Two blocks, one 0.8 kg and the other 2.0 kg are connected by a massless string over a frictionless pulley. The coefficient of kinetic friction is 0.14, and the downward ramp angle is 60 degrees. a) Determine the acceleration of the blocks?

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Answer 1 · 2017-09-01T01:46:29

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Let the acceleration of the blocks be $am"/"s^2$ and tension on string be $T$ N

Considering the forces on the block of mass $m=0.8kg$ block

$0.8a=T-0.14xx0.8g.......[1]$

Considering the forces on the block of mass $M=2kg$ block

$2a=2gsin60^@-T-0.14xx2gcos60^@.......[2]$

Adding [1] and [2] we get

$2.8a=2gsin60^@-0.14xx0.8g-0.14xx2gcos60^@$

$=>2.8a=2gsin60^@-0.14xx0.8g-0.14xx2gxx1/2$

$=>2.8a=2gsin60^@-0.14xx0.8g-0.14xxg$

$=>2.8a=2xx9.8xxsqrt3/2-0.14xx1.8xx9.8$

$=>a=2xx9.8/2.8xxsqrt3/2-0.14xx1.8xx9.8/2.8$

$=>a=3.5xxsqrt3-0.14xx1.8xx3.5~~5.2m"/"s^2$