| Problem statement Solution video |
DISCUSSION THREAD
Ask and answer questions here. You learn both ways.
DISCUSSION and HINTS
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw a free body diagram for the block.
Step 2: Kinetics (Newton's 2nd Law)
Since the position of the block is given in terms of a radial distance r and a rotation variable θ, a polar description is recommended for resolving the forces acting on the block.
Step 3: Kinematics
Since you have used a polar description for resolving forces, you should also use a polar description for acceleration; that is, aP = (r_ddot - r*θ_dot2)er +(r*θ_ddot + 2r_dot*θ_dot) eθ. What is true about r_dot and r_ddot when the cable remains taut?
Step 4: Solve
At this point you will have two equations in terms of two unknowns: the normal contact force and the tension force. Does your answer for the normal force on the block make sense?
Would r_dot in this case a constant? Or do we need to solve for the r_dot and r_ddot since the statement seems like it’ll move as the arm moves. The problem statement doesn’t say explicitly if r is a constant or not.
The cord holds the block in place within the tube. Therefore, r does not change in time (r_dot = r_ddot = 0).
Would you include the normal force acting on the top and bottom of the block or would it be the same thing?
From my understanding, you are asking about block M. Since the top and bottom guides acting on the block to guide it are parallel, the normal forces would effectively cancel out.
Actually, the contact forces do not cancel. The block will be in contact with only one side of the guide. The force acting on the block by the guide is the force that is needed for the block to maintain its path.
Typically, you do not know on which side that the contact occurs. Just make an assumption of one or the other, and let the "sign" of final answer tell you on which side that this contact occurs.
If the block is contacting the slot, it will be in contact with only one side, and not both. Generally, on problems as this, you will not know on which side of the slot that that the contact occurs. Simply choose one side, and solve the problem based on this.
* If the sign for the contact force is positive, then your choice was correct.
* If the sign for the contact for is negative, then your choice was incorrect, and the block contacts the other side.
for part C, do you assume that the tension force =0 to find the minimum angular velocity needed to keep the cable taunt?
Yes, that will work.
This is what I did, because if the tension is zero you can use all the other known values to find the minimum angular velocity
Should we give our answer as i-j vectors or just scalar values?
I gave part (a) as a scalar with units of Newtons, part (b) as a vector in the $\hat{e}_{\theta}$ direction with units of Newtons, and part (c) as a scalar with units of rad/s.
I am not sure if that's correct, but it seems ok.
That is fine.
For part c), when the cable slackens, I set T = 0 to find ω. But to do this, it seems to me that we have to find r_dot and r_ddot, which will not necessarily be zero if the cable is not taut. How can we do this?
You are asked for the minimum rotation rate that puts the tension equal to zero at the position of interest, but not slow enough that the block is sliding along the slot at that position. At that rate, the block will begin to slide for subsequent rotation of the arm.
Should we report tension and normal force as vectors?
Yes, I think we report the solution in the coordinate system used to solve the problem.
If we need to answer as a vector, should we answer in terms of er and e(theta) unit vectors or as i and j unit vectors? Or, would it be acceptable to answer as scalar quantities?
Should we include the components of mg in the kinetics equations? I thought it should be included as it is a force acting on the block, but it was not included in example 4.A.10 done in class.
The problem statement for 4.A.10 says that the arm moves in a HORIZONTAL plane. This means that the gravitational force acts perpendicular to the page. As a result, the gravitational force does not influence the motion of P and does not influence the reaction forces in the plane of the motion.
For this problem, the figure shows that the gravitational force acts downward in the plane of the page.
When solving for w^2, I ended up with a negative value. Can we ignore this negative sign when solving for w?
Wait, never mind. I just answered my own question.