5. A block of mass 7.60kg is on a flat horizontal table top. One end of a piece

Question

5. A block of mass 7.60kg is on a flat horizontal table top. One end of a piece of string is attached to what, from your point of view, is the top right edge of the block. The string extends upward and rightward, at an angle of 16.0° to the horizontal, away from the block and over a frictionless pulley A ball of mass 3.20 kg hangs at rest from the other end of the piece of string. The block is at rest. Neglect the mass of the string a) Find the frictional force exerted on the block by the table top. b) Would the block actually remain at rest, as specified in the statement of the problem, if the coefficient of static friction for the interaction between the block and the table top wa 0.450? (114-10)

Explanation / Answer

Given

M = 7.6 kg, m = 3.2 kg

angle theta = 16 degrees

a)

here T cos theta = mue*Mg cos0

and the tension in the string is T = mg = 3.2*9.8 N = 31.36 N

T cos theta = 31.36 cos 16 N = 30.1452 N

now the coefficient of static friction is mue_s = 0.450  

then the frictional force is 0.45*7.2*9.8 = 31.752 N  

b)

YES the block will be at rest if the coefficient of static friction is mue_s = 0.45

because the frictional force is greater than the tension acting on the block by string due to the mass on the other end

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