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A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. An 856-kg helicopter r...

Question

A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. An 856-kg helicopter rises from rest to a speed of 6.2 m/s in a time of 3.81 s. During this time it climbs to a height of 9.33 m. What is the average power generated by the lifting force? (g = 9.80 m/s2)

A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. An 856-kg helicopter rises from rest to a speed of 6.2 m/s in a time of 3.81 s. During this time it climbs to a height of 9.33 m. What is the average power generated by the lifting force? (g = 9.80 m/s2)



Answers

A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. An 856-kg helicopter rises from rest to a speed of 6.2 m/s in a time of 3.81 s. During this time it climbs to a height of 9.33 m. What is the average power generated by the lifting force? (g = 9.80 m/s2)

So we have two ah, masses mass of the helicopter. Ah, mass of the frame and then they're connected by a wire. This is goingto have forced tension and then here it will be force of the frame twelve state for the mass of the helicopter Times G. So the force of the gravity of the frame and the helicopter and then lifting it is the force of lift which in this case, we're gonna have to calculate for party. We know that Sigma af and the wind direction equals ems of age plus amps of t. So I mess frame rather time's tree or other times a the acceleration and this is going to say force of the lift minus the force of gravity. So M Soleil, JJ plus M sub F G, and this is going to equal the acceleration of the system times the total mass of the system for party. We can say that the force of lift there's going to be equal to the mass of age because the mass of the frame time's a G and we can solve and say begins on, say, seven thousand one hundred eighty is the mass of the helicopter kilograms plus one thousand eighty kilograms The mass of the frame. Now this will be point nine point eight plus point eight zero the mass of the magnitude of the acceleration. So this is going to equal, Oh, eleven thousand four hundred and forty, four hundred forty eight noons, and this would be up on the frame. So this will be your answer for part and the fink part B. Ah, we can say that. Or rather my apologies, computational error. This is actually going to be eight thousand eighty seven thousand five hundred fifty six. My apologies. And then for part B, we can say that a Sigma f why equals massive the frame, eh? And this equals force tension minus mass of the frame G. Which means that force tension simply equals mass of the frame. And then times G plus A. And this is equal to ten eighty, a nine point eight plus point eight and then force of the tension is going to equal eleven thousand four hundred forty eight years. My apologies. So here, up on the frame. So here we're trying to find the force of the tension on the frame and then here. We simply wanted the force of the lift for the helicopter and the frame. So yeah, this value should be much greater than simply the force of the tension. And then, for part C is asking for the force of the tension down on the helicopter. Well, do this. Newton's second law. This is going to be the same exact thing. So the force of tension eyes going to equal negative eleven thousand four hundred forty eight noons. However, this going to be down on helicopter and this is simply due to Nunes there, Law of Motion. Any action has an equal and opposite reaction, which means that if the frame is has attention going up, pulling up on the frame of eleven thousand four hundred forty eight noons, that means that the same amount of force is pushing down on the helicopter. That is the end of the solution. Thank you for watching

For party. The helicopter in the frame both have the same acceleration and could be treated is one object. If no other information about internal forces is needed, some of sin which one? One object So they look at the forces in terms of the floor. Some of the forces equals the force. Elf lift minus massive helicopter plus the mass of the frame equals massive helicopter plus mass of the frame times salaries An AK use us The force of lift equals massive helicopter, plus the mass in the frame times G plus a acceleration. So we plug in things fucking values. 76 50 kilograms plus 1250 kilograms times 9.8 your second squared plus pointing 1.8 meters per second squared. Plus when eight years her second squared. So you add and multiply. Simplify and you can me Final answer. Foursome left of nine point for three times 10. Their fourth nudes hard. A reinforce part B the free by diagram for the frame alone In order to find attention to cable force Attention minus mass times gravity master the frame times gravity equals massive frame times acceleration. So force attention vehicles, massive the frame Times G plus a equals by the numbers 1250 kilograms times 9.8 used second squared plus 0.8 meters per second squared 12 50 times of some of these two numbers and you can't value of one point 33 times 10 fourth Nunes That is the force tension in the kale for part c Attention the cables the same. Both ends. So the cable exerts a force saying downward on the helicopter. So the answer for part C is the same as well. 1.33 times 10 34th newts.

