Problem statements
Solution video - H20.A
Solution video - H20.B
DISCUSSION THREAD
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HOMEWORK 20 - Fall 24
58 thoughts on “HOMEWORK 20 - Fall 24”
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What should the answer be in terms of? The best I can get is in terms of μ and W, and I'm not sure I can simplify it further. Do I need more equations to solve for μ and W?
My answer was in terms of μ and W
Yes, I think that's the only way that you can do the problem. I'd just make sure you simplified completely
My answer was also in terms of μ and w. I don't believe you need any more equations to simplify it further.
Since we are not given a value for μ, my answer included it.
Since the problem statement gives values in terms of μ and W and no values are given for them, I believe you can assume they can be used in your final answer.
The answer should be in terms of mu and W. After this state you cannot simplify it any further.
Should we assume there is friction between the wedge and the ground or just between the wedge and the block?
I would say you also need to assume friction between the wedge and the block since there is a μs pointing to the intersection of the ground and wedge in the lower left corner.
the friction is the same for both I think
Do we have to do anything with reaction forces at B because it is a pin joint?
Due to B being a pin joint there are no moment reactions at B. There are X and Y reactions at B, but if you define the moment equilibrium equation at B, you need not consider them as their lines of action pass through B.
Yup, if you calculate the moment around point B that will help eliminate the reaction forces and some of the component forces from force normal/friction from the wedge in your overall calculation
You need to put them in your X and Y equations, but you dont really use those on to solve bc you don know the reactions, and then when you take the moment at b they don't matter.
You might have to consider the x and y reactions as a pin joint, but given the method you might use to solve the problem you can definitely cancel out those forces. At the same time, you can't initially, without defining how you plan on solving the problem, ignore those reactionary forces.
Yes, you need to consider the reaction forces at B because the pin joint can provide both horizontal and vertical reactions. These reactions are necessary to maintain equilibrium, especially since the wedge force P and the friction at A will introduce forces in both directions. Make sure to include them when writing the equations for equilibrium to solve for P.
Do we write our answers in terms of the coefficient and W? Also, is it only necessary to use one equation for the block(moment)>
My answer contains both the coefficient and the Weight as we are not given a value for the coefficient of static friction, so there is not a way for us to cancel out the value for our answer. When solving for the normal forces you're going to have to equate the friction forces to the coefficient times the normal forces. Therefore, your answer could be in terms of both coefficient and the Weight of the block.
My answer contains both the coefficient and the Weight as we are not given a value for the coefficient of static friction, so there is not a way for us to cancel out the value for our answer. When solving for the normal forces you're going to have to equate the friction forces to the coefficient times the normal forces. Therefore, your answer could be in terms of both coefficient and the weight.
My answer had both μ and W, that's fine?
That should be fine, I don't think its possible to be able to answer it without both (unless their given). The way I thought about it is that P is dependent on the friction caused by the object on the ramp.
Yes because there is nothing saying the values of mu and W, so they are okay to leave in the final answer if it doesnt simplify further.
Do, we need to factor in the weight of the wedge? I don't know if factoring it in would have any impact, but often the question specifies not to, such as in the lecture examples.
In my lecture and the lecture book, we were told that the wedge will often be of negligible weight and dimensions in comparison to the block. Considering that the problem does not specify a weight for the wedge, I think it's valid to assume that the weight of the wedge is negligible in this problem too.
According to my professor, we can pretty much always assume that the weight of the wedge is negligible. They'll either tell us, or we can assume that it is not necessary within the problem.
Since the point of contact with wedge of the block at A is round, are the friction force and normal force aligned with the x and y axes respectively (straight up and horizontal), or are they at the angle of the wedge and normal to the wedge respectively?
The friction force is aligned with the angle of the wedge and the normal is perpendicular to that. They are not aligned with the axes even though it is a round surface contact.
I assumed that the friction force would be along the slant of the wedge since the corner of the wedge would move along the slant as the wedge is moved. For the normal I set it orthogonal to the wedge.
