A block of mass 220 grams is held stationary on a level tabletop?

Question

A block of mass 220 grams is held stationary on a level tabletop.
• A mass of 43.9 grams is attached to the block by a string over which runs horizontally fromt the block to a pulley located at the edge of the table; the mass hangs freely from the string over the pulley.
• The frictional force on the block is .044 times the normal force between block and table.
• When the block is released, what will be its acceleration?
• Sketch and label a reasonable facsimile of a scaled diagram showing the forces acting on the block.

Answer 1

I will assume that the pulley is massless

First, I will test if the hanging mass can move the mass on the table

Kinetic friction 0.44*220*g
Requires 96.8*g hanging mass to keep the block moving

With only 43.9 g hanging, this will not move since the kinetic (or static) friction will be greater than the tension in the cord

Was it 22.0 Grams?
I will give a solution under this condition

Looking at fbds of each mass
Since the pulley is massless the tension in the cord will be constant and the accelerations of the masses will have equal magnitudes
on the table
T-.44*.022*9.81=.022*a

Hanging

.0439*9.81-T=.0439*a

Solving for a

T=.0220*a+.44*.0220*9.81
T=.0220*a+0.09496

T=.0439*9.81-.0439*a
T=0.430659-0.0439*a

Subtract the first from the second

0.430659-0.09496=
(0.0439+0.0220)*a

a=(0.430659-0.09496)/
(0.0439+0.0220)

a=5.094 m/s^2

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