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Sunday, July 12, 2015

Simple Kinematic Problem

Problem: Find the magnitude of the force P in the figure below.

Let Fd=(m1+m2)¯a  where  ¯a  is the acceleration to the right.

Note the following relationships:

tan(θ)=FvFhFh=Fvtan(θ)
F1=μN1=μm1g
F2=μN2wherem2g=N2+Fv
Fh=Fd+F1+F2

Making the appropriate substitutions give:

Fvtan(θ)=(m1+m2)¯a+μm1g+μ(m2gFv)

After some algebraic rearrangement, we arrive at:

Fv=tan(θ)1+μtan(θ)[m1+m2(μg+¯a)]

Hence,  P=Fvsin(θ)=tan(θ)sin(θ)[1+μtan(θ)][m1+m2(μg+¯a)]

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