A 2.20 steel block is at rest on a steel table. A horizontal string pulls on the

Question

A 2.20 steel block is at rest on a steel table. A horizontal string pulls on the block. The coefficient of static friction of dry steel on steel is , the coefficient of kinetic friction of dry steel on steel is , and the coefficient of kinetic friction of lubricated steel on steel is .

a) What is the minimum string tension needed to move the block?
b) If the string tension is 20.0 , what is the block's speed after moving 1.00 ?
c)If the string tension is 20.0 and the table is coated with oil, what is the block's speed after moving 1.00 ?

Explanation / Answer

a) tension in the string T = limiting friction fL = us m g = 0.8 x2.2 x9.8 = 17.25 N b) when T = 20 N, the resultant force on the block is Fr = T - fk = T - uk m g = 20 - 0.6 x 2.2x9.8 = 7 N accelerarion a = Fr / m = 7 /2.2 = 3.2 m/sec^2 so that speed of the block after travelling 0.8m is V = square root of ( 2 a S )= square root of ( 2x3.2 x 0.8 ) = 2.26 m/sec c) for the lubricated surface Fr = T - uk m g = 20 - 0.05 x 2.2 x9.8 = 19 N aceleration of the block a = Fr / m = 19 / 2.2 = 8.64 m/sec^2 so that speed of the block V = square root of ( 2 a S ) = square root of ( 2 x 8.64 x 0.8 ) = 3.72 m/sec

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