by the engine during this motion?
(A) 20 $\mathrm{N}$
(B) 40 $\mathrm{N}$
(C) 80 $\mathrm{N}$
(D) 160 $\mathrm{N}$

Guilherme Barros · Accepted Answer

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&#x27;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&#x27;s given by the the engine? And we know that the power is equal to Theo. Energy that&#x27;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&#x27;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&#x27;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&#x27;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&#x27;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.

Averell Hause · Answer

so the work performed by the engine is actually equal to the change in the kinetic energy of the car. So this would be equal to 1/2 times the mass of the car multiplied by the final velocity squared minus the initial velocity squared. This is going to be equal to 1/2 multiplied by 2000 kilograms. This will be multiplied by 30 meters per second quantity squared minus zero. And so we find that then the work performed by the engine is 900 1000 jewels, so the average power would be equaling than the work performed by the engine over the time interval. So there&#x27;s gonna be 900,000. Jules, this would be divided by six seconds and this is giving us 100 50,000 watts, or we can say 100 and 50 kilowatts. So Option B, that is thean of the solution. Thank you for watching

Ze-Han Lee · Answer

So in this problem, we know that we need to exert a force equal to 100 to keep to keep this object. Ah, movie on the rough plan. So this stuff with a velocity of equal two meters per second, right? So we&#x27;re gonna see the power off this force equal half times we So this gives you 400 waltz. All right?

Kristela Garcia · Answer

we were given a mass of 1000 kill Gramps. That experience is a force of 3500 mutants and moves with a constant speed of 15 meters per second. And whereas to calculate the power output well, our power is equal to our work done in our time interval because it&#x27;s a horizontal force. Our work done can be calculated by doing our forest times. Our distance traveled in the same time interval and you know the distance over time if you&#x27;re moving at a constant speed is V So our power output is just going to be our fours multiplied by our velocity to give me a power output of 52,500. What? Or did you 0.5 kill? What&#x27;s

Adnan Gill · Answer

for Park Gae. Let&#x27;s calculate the mass off the car, which would be nine point your times 10 to the power three, divided by 9.8 that comes out to be equal to 918 kilograms. Next, let&#x27;s calculate the work done, which is equal to the change in kinetic energy, which is 1/2 M times V squared minus me not squared. So we have 1/2 times 9 18 times. The final speed is 20 squared minus zero squared. So the work done is equal to 183,600 jewels, and then power equals work overtime, which is 183600 divided by 5.6 seconds. So the power is 3.28 times 10 to the power four watts. So that&#x27;s part a. And in the same way, Part B start by calculating the mass off the car, which is 1.4 times 10 to the power four divided by 9.8, comes out to be cool to 14 28 kilograms. Work is equal to Delta Key, which would be 1/2 times 14 28 times 20 squared, minus zero squared equals 205,600 jewels. And then power is equal to work overtime or 205 600 divided by 5.6 seconds. The power is 5.1 times 10 to the power for what?

Problem

It's difficult to imagine an epidemic on this kin…

Problem 19 Easy Difficulty

A car's engine must exert a force of $2,000 \mathrm{N}$ to maintain a speed of 30 $\mathrm{m} / \mathrm{s}$ up an incline. What is the power provided by the engine during this motion?
(A) 20 $\mathrm{N}$
(B) 40 $\mathrm{N}$
(C) 80 $\mathrm{N}$
(D) 160 $\mathrm{N}$

Answer

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