One body with mass +1 kg moves down an inclined plane with tan angle 45’ without

Question

One body with mass +1 kg moves down an inclined plane with tan angle 45’ without friction. The resulting acceleration along the inclined plane is a1. A second body with mass m2=1.0001 moves down on an identical inclined plane but friction is described as 0.25, the acceleration of second body is a2 , determine the ratio between a1 and a2 . ( you do not know values of gravitation acceleration One body with mass +1 kg moves down an inclined plane with tan angle 45’ without friction. The resulting acceleration along the inclined plane is a1. A second body with mass m2=1.0001 moves down on an identical inclined plane but friction is described as 0.25, the acceleration of second body is a2 , determine the ratio between a1 and a2 . ( you do not know values of gravitation acceleration

Explanation / Answer

Given

mass m1 = 1 kg theta1 = 45 degrees , acceleration a1, friction zero

mass m2 = 1.0001 kg , theta2 = 45 degrees, acceleration a2, coefficient of kinetic friction mue_k = 0.25

as the mass is moving down the incline plane then

here theta1 = theta2 = theta

the net force acting on it is  

for m1

m1*a1 = m1*g sin theta

a1 = g sin theta

for m2

m2*a2 = m2*g sin theta - mue_k*m2*g cos theta

a2 = g( sin theta - mue_k*cos theta)

now  

a1/a2 = (g sin theta)/(g( sin theta - mue_k*cos theta) )

a1/a2 = sin theta /( sin theta - mue_k*cos theta)

a1/a2 = sin45 /(sin45-0.25 cos45)

a1/a2 = 1.333

the ratio is 1.333

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