So here we have the free body diagram for the helicopter and the frame with with which it is carrying. So we can say that the sum of forces in this case would be in the UAE direction. There isn't any force in the extraction and this is going to be equal to the force of lift minus the mass of the helicopter, plus the mass of the frame times the acceleration due to gravity G. And this is equaling the mass of the helicopter, plus the mass of the frame times the system's acceleration. So we can say that the force of the lift would be equal to the mass of the helicopter, plus the mass of the frame multiplied by the acceleration of the system, plus the acceleration due to gravity. And at this point, we can solve. So the force of the lift well, then the equal to 7650 kilograms before the mass of the helicopter plus 1250 kilograms, which would be the mass of the frame, multiplied by 9.8 plus 0.8 meters per second squared. And so we can say that the force of the lift is going to be equal to 9.43 times 10 to the fourth Nunes. This would be our answer for the force of the lift. Now this is the free body diagram for the frame. And so we can say that the sum of forces in the war direction would of course be forced tension minus the mass of the frame times G. And this is again equaling the mass of the frame times the acceleration of the system itself. Therefore, the force tension in the when the cables that is carrying the frame would be equal to the mass of the frame multiplied by the acceleration due to gravity, plus the acceleration of the system itself we can then solve. And this is equally 1250 kilograms. This would be the mass of the frame times 9.8 plus 0.8 a meters per second squared and we find that the force tension would be equal to 1.33 times 10 to the fourth Nunes. Now, this would be our answer for the force tension. Now, at this point, we can. For part C, it's going to be the exact same answer. So this is your answer for part B. However prepared to see is asking us for the ah force tension that acts downwards on the helicopter. And due to Newton's second law of Motion, every, um, uh, every force, right? Every force produces an equal and opposite reaction. Therefore, the forced tension would be equal to 1.33 times 10 to the fourth noons. And then let's specify direction downwards on the helicopter. That is the end of the solution. Thank you for watching.

This problem. We have a health doctor and we want to calculate the first of the rest. Uh, by the plates on the year. And how we're gonna do this is that we know that the net Force is equal to the first of thrust if t minus fg percentage is Cindy opposite direction. And every so for every team we get that 58 sequel to that minus 50. I'm sorry. Plus 15 If we make some substitutions, we get that 52 mass times acceleration plus acceleration to ready. So this is the equation we're going to use, uh, for part A were told that the helicopter is hovering at a steady precision at a constant altitude. So what this tells us is that the force of thrust on the force of gravity are equal. There is no acceleration. So if we use our formula, we get that FD is equal to AM list you. There is no acceleration so we can cancel this we get that FD is equal to mg. Now I'm gonna substitute We know that I am is 4000 300 kilograms engine is nine put egg meters over second squared and now you complain that into your calculator and get that the force of trust a secret, too. 40,000, 140 mutants. So this is our answer for part A. Now I'm gonna move on to part B in part B. Ah, we're told that the helicopter is going down on the speed is decreasing. So what this tells us is that the force in the opposite direction to the movement is the bigger force. So there is acceleration in the positive direction. So we've used for fertility of the physical and same sex acceleration plus gravity. We can substitute and get that if the sequel to 4300 kilograms times acceleration, which is 3.2 meters over second square, plus 9.8 meters over second squared. And did you complete that into your cast later and get the first of the trust is equal to Sorry, that's 55 1000 900 Newtons. So this is Iran surfer part be now let's move on to part Sit. Part C. We're took that the helicopter is racing on, the spirits increasing. So what this tells us is that the big air force is in the direction of movement in this case, FT is the bigger force and acceleration is the same as in the previous case. So we could the same answer. I seem party. Okay, so this is our answer for part C. Let's move on to part dick. Important. The the helicopter is rising at a steady speed. So what this means is that there is no acceleration. Uh, the forces cancel each other so f t and F d r equal in magnitude. So now we can just substitute if g really in the G eso for 50. So must was 4300 kilograms energy his 9.8 meters over second script. So you replace that intercultural enduring you'll notice that this answer is the same a sport A because in both there, there is no acceleration. So this is 42,000, 140 new tints, and this is sir answer for Part D. So let's move on to art. Hey, import. The helicopter is racing. So moving upward on this page is decreasing. So what this tells us is that the big air force is the opposite to the direction of movement. So force of gravity is bigger than 50 and acceleration is in the downward direction. So we're gonna use a Formula 50 sequel to mass acceleration. Those brevity, but acceleration this time is in the negative direction. So when was substituted, I'm gonna go ahead and substitute. So this is was 43 Alison, gender grams acceleration, we're told, is 3.2. So it's gonna be negative. 3.2 major silver, second squared and gravity his name make meters over second screen. Okay, so now Rican soul for EFTY and we get that it is equal to 20,000 uh, 300 80 new tents, and this is our answer for part.


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