Problem statements
Solution video - H18.A
Solution video - H18.B
DISCUSSION THREAD
Please post questions here on the homework, and take time to answer questions posted by others. You can learn both ways.
HOMEWORK 18 - Fall 24
45 thoughts on “HOMEWORK 18 - Fall 24”
Leave a Reply
You must be logged in to post a comment.
For the approach to part A, do we treat the cylinder as a point particle force acting on the block to find the maximum W_c in terms of W?
I believe you have to consider the normal force acting on the cylinder as well.
I think you also have to consider the north forces on the cylinder. Because of this you are not able to treat it as a point particle
I believe that you might be able to treat it somewhat as a point particle, because there is a normal force between the angled surface and the cylinder which is going through the center of the cylinder, and the force from the cylinder on the block, which is directly in the x direction, which is also going through the center of the cylinder, so every force acting on the cylinder is going through the center point, which is pretty much the definition of treating something as a point particle.
You can treat it as a point particle because all of the forces run through the same point so there is no moment. From this, you can use your equilibrium equations to solve for forces between the block and the cylinder and continue from there
I believe that you should consider the normal forces on the cylinder. Since it is at an angle with the surface, it would likely be easier to break the normal force into components in the x- and y-directions. It also is a smooth cylinder, so there is not going to be any frictional forces on the cylinder with the surface.
In the sense that you do not consider any moments about the cylinder, you are treating it as essentially a point particle.
I think you can as you have to consider the normal forces on the cylinder
Should I be looking for the resulting moments from the forces to find the tipping or sliding of the block?
Moments are typically used to find the tipping case solution, for sliding you will want to use your typical x and y force equillibrium equations. To find the tipping case you will need to take the moment about the point the block will tip over (which I believe is A).
You use the Moment to find the maximum weight before it tips, and the Fx equilibrium equation to find the maximum weight before it slips.
I think you have to take into consideration the Normal Force N acting towards the cylinder isn't it?
For finding the largest weight for which the system remains in equilibrium you would have to consider the normal force of the angled plane on the block and the normal force acting on the block by the cylinder. The normal force of the block also is used as is it is equal to the weight of the block.
For the cylinder, because it is smooth, am I right by assuming there is no friction acting on it, even though the surface is rough? The diagram makes it unclear if the surface to the right of the cylinder is also rough or not, but I assume it isn't due to the problem statement not mentioning it. Thus, are the only forces acting on the cylinder are the two normal forces from the block and the surface, along with the weight?
I believe that is correct. I think that is the point of including the detail about the cylinder being smooth. If the cylinder wasn't smooth, we would need its specific coefficient of friction, which we have not been given. And it would be and equal assumption as having no friction, if we assumed the cylinder had the same coefficient of friction as the block.
Would we solve this problem using two FBS, one for the cylinder and one for the block or would we only use one for the whole system?
You would use two because there are two different components of the system that you are focusing on. This way you can put each part in equilibrium independently.
You would usually draw as many FBD's as there are parts of the system. It is most helpful for visualizing different tensions that may appear on the same cable.
Yes, I would use two FBDs, one for each object because the interacting forces on the two objects, while related in part, are different.
When considering tipping or slipping are you supposed to look at the moment at point N since that connects the two objects or can you find the moment separately and then add them to see if it is positive or negative?
I think you can take the moment at point A (since that is where the block would tip at), then solve for Wc.
Yes, for tipping consider the moment about A. For the slipping condition, you should not need moments.
For part a, do we just use the equilibrium equations to solve for the weight, or do we also have to use the moment?
For part a I only used equilibrium equations. By splitting it up into the equilibrium for the cylinder and the block and then substituting values between the two you can solve for Wc in terms of W. The reaction force between the cylinder and block is present in both sets of equations so you will end up using that value, at least that's how I solved it.
I used the moment equation to solve for the weight in the tipping case, then used equilibrium equations to find the weight after finding the normal force from the moment equation.
So the force of the cylinder acting on the block is what causes slipping or tipping right? If the force is just right below slipping conditions but above tipping does that mean it is currently tipping and impending slipping or just tipping?
The slipping and tipping is based off the Wc value that you get in terms of W. The smaller value will intend either tipping or slipping.
Is it correct to assume the weight, and proportional normal force, factor into our guess weather the object is slipping or tipping?
The way I approached this problem is by finding two values of Wc: the maximum value of Wc that would prevent slipping (eg: the sum of forces in x and y direction for the box is 0) and the maximum value of Wc that would prevent tipping (eg: the moment about a point on the box is 0). The lesser of these two values will be the largest possible value to remain in static equilibrium. Whichever value you discover is smaller, whether the tipping or slipping, will be the impending motion if Wc were to increase ever so slightly.
While solving this, are we supposed to find a relationship between the normal forces so then we can have an equilibrium equation where the only unknowns are b and h?
If I am not mistaken, yes, a relationship between the normal forces is needed in order to setup the equilibrium equations, and then you will proceed to solve for the unknowns.
I may be misinterpreting your question however I will answer to the best of my abilities. There exists two systems the block and the cylinder. The relationship between the two come from the normal force of the block acting on cylinder and vice versa. Solving for this force is the same in both scenarios, slipping and sliding. The difference comes from which equation is in equilibrium for the system of the block. Through these equations the h and bs within them should cancel out and a relationship between the weight of the block and weight of the cylinder should appear in both the moment equilibrium and horizontal equilibrium. I hope this helped answer your question.
I don't understand part b. Is it asking the impending state for the block or the cylinder? At first it says "for the cylinder weight" and then says "is the block" so I'm confused.
What it is trying to imply is how the cylinder weight affects the block. In other words, from your answer in part A, you found the largest weight of the cylinder for the system to remain in equilibrium. The cylinder acts on the block, which is the only object that can tip or slip. If you were to assume it is tipping or slipping, you want the lower of these values since that is the maximum value you can have for equilibrium. Hope this helps.
I am struggling to figure out the angles at which the normal forces act on the cylinder and block, nothing I think of seems right
The normal force from the block on the cylinder, acts purely horizontally to the right because it's perpendicular to the block's vertical surface. On the other hand, the normal force from the inclined plane, acts perpendicular to the surface of the incline. When you use trig and the incline 4:3, you can calc the angle of theta. Hope that clears things up!
Does this mean that the normal force on the block from the cylinder also is vertical, just in the opposite direction?
*horizontal
Is the first step just writing out the forces in the x and then the y direction and then finding the moment at A?
Yes, find the sum of the forces in the y and x directions acting on the block, then again on the cylinder. Find the moment about A in order to find the state of the block (tipping/slipping).
The moment about a would help you to find the slipping vs tipping whereas the sums of forces are going to be able to help you with finding the largest weight to remain in equilibrium. You should not need to find the moment in part a since there is nowhere to find the moment from.
When summing the moment about A, do you have to add the distance from the radius R to h to get the contributions of the normal force from the incline and the weight of the cylinder in the moment equation?
Yes I believe you need to include the distance from the cylinder’s radius R to h for the moment contributions of the normal force and the cylinder’s weight.
I know this homework is past due, but you do not need to include R when summing the moments about A. The force contribution of the weighted cylinder is only horizontal and applied at a height of 3h. So that is all you need. Another way to think about it is that when poking something with a long stick, the force on the object is equivalent to if it was a short stick as long as the direction stays the same.
It makes me wonder if we’re solving for impending slipping or impending tipping for the block, will the cylinder also follow along similarly to if the block were to slip for example? I know we aren’t solving for the cylinder but it’s a hypothetical thought to think about for other system(s) acting on the one we solve. Maybe at least something to think about for the real world.