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 #(7 pi )/8 # and the coefficient of friction is #5/3 #, what is the maximum mass that can be pulled up at one time?

Question

908 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-23T08:57:25

The mass is #=396.8kg#

enter image source here

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

Let the force exerted by the truck be #=FN#

Let the frictional force be #=F_rN#

The coefficient of friction #mu=F_r/N#

The normal force is #N=mgcostheta#

Therefore,

#F=F_r+mgsintheta#

#=muN+mgsintheta#

#=mumgcostheta+mgsintheta#

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

#=4500/(9.8(5/3*cos(7/8pi))+sin(7/8pi))#

#=-396.8kg#