A mass of `80 kg` stands on a horizontal weight machine of negligible mass , attached to a massless platform `P` that sliding down at `37^(@)` incline. The weight machine reads `72 kg` the man is always at rest weight machine calculate

a. the vertical acceleration of the man.
b. the coefficient of kinetic friction `mu` between platform and incline.

Options

A. `13/24`
B. `15/24`
C. `11/24`
D. `17/24`

Answer

A

Explanation

Weighting machine measure normal reaction . Draw FBD of man system of man . System at an angle of `37^(@) a_(x)` and `a_(x)` are a and y component of acceleration What is cause of verticle acceleration and hirizontal acceleration

`(80 - 72) g = ma_(3)`
` a_(y) = 1 m//s^(2)`
Now `a g = a sin 37^(@) = 1 ms^(-2)`
or `a = 5//3ms^(-2)`
Now apply Newton's secont law on man is direction of acceleration Note that a component of acceleration of man is due to friction
`mg sin 37^(@) - mu cos37^(@) = m xx ((5)/(3))`
`6 - 8 mu = (5)/(3)`
`6 - ((5)/(3)) = 8 mu rArr mu = (13)/(24)`