10. Conservation of Energy

Energy with Non-Conservative Forces

# Energy Conservation with Air Resistance

Patrick Ford

863

11

6

Was this helpful?

Bookmarked

Hey guys, let's put this one out together here. So we have a two kg object, gets dropped from a height of 80 m and reaches the floor with 30. But in this case there's actually some air resistance here. We're going to calculate the work that's done. Let's check out this problem here. Let's go ahead and draw our diagram. So we've got the floor like this, this y equals zero. I've got a two kg object and it's gonna be dropped. Which means that the initial speed is zero, but once it falls to the floor, what happens is that it's going to reach the floor with some final speed. This is the final and this equals 30. Doesn't matter if it's positive or negative because their kinetic energy is always gonna be final, right or is always gonna be positive. Now, what happens is throughout the motion throughout the fall of this object, it being pulled down by gravity, there's MG. But there's also air resistance that I'm going to call this f air. Usually we kind of neglect air resistance but in this problem we want to calculate the work that is done by this force. So let's go ahead and check out our energy conservation equation. Right? We're gonna use conservation of energy. We've got our diagram and now we're gonna go ahead and do our conservation of energy. So this is gonna be K initial um Plus you. Initial plus work done by non conservative equals K final plus you final. So we got one last thing here, you're actually falling from an initial heights. This is why initial of 80. So this is the initial. Okay, so we have no initial kinetic energy because the initial speed is zero. We do have some gravitational potential because we're at 80 m and that's above are zero points. So we're gonna set the zero point of gravitational potential here. The risk that work done by non conservative forces because we do have a resistance and that's a non conservative force. Remember that worked? Non conservatives either work that's done by you which there's none of in this problem. Plus the work done by friction, basically friction and air resistance are kind of the same thing. Air resistance is really just friction through the air. So this is really just gonna be F air. The work that's done by this force here and this is going to be equal to K final place you final. So there is some kinetic energy final but there's no gravitational potential interview because you're at the ground. So what happens is our equation simplifies to this is gonna be M. G. Y initial plus the work that's done by F air and then equals the kinetic energy final is going to be one half mv final squared. So, let's see here, I know em I know g I know the initial heights. I also know em and I know the final squared. So all I have to do is just go ahead and move everything over. So this W. F. Air here, W. F. Air is just gonna be um this is gonna be uh let's see. You actually can't cancel out the masses because it doesn't exist in every single one of these terms, Right? This W. F. Air doesn't have an eminence. We can't cancel that out. So what ends up happening is you're gonna get let's see um you're gonna get one half. This is gonna be one half. Do I have this here? Yeah, there's one half of two Times 9.8 And then Times 80. So that's the first time. And then when you subtract it, you're gonna subtract it from two times 9.8. Uh and then this is gonna be I'm sorry. This is not A. T. This is the the final. So this is actually 30 square. There we go. Sorry about that. So you've got one half 9.8 and then we've got 30 squared minus two times 9.8 times 80. Alright, so that's initial heights. So then you go ahead and work this out. What you're gonna get is you're gonna get negative 670 jewels. So why don't we get a negative sign? It's because work is actually removing energy from the system. That's exactly which we should expect. So, we got a negative number here because we got we have energy that's being taken out by air assistance. All right. So, we can use energy conservation equations to solve problems with resistive forces. Like when we have air and water resistance basically because they just act like friction. So we can just sort of calculate them as a non conservative work. All right. So let me go ahead and quickly solve part B. Now. Barbie is now asking for the average force of air resistance. All right. So we want to figure out basically what is this F air? What's what is this F air? What happens is you can think of this F air as being a constant force that's acting on this object as it falls. So it's a constant force that's being act that's being exerted over some distance D. Which is really just my delta Y. So what happens is I can use the work energy or sorry, the work done by constant force equation. Work is really just gonna be F. Air time's D. Times the co sine of the angle between those two things. So you're displacements down your forces up. Therefore this is just going to simplify, this turns into a negative one. And basically what happens is you're going to get that the W. F. Air is equal to f. Air time's D. So now we want to figure out what's this force. We actually know what the distance is. It's just gonna be my delta Y. So I can go ahead and calculate this. So my F air is really just going to be the work that's done. Which I know is negative 670 divided by my delta wine. My delta Y. Is actually just 80. Or it's actually rather just negative 80 because technically um it's gonna go downwards like this. Also I just want the negative science to cancel so that I get the magnitude of the force and the force is equal to um what I get Is 8. Newtons. So that's the average force of your resistance. All right, so that's it for this one. Guys, let me know if you have any questions.

Related Videos

Related Practice

Showing 1 of 8 videos