Please show your work. m1 Problem #1) In figure, block 1 of mass m 2.0 kg and bl

Question

Please show your work.

m1 Problem #1) In figure, block 1 of mass m 2.0 kg and block 2 of mass m2 6.0 kg are connected by a massless string over a massless and m2 frictionless pulley and are initially held in place. Block 2 is on a rough surface, with coefficient ofkinetic friction of 0.1 and tilted at 0-300, while a horizontal force F of magnitude 3.0 N acts on it. Block 1 is on a frictionless surface. (a) Draw free-body diagrams for each block and label all the forces. Draw and label coordinate system you will use for each block, to solve the problem. (b) Find the normal force acting on block 2. (c) Find the magnitude of acceleration of block 2

Explanation / Answer

I think the problem implies that the weight of the block causes the wedge to accelerate against the horizontal surface. If all surfaces are frictionless, this will happen.

EDIT: I was a little mixed up on the geometry:

Vertical force on the block (ay is the vertical component of the block's acceleration):

Fy = m*g - m*ay

Let Fn be the normal force of the block against the wedge


Fn = Fy*cos?
Fn = (m*g - m*ay)*cos?

The horizontal component of the normal force Fx causes the wedge to accelerate horizontally:

Fx = Fn*sin?

the horizontal acceleration of the wedge is then ax = Fx/M = Fn*sin?/M. If the wedge moves a horizontal distance ?x then the box drops a vertical distance of ?y = ?x*tan?. This means

ay = ax*tan? = Fn*tan?*sin?/M substitute for ay in the eq above: Fn = (m*g - m*ay)*cos?

Fn = [m*g - m*Fn*tan?*sin?/M]*cos?
Fn = (m*g*cos? - (m/M)*Fn*sin

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