A truck pulls boxes up an incline plane. The truck can exert a maximum force of #4,000 N#. If the plane's incline is #(5 pi )/8 # and the coefficient of friction is #9/8 #, what is the maximum mass that can be pulled up at one time?

1 Answer
Mar 8, 2018

Answer:

The mass is #=501.9kg#

Explanation:

http://spmphysics.onlinetuition.com.my/2013/06/inclined-plane.html

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

Let the force exerted by the truck be #F=4000N#

Let the frictional force be #=F_rN#

The coefficient of friction #mu=F_r/N=9/8#

The normal force is #N=mgcostheta#

The angle of the plane is #theta=5/8pi#

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

Therefore,

#F=F_r+mgsintheta#

#=muN+mgsintheta#

#=mumgcostheta+mgsintheta#

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

#=4000/(9.8(9/8*cos(5/8pi)+sin(5/8pi))#

#=-501.9kg#