37 thoughts on “HOMEWORK 19 - Fall 24”

      1. Yes, you will need to determine the angle of wrap. Since there is friction along the cylinders, the tension will not be uniform throughout the cable. Thus, you will have to use the equation we learned last class period to solve for the tension along each segment of the cable.

      2. Yes! as I previously stated you need the angel of wrap for the Tl/Ts=e^uB equation. In this problem it is easy to look at it as 2 sperate systems, each with their own wrap angle.

      3. Yes! as I previously stated you need the angel of wrap for the Belt friction equation. In this problem it is easy to look at it as 2 sperate systems, each with their own wrap angle.

      4. You are correct. The angle of wrap is important for this question as the tension is not the same throughout the cable. Because of this you will have to use the angle of wrap and plug it into the equation to find the minimum and maximum tensions.

    2. The angle that F is applied does matter. Use the 3, 4, 5 triangle given to determine the angle at which it is applied with respect to the horizontal.

    3. Yes, you'll need it when finding the components of forces for equilibrium. You can use cos and sin of the 3-4-5 triangle to find the force in the x and y direction.

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    4. Yes! the angle the force is applied at is very important because it is the beta value in the Tl/Ts=e^uB equation, which is used in the solution. To find the angle of wrap around the pole 2 you need to know the angle, make sure to convert to radians.

    1. I believe that yes, you should check both scenarios. One should be when the block is sliding up, so impending upwards motion, and the other should be when the block is sliding down, so impending downwards motion. That way you can find the minimum and maximum forces in terms of W and thus have a range of values.

    2. For sure!! To find the total range of the force, you'd have to consider the impending force in both directions; both in the direction of the force and the direction of the weight. As a result, you'd know the necessary range for static equilibrium.

    1. You could think of it as two separate systems by sectioning off cylinder A with block C and the other system cylinder B with upward Force F. However, it just involves more time and work while you could just take it as one system and find the Max force and the min force. The Max force you just equate F to the larger tension and W for the smaller tension and for the min force you just do the opposite.

    2. By thinking about the problem as two separate systems around each cylinder you make the problem much more clear to solve. In lecture we covered a similar problem and I was told that in a case like this we should draw a free body diagram for each cylinder cable interaction so your work should follow that.

    1. Yes, I believe you can assume that! Assuming you have a standard x and y coordinate system the weight will always be straight vertically down in line with gravity.

      1. Can you still think of it as one system with one angle of wrap being pi/2 and the other being 53.13? Or because there are two angles of wrap does it have to be considered as two different systems?

        1. Yes, you can think about it as one system that has a total angle of wrap equal to the sum of the two angles you mentioned; also, make sure it is in radians, not degrees for the second angle.

        2. You should have 4 FBDs, but you should have two friction equations (then use the other force equations to find F and relate the tensions to W). The two friction equations should have three tensions in total, so you can use the tension that they have in common to combine the equations.

          1. For your 4 FBDs, did you create two for differing scenarios of each cylinder? For example, two FBDS of cylinder A assuming two different directions of friction?

    3. You can assume that the wrap around A is pi/2 radians since the cable is horizontal between A and B, this means that the wrap makes full contact with the entire quarter of the circle that it is wrapped around, unlike at B where the cable is at an angle and it doesn't make complete contact with the cylinder.

  5. In order to produce a range response for the answer, is this gathered from assuming that F is greater than T as a scenario and F is less than T for the other scenario? If not how is a range result determined?

    1. The range result is determined based off of what direction the friction force is with respect to the cable. If the direction of force friction is suppose to the right, it would take less force to pull up block C. That would be your lower value of force in the range. The same goes for the opposite direction of force friction.

    2. I believe that a range result is found by assuming two cases for which the impending motion is directed, one of the block moving up and one of the block moving down. The scenarios will give one smaller force and one larger force.

      1. I also did this. I first got both angles and multiplied by pi/180 to turn them into radians and summed them up to get theta, after that I just used the equation seen in class (TL/TS = e^ coefficient of static friction * theta. And I then solved for both cases which was finding the minimum and maximum force applied to D to make C remain in static equilibrium. Let me know if this process makes sense.

        1. Yup, this worked for me. If you know the TL/TS equation you can simply switch the variables around for the two cases and get your answer super simply!

    3. I think I understand what you are trying to say and I believe that is correct. To find the range, you need to consider impending motion in both the upwards and downwards directions. This means when the system is about to move downwards towards point C due to the weight(when, as you say, T is greater than F at point D), as well as when the system is about to move upwards due to F(F>T at point D). One of these values will be your minimum while the other will be your maximum F.

    1. Yes the range values are all that exist between the maximum and minimum values. There are no other values because the inequalities that come from each impending motion assumption lineup allowing for one long inequality between a max and min.

  7. Please let me know if this is wrong, but I think the allowable range is the minimum force less than or equal to F less than or equal to the maximum force? It makes logical sense to me but I wanted to ask before I left that as my final answer.

  8. The angle that the force F is applied at is important because it affects how much of the cable wraps around the cylinder. This wrap angle determines the amount of friction between the cable and the cylinder, which influences the tension. You can use the 3-4-5 triangle to find the angle at which the force is applied, and you also need to calculate the wrap angles for both cylinders. These angles are necessary to apply the equation for tension around each cylinder and find the correct range of forces for equilibrium.

  9. Would the wrap angle calculation be the angle between C to A minus B to D? We don’t calculate the angle from A to B cause it’s straight which is 0.

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