Block \" M\" (mass of 15.65 kg) is initially moving to the left with a speed of

Question

Block "M" (mass of 15.65 kg) is initially moving to the left with a speed of 2.96 m/s. The mass of block "m" is 8.26 kg and the coefficients of friction are static friction = 0.411 and kinetic friction = 0.304. The string is massless and the pulley is massless and frictionless.

*** In the diagram, block "M" is on top of a surface moving left with a string attached to the left side of the block and block "m" is hanging vertically with the string going over the pulley and attached to the top of block "m".

How fast (m/s) will "M" be traveling when "m" has fallen through a height h = 2.47 meters?

Explanation / Answer

Here

Acceleration = Net Froce / Total Mass

Here

Net Force = mg - ukMg

So

Acceleration = (mg - ukMg)/(m + M)

= (8.26*9.8 - 0.304*9.8*15.65)/(15.65+8.26)

= 1.4355 m/sec^2

As we know

v^2 - u^2 = 2aS

Therefore

v^2 - 2.96^2 = 2*1.4355*2.47

v = 3.98 m/sec

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