Basic Physics Question -- Help Please?

[Thelas]

Okay, I'm having trouble with one of those string-and-pulley-on-an-inclined-plane problems. The pulley is where the two inclined planes meet, distance doesn't matter because the question is to find acceleration and tension.

m1 = 20 kg
theta1 = 40 degrees
mu-k1 = 0.20
m2 = 30 kg
theta2 = 60 degrees
mu-k2 = 0.30

(The inclined planes are set up to make a triangle.)
I need to find the acceleration.
I tried making force diagrams, but I'm not sure if I'm doing it right at this point, so I'm going to ask for some help... can someone show me what to do here?

Thanks in advance for your help.

[Raewyn]

Gah! I knew how to do this sort of thing four years ago, but I've completely forgotten now.

Alas, my physics/google-fu is weak, so the only suggestion I make is to head to a physics-specific forum like http://www.physicsforums.com/ and pose your question there. You'll likely get a quicker response, which could be crucial if this is homework.

[RS14]

Any diagram you can provide would be helpful, as I frankly don't understand the exact configuration of the system.

[Raewyn]

Any diagram you can provide would be helpful, as I frankly don't understand the exact configuration of the system.

Now that I can do.



The big circle is supposed to be a pulley.

EDIT: I have no idea what I'm talking about when it comes to physics.

[The Extinguisher]

Which mass do you need to find the acceleration for?

Find the forces acting on the the masses, specifically parallel to the incline of the larger mass, as that will help you find your tension force for the smaller.

Then just find the net force. Go go vectors.

[RS14]

That makes sense, thanks.

There must be a force exerted on each block by gravity: <0,g m_1> and <0,g m_2> respectively.

There must be a normal force exerted on each block by the planes: <- n_2 sin(theta), n_2 cos(theta)> and <n_1 sin(theta), n_1 cos(theta)> respectively. Convince yourself of this now, as the geometry is unintuitive, and I don't care to create a diagram to demonstrate this easily.

Additionally, there are tensional and frictional forces parallel to the inclined planes.

Consider for each plane a coordinate system with one axis x' parallel and one y' perpendicular to the plane. Note that the sum of the normal vector with the projection of the gravity vector into y' must be 0, as the block does not leave the surface. Thus the magnitude of the normal vector can be computed.

From the normal vector, the frictional vector can be obtained. It is proportional in magnitude to mu_i and n_i for all i and is in the plane of its respective incline.

That leaves only the tension and acceleration to be computed.

Suppose the blocks accelerate at speed a in their respective planes. . Because they remain coupled, the magnitude of the acceleration must also remain equal for each block. Then the net forces are equal to a/m1 and a/m_2 respectively.

Some tension acts on each block. In both cases, it has magnitude T and is oriented in the direction of the pulley.

Consider only the x' component of each vector. Thus the tension has magnitude T along this axis in both cases, while the contribution of the gravitational force varies with angle, as might be expected. The normal force can be disregarded, as it has a contribution of 0 in x'.

Sum the contributions of the projections of all forces on each block. Each must equal the net force on that block (which is in x' already). This gives a system of two equations that can be solved for a and T.

This should work. Let me know if you have problems or need clarification.