When looking at the sum of the moments about point B, wouldn't the friction and normal force from the friction have to be horizontal and vertical because you don't have any known height of the block?
I don't think so, because if you look at how the friction and the normal force are on the bottom left corner, the normal force would have to be diagonally up and to the right and the frictional force would have to be diagonally downward and to the right to keep the block stationary on the wedge. When you do the sum of moments you will have to use cos/sin of the angle for each force and then multiply 3d, but an angle will be necessary because having to keep the block stationary on the wedge means the forces will have to be at an angle to cancel out the angle from the wedge.
You have to remember that because this is a pin joint. There is no moment at B. What is happening at B are X and Y reactions at. So, when solving this problem you need not consider the reactions, Fx, and Fy, as passing through B. After that solve for their respective forces and then after finding the required normal force equations for the normal force between the floor and ramp, and then in between the ramp and the block, after this you can solve for P.
In the given statement it mentions that the block is inhomogeneous, in examples I have seen strictly homogenous blocks. Does this effect our approach to this style of question at all?
Inhomogeneous means that the density of the block is not uniform, meaning the block's center of mass is not acting directly in the middle like we usually see. In this case, note that the block's center of mass is shifted slightly to the left. This difference shouldn't change your overall approach to the question, just be sure to account for this new position of the center of mass when summing the moments.
It just means the density isnt uniform. you only need to focus on the block's center of mass, though, which is given.
This simply means the density of the block isn't uniform and therefore its center of gravity is not at the center of the block. The approach is the same though the force W doesn't act in the center as is shown in the image.
Why do we say that there is friction between the wedge and the ground as well?
There is friction between the wedge and ground because of the force P acting on the wedge to the right. You can imagine pushing the wedge in the direction given and since the surface is rough, there will be friction on the wedge and ground as well as the block in the same direction.
You know there is frictions because the system diagram shows the coefficient in between the ground and the wedge
When looking at the impending motion should you do it by each object or can you assume they would be moving in the same direction?
I believe that you should do it by each object.
Great question, I believe it's generally best to treat them separately. Different external forces are acting on each of the objects, for example, the wedge has applied force P and friction with the ground, and the block has friction between itself and the wedge and weight - from an example we saw in lecture, there could also be a wall restricting either object from moving horizontally. To generalize the process, I would analyze the forces for each system individually before assuming that the objects move together in the same direction because that might not always be the case.
are the joints, a roller and a pin?
I'm pretty sure that's correct, a roller at A and a pin joint at B.
Since the problem is asking about the minimum force needed to "raise" the block at A, should we assume that the IM of the block is upward?
I assumed the IM of the block is upwards since the wedge provides an upward force.
Is it ok for my answer to be in terms of both u and w?
Yes it should be fine for the answer to be in terms of u and w , as they don't provide specific values.
Yes, the answer should be in terms of both u and w.
Does the force between the block and the wedge act at an angle, perpendicular to the wedge's angle, or vertically?
It acts perpendicularly to the wedge's surface. Hope this helps.
Do we need to draw 2 separate systems for this? Also, is there a normal force from the ground on the wedge acting vertically up?
Does the friction force at just the wedge act perpendicular to the surface? Or does it go against the P force?
In the first step, I set the sum of vertical forces to zero to find the conditions where the block starts lifting at A. For the second step, how do you correctly set up the moment equation about point B while accounting for the friction force at A?
Does having a quadratic in the final answer sound right?
Does the round surface generate any other reactions than the perpendicular normal force?
I believe the surface between the triangle and the block you are referencing would only have the normal force and the frictional force. Keep in mind that the friction force would act in opposite directions as they block moves. But yeah, you are correct that it has a perpendicular normal force at that rounded surface point.
Did this problem needed to be solved for if the box was in impending tipping or impending slipping?
This is not a slipping or tipping problem, it is a wedge problem. It says in the problem statement that you should find the minimum value of the wedge force in order to raise the block. Thus, to raise the block, you would need to push in the wedge. That means that your impending motion would be the wedge moving in the positive direction to raise the block. From there, you can determine the direction of your friction forces and solve for the correct forces.