A truck pulls boxes up an incline plane. The truck can exert a maximum force of #4,500 N#. If the plane's incline is #(2 pi )/3 # and the coefficient of friction is #7/6 #, what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2017-12-30T15:15:58

The mass is #=1624.3kg#

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Resolving in the direction parallel to the plane #↗^+#

Let the force exerted by the truck be #F=4500N#

Let the frictional force be #=F_rN#

The coefficient of friction #mu=F_r/N=7/6#

The normal force is #N=mgcostheta#

The angle of the plane is #theta=2/3pi#

The acceleration due to gravity is #g=9.8ms^-2#
Therefore,

#F=F_r+mgsintheta#

#=muN+mgsintheta#

#=mumgcostheta+mgsintheta#

#m=F/(g(mucostheta+sintheta))#

#=4500/(9.8(7/6*cos(2/3pi)+sin(2/3pi))#

#=1624.3kg#