Find the Angle for Physics Problem Involving Pulleys & Friction

[robobot4]

alright, so I was searching for a physics problem, and i came upon this http://www.fearofphysics.com/Probs/mech041.html .This is exactly the problem I was looking for, except, rather than you providing the angle, you are provided with the coeffifient of friction (.620) , as well as the 2 weights (m1 = 130 N, m2 = 45 N), and you are asked to find what the angle is. I was just looking for some guidance on how to go about solving this..Thanks!

 

[hotvette]

We here taught to always, always, draw free body diagrams of forces, then write equations of motion for the objects involved. In this case, there will be a relationship between the 2 equations of motion, because the masses are connected by a cable.

 

[Diane_]

First off, you've labeled things incorrectly. The weights may well be 130N and 45N, but you've labeled them as masses. I know this seems trivial, especially if you understand the difference, but those small inconsistencies can lead to major problems later on.

I take it you're asking how to solve a problem where you have to find the angle? The trouble is that you haven't provided enough information to do so. If we knew the acceleration of the blocks, then we could make a start - otherwise, the system is underdetermined.

Some general hints: in problems like this, it's always a good idea to start with a free-body diagram of each of the masses. List every force acting on each mass, including the direction. Decide on a convenient set of axes and resolve the forces into their appropriate components.

For instance, the forces on your block 1 will be weight (straight down), the normal force (perpendicular to the plane, upwards), friction (parallel to the plane, towards the bottom) and the tension in the rope (parallel to the plane, towards the top). Given this, the best axes are probably parallel to and normal to the plane. For your block 2, the only forces are the weight (down) and the tension in the rope (up), so there's no resolution necessary.

After that, it's a matter of resolving everything. Remember that the net force on the object is both the vector sum of the forces acting and the product of mass and acceleration. If you know the acceleration, then you can figure the net force pretty easily. From there, it's a relatively simple matter to determine the angle necessary to give you that net force.

Does that help?

 

[robobot4]

Yes it does a bit, but I think I managed to solve for the accelleration. Correct me if I'm wrong.

(45 - (.620)(130))/ (4.591 + 13.26)...and this yielded an accelleration of 2 m/s^2. Would that enable me to solve my problem with this information?

 

[Diane_]

I need to know more about how you solved it. Frankly, I don't see any way to solve this problem without first knowing either the angle involved or the acceleration. If I don't know either, the system could be in any state at all and I wouldn't know it.

What problem are you trying to solve? What information (other than the masses and the coefficient of friction) do you have?

 

[robobot4]

Ok..heres the question verbatim, I think I just realized something, a will be 0, according to the question

A block weighing 130 N is on an incline. It is held back by a weight of 45 N hanging from a chord that passes over a frictionless pulley and is attached to a block as shown below [seen in the site]. Find the angle (Theta) at which the block will slide down the plane at constant speed. The coefficient of friction is 0.620

for the record, I have no idea how i managed to get 2 m/s^2, I think I plugged it into some odd formula in my physics book

 

[robobot4]

anyone got any ideas?...I messed around with the site program thing they have using the aforementioned values, and through trial and error, managed to get 20.3 degrees to = 0 accelleration...that might be right, might be wrong, but if anyone has any input, feel free to comment

 

[Diane_]

You're right - the question says that the velocity is constant, which means the acceleration is 0, which means (of course) that the net force is 0. So - set up your equations. You'll have three sets: one set for the hanging mass (which will be pretty trivial - weight = tension), one set for the components of the force on the other mass normal to the plane (normal force = perpendicular component of the weight), and one set for the components parallel to the plane (friction + tension = parallel component of the weight). You'll need all three to solve it, but the solution should be pretty easy. Remember - you're using a simplified model of friction, so that friction = coefficient x normal force.

Is that enough?

 

[robobot4]

Yea thanks a lot Diane, you've been a great help, I'll see what I can manage, but - I'm a bit confused as to what these "equations" will look like. We've only just touched on this friction chapter, and its all somewhat new to me.

 

[Diane_]

I wish I knew Latex better. Let me know if you're still having trouble and I'll try to set them up so you can see them. Trust me on this - it's not hard. The most difficult thing about introductory physics (in my occasionally humble opinion) is getting used to seeing the physical relationships inherant in the mathematical models you're using. A large part of that is learning to use the standard symbols. Another part is getting your head around the concepts you're learning. For me, that involves being able to picture the physical process and - uhh - "feel" the forces and accelerations involved. You've spent your entire life learning physics, at least in terms of knowing intuitively how and which way things move. Now you just have to put it on a firm foundation.

It can really be a blast, I promise you. And I say that as a girl who majored in mathematics. :)

 

[robobot4]

Oh believe me, I understand...AP Phys is by far my favorite class outta my 4 years of HS. And I finished Calc II last year, so I'm not exactly amateur with the mathematical part, but as you said, putting it all together is where I'm falling here. But If you could possibly give it a shot at trying to put them together, it would be much appreciated.