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#