A 6750-kg helicopter accelerates upward at 0.80m/s² while lift...

Question

A 6750-kg helicopter accelerates upward at 0.80m/s² while lifting a 1080-kg frame at a construction site, Fig. 4–66.

(c) What force does the cable exert on the helicopter?

Accepted Answer

Hey, everyone in this problem, a 6800 kg aircraft ascends at 0.82 m per second squared while lifting an 1150 kg container. We're asked to determine the magnitude of the force exerted on the aircraft by the rope. We're given this little diagram. We have our aircraft, we have this rope between the aircraft and the container. Then we have our container and we're showing that the container has this force of tension acting upwards. And so that's the rope connecting it to the aircraft. And then we have the force of gravity mg acting downwards and we have this upward acceleration. We're given four answer choices. All in Newton's option, A 1.2 multiplied by 10 to the exponent four. Option B 2.2 multiplied by 10 to the exponent four. Option C 4.0 multiplied by 10 to the exponent four. And option D 5.2 multiplied by 10 to the exponent four. So we're looking for the magnitude of the force exerted on the aircraft by the, so let's think about the aircraft and all of the forces we have acted. Ok. So if we look at our aircraft, ok. We know that we're gonna have this tension force acting downwards and the container is below it. So we have this force of tension ft acting downwards and we also have the force of gravity, which we'll call FG A. Ok. So the force of gravity acting on the airplane. Now, this airplane is accelerating upwards. So we know that there must be some upward forces and so maybe the airplane's engine or the propeller or the wings, some combination of those are providing some upward force for this aircraft. So we're just gonna call this F up. So we have some upward forces and we really don't have a lot of information about this, right? So to look at the aircraft itself and try to figure out this tension force that we're looking for is gonna be difficult. Ok. So let's switch over to the container and think about the container and see if that's gonna help us. Let me think about the container. We know that we have a force of tension acting upwards and we have the force of gravity acting downwards and that's it. Those are the only two forces acting on that container. Now, this force of tension acting on the container is the exact same as the force of tension acting on the aircraft, right, equal in magnitude opposite in direction, but it's the same tension force because it's the same rope. And we just have this single rope connecting the two. So what we can do is use what we know about the container to find the magnitude of this tension force. That's what we're really looking for. So we know that the container is going to accelerate upwards at 0.82 m per second squared because again, it's connected to the aircraft by the rope. So if the aircraft is ascending at 0.82 m per second squared, then the container must be ascending by that much too. Otherwise, this rope would break. Ok. So that container is gonna have that same acceleration we're gonna take upwards to be our positive direction. And now we can think about the sum of the forces acting on this container. When we do that, we're gonna look strictly in the vertical or the y direction because that's the only direction that we have forces. So we have the, the some of the forces acting on the crate. It's gonna be equal to the mass of the crate multiplied by the acceleration of the crate that's using Newton's second law. Now the sum of the force is acting in the positive direction. We have the force of tension in the negative direction, we have the force of gravity. So we get FT minus FGC. This is gonna be equal to the mass of the crate. MC multiplied by the acceleration of the crate, which we've just talked about being the exact same as that acceleration of the air and we just have MC multiplied by that acceleration. A and we want to solve for the force of tension. So we're gonna move the force of gravity to the right hand side. We get that the force of tension is gonna be equal to the force of gravity acting on the crate plus the mass of the crate multiplied by the acceleration. The force of gravity we call is given by MG. So we get the FT is gonna be equal to the mass of the crate multiplied by the acceleration due to gravity G. Whilst the mass of the crate multiplied by the acceleration. A. Now we can go ahead and substitute in our values. When we do that, we're gonna factor out this mass of the crate that we only have to write at once. So we get that the force of tension is equal to 1150 kg multiplied by G 9.8 m per second squared plus a 0.82 m per second squared. And when we work this out, we get that our force of tension FT is gonna be 12,213 newtons. We're gonna write this in scientific notation with two significant digits like the answer choices. And so we can write this as the force of tension is approximately equal to 1.2 multiplied by 10 to the exponent for noons. OK. Now, in terms of the direction it doesn't matter. We were asked just to find the magnitude. And so that's what we found here is that magnitude. Again, this is the force of the exerted on the aircraft by the rope. Ok? In this case, we're looking at the container, this is the force of that rope on the container. But we know that those forces are the same because it's the same rope, right? So if we take a look at our answer choices and we compare what we found, we can see that this force exerted on the aircraft by the rope is going to be option A 1.2 multiplied by 10 to the exponent for noons. Thanks everyone for watching. I hope this video helped you in the next one.

Struggling with Physics?

A 6750-kg helicopter accelerates upward at 0.80m/s² while lifting a 1080-kg frame at a construction site, Fig. 4–66.
<IMAGE>
(c) What force does the cable exert on the helicopter?

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Struggling with Physics?

A 6750-kg helicopter accelerates upward at 0.80m/s² while lifting a 1080-kg frame at a construction site, Fig. 4–66.<IMAGE>(c) What force does the cable exert on the helicopter?

Watch next

Vertical Forces & Acceleration practice set

A 6750-kg helicopter accelerates upward at 0.80m/s² while lifting a 1080-kg frame at a construction site, Fig. 4–66.
<IMAGE>
(c) What force does the cable exert on the helicopter?