https://youtu.be/vgFw-wCIGSo
PHYS 1101: Lecture Thirteen, Part Eight
The next example has you putting these ideas together from the previous examples that I’ve done. You have a tilted coordinate system to work with, very similar numbers to what you had above, a 10-kilogram mass on a slope. I’ve changed the angle of the slope. And you need to, then, evaluate the motion of this block. Not, now, it’s no longer on its own sitting on the surface, but there’s a rope attached to it that goes over a pulley and is attached to this 3-kilogram block hanging at the other end.
There’s a whole series of quiz questions now that ask you about different aspects of that to help you solve this problem. Ultimately, you’re going to be typing in the value of the acceleration of the block along the slope.
When you’re faced with a scenario like this where you don’t immediately know for sure what direction it’s going to move, is this block going to accelerate down the slope or up the slope? This scenario, each scenario would be possible depending on the angle of the slope and these masses.
I advise that you pick one and then be consistent with that. When you get a number for your acceleration; if it turns out to have the opposite sine to what you thought, then it would tell you that it’s the other scenario that’s happening, given the masses and the angle.
So, let me start you off by assuming you have a motion diagram for the block along the slope that looks like that. That says that the force due to gravity or the part of it along the slope for this 10-kilogram block overcomes the tension in the line trying to keep it from sliding down the hill. Therefore, the acceleration is in that direction. Assume that and work with it as you work the problems.
Regardless of this assumption, you still can consider how the accelerations compare. That is, the acceleration of block two compared to the magnitude of the acceleration of block one. That’s question 15.
Question 16 is asking you about the direction of the acceleration vector for these blocks. Go with the assumption that I noted at the top. For block one, what arrow best represents the direction of its acceleration? Everyone should get this right. That’s question 16.
Question 17 is going to be what arrow best represents the direction of the acceleration for block two? For question 18, what’s the best coordinate system to use to evaluate our f equals ma problem for mass one?
Remember, you can pick the coordinate system that you want for each object and they don’t have to be aligned the same; they can be separate. The only thing you have to be sensitive to is be sure that you connect the accelerations properly given those two coordinate systems. And that likewise, the direction of Third Law pair forces get assigned properly, based on the coordinate systems. So, for mass one along the slope, what’s the best coordinate system to use? Everyone should get this right.
Question 19, this is for block mass 2. What’s the best coordinate system to use to apply the problem solving steps to the mass hanging off the end of the ramp? And if you’d like, do it as I do where I separate it on the page. On the left side of the page, I’m going to write out my problem solving steps, applying Newton’s Second Law to block one. On the right side of the page, I’m going to write them out for block two.
And that’s what my subscripts here indicate. For block two, the one hanging off to the left, how will the acceleration direction, the scalar components compare? Let’s assume you go with the typical convention with positive being up for the block off to the left. Which of these is right?
Question 21, what’s the magnitude of the component of the gravitational force for block 1 that’s along the slope? What’s the magnitude of the gravitational component that’s perpendicular to the slope?
Question 23, calculate the value of the normal force on block 1.
Twenty-four, enter the number for the magnitude of the friction force on block one. You have the same coefficient of kinetic friction of 0.1 for the scenario.
Question 25, how large is the tension in the rope? And then, last, you should have all the pieces that you need to put it together, then, for what’s the magnitude of the acceleration?
And then, I’m going to end the lecture with a bonus point opportunity for exam two. We’re still going to have our sample exam where you can earn bonus points, which is a copy of last semester’s exam two. But in addition to that, you can earn two extra points if you can correctly solve this problem that I laid out at the very beginning of the lecture to motivate Newton’s Third Law.
What is the tension that you need in this rope in order for the blue block to accelerate to the right at 4 meters per second squared? You should have enough tools, now, to be able to solve that and this is about as complicated as it gets. You have to take it slowly and just break it down.
Again, the strategy I might use, it’s a lot like what I pointed out here at the end of question 26. This quantity that you’re after, you know it’s going to show up. It is one of the forces on block one. Therefore, you really want to start with the a(x) is equal to the sum of the horizontal forces divided by m for the purple block. Start there.
This variable will be in this equation, but you’ll discover that there are other force values that you don’t know that you need a value for. And that’s then, what’s going to have you focusing on equations involving this block to solve that. So, keep breaking it down, keep going after the pieces that you need in order for this equation to give you the value of T1.
Okay, work that out. Send me your answer, three digits is fine. Send it to adavies@uncc.edu. That’s the end of lecture 13.