Inclined Plane, 2 masses, 1 pulley - Friction

[glossolalia]

Homework Statement

A block with mass 10.7 kg is placed on an inclined plane with slope angle 24^\circ and is connected to a second hanging block that has mass 15 kg by a cord passing over a small, frictionless pulley. The coefficient of static friction is 0.47 and the coefficient of kinetic friction is 0.35.

a) What is the normal force on m_1?

b) If the inclined slope is frictionless, what is the acceleration of the 2 masses? Use up the incline as your + x direction.

c) What is the tension in the cord in this case?

d) Assume friction is down the incline. If friction is down the incline and the 2 blocks are not moving, what is the value of friction?

and e) What is the maximum static friction?

Homework Equations

The Attempt at a Solution

a) is easy, knocking out 10.7*9.8*cos(24) = 95.8N

e) is easy, with 95.8N(.47) = 45.0N

the rest, I'm having trouble with and don't know where to begin.

 

[Mandeep Deka]

Hoping that you know all the Newton's laws of motion,
for part (b) and (C):
Draw the free body diagram of the bodies individually.
Assume that the tension in the rope is 'T'. Now, just by intuition you can of course guess the direction of movement of both the bodies. Since the rope length will not change, the acceleration of both bodies will be equal (let that be 'a'). So equate the net force along the direction of motion of each body to their respective mass times accelerations. That will give you two equations with two unknowns, 'T' and 'a'. Solve them!

First, complete them, then we will discuss about the part (d). Hope i haven't confused you!

 

[glossolalia]

I guess I'm having trouble visualizing the forces, which is frustrating as I knocked projectile motion and angular acceleration and all that on its butt in our last section.

I keep picturing Block B with a downward force of 147N and the rope pulling up towards the pulley, down the incline towards the other block with that same 147N...stop me right there if I'm wrong. And then that same rope pulling up the incline towards the pulley and down to Block B with mg(sin24)N. A mystical, magical rope with 147N heading along negative-x and 42.6N heading up the slope. Do you see why I'm getting frustrated? :)

by the way, thanks for replying

 

[Mandeep Deka]

I keep picturing Block B with a downward force of 147N and the rope pulling up towards the pulley, down the incline towards the other block with that same 147N...stop me right there if I'm wrong.

STOPPED YOU...right there
The block pulls the rope with a force of 147N but no one on Earth said you that the rope too pulls the block with the same force, in fact, you have just disproved it...

A mystical, magical rope with 147N heading along negative-x and 42.6N heading up the slope. .

...which is a contradiction, as a rope can (under the given conditions of a mass-less frictionless pulley) never have have two different tensions on the two ends.
Moreover, if you are thinking that the block pulls the rope with a force of 147N and the rope too pulls it up with a force of 147 N then, it should be in equilibrium!


It never happen that way.The rope will have a uniform tension throughout. So if it pulls the block A with a force of 'T' it will pull the other block with same force 'T', and because this tension in your case can't be equal to the downward components or mg of each of the block, the force acting on the blocks will remain unbalanced and will lead to an acceleration of the blocks in a particular direction.

I suggest you have a good picture of the theory part, first, refer some good books like 'Fundamentals of Physics by Halliday, Resnick, Walker', or maybe 'University Physics by Sears and Zemansky'.