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

Question

5. A block of mass 7.60kg is on a fliat 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. rightward, at an angle of 16.0 to the horizontal, away from the block and over a fric A ball of mass 3.20 kg hangs at rest from the other end of the piece of string. The Neglect the mass of the string The string extends upward and tionless pulley block is at rest. 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 ro , if the coefficient of static friction for the interaction between the block and the ta 0.450 ble top was (114-10)

Explanation / Answer

given m = 7.6 kg

theta = 16 deg

M = 3.2 kg

a. for the bloakc to be at rest

let the fricitonal force be f

then

tension in string = T

then from force balance

Tcos(theta) = f

mg - Tsin(theta) = N

hence

f = Tcos(theta)

but T = Mg

hence

f = Mg*cos(theta) = 30.175927 N

b. if us = 0.45

maximum possible value of static friction is us*N

us*(mg - Mg*sin(theta))

0.45(7.6 - 3.2*sin(16))9.81 = 29.656436456 N

hence as the value of frictino we found out exceeds this value, hence the block actually does not remain in rest for this value of coeficneit of friciton

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