| Problem statement Solution video |
DISCUSSION THREAD
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DISCUSSION and HINTS
Shown below is an animation of the motion for particle P as it moves around on its circular path. Note that the normal force acting on P switches from contact on the outer surface (normal force pointing inward) to contact on the inner surface (normal force pointing outward) and back to contact on the outer surface. Also note that the friction force always opposes the sliding motion of P, as should be expected. (Note that the parameters used in the simulation producing this animation may differ from the ones used in this semester's homework set.)
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw a free body diagrams for P. Be sure to show the friction force opposing the motion of P in your FBD.
Step 2: Kinetics (Newton's 2nd Law)
Using a set of path unit vectors for resolving forces into components is recommended here. Write down the appropriate Newton's 2nd law equation in normal and tangential directions. Recall that f = μk*|N|.
Step 3: Kinematics
Since you have used a path description for resolving forces, you should also use a path description for acceleration; that is, aP = v_dot et +(v2/r) en.
Step 4: Solve
At this point you will have two equations in terms of two unknowns: N and v_dot.
The problem Statement links to a YouTube video that is private.
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How would you determine the angle to multiple mg when solving for the equation after you set it up in its path coordinates? It’s kind of confusing when to use cos or sin.
You need to draw your FBD first. From that figure, you will be able to use trig to determine the component of the weight force in the e_t and e_n directions.
When setting the kinetics equations I am confused on the signs of the forces shouldn't the weight of the particle be positive and then the normal force be negative or does it matter?
Forces that are known should be drawn in the correct, known direction. For example, a weight force should be drawn downward.
For forces that are unknown, choose a direction and stick with it throughout. The sign on your answer for the force will tell you if your original choice was correct.
In this problem, you do not know if the normal force is pointing inward or outward. Your solution will give you that answer.
Do we assume the ball is always in contact with both slot surface edges? The dimensions of particle P were never given.
If the particle 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.
I believe that we assume particle P is in contact with one of the walls, considering that friction force is acting upon it. On that note, even though it looks like it's suspended in air in the diagram it is most likely making contact with the wall, dimensions of P don't matter in this case
Do we assume g to be 9.81 m/s^2 or do we leave it as a variable g in our answer?
Since you are provided with numerical values for all of the parameters in the problem, please use the numerical value for "g".
There is no numerical value for g given in the problem.
But, you know what it is. Right?
Yes, sorry I was just confused by your answer to the previous comment. Thank you.
Is it incorrect to express the answers as vectors?
For Part a) the answer can be either a scalar or a vector, since by definition, we know that the "normal" force is perpendicular to the path.
For Part b), the "rate of change of speed" is a scalar. It should be presented as a number (with a sign), not a vector.
For force of friction should it be multiplied by 2 since its in contact with both sides or not?
The particle can be in contact with one side or the other, not both.
When writing the kinetics equations, how would we go about writing ma in terms of et and en? Since we don't know the direction of ma.
When you draw your FBD, make sure to add the et and en directions based earlier discussions of path coordinates. Then you can make the Fn and Ft equations based on the forces and angles included in your FBD. Make sure the angles are correctly marked on your FBD, too.
Is the v^2/r in the path coordinates for ap what centripetal force would have been? Should we always show it in path coordinates form instead of F centripetal for these questions?