An object with a mass of #6 kg# is on a plane with an incline of #pi/12 #. If the object is being pushed up the plane with # 6 N # of force, what is the net force on the object?

1 Answer
Jul 17, 2017

#sumF = 9.23# #"N"# directed down the plane

Explanation:

I'll assume the surface is frictionless, as there is no information regarding friction given.

Referring to the image below:

upload.wikimedia.org

I'll call the positive #x#-axis going down the plane.

We know the normal force #n# and quantity #mgcostheta# are equal in magnitude, so we need not resolve the vertical direction.

Since the surface is (supposedly) frictionless, the only forces being applied are

  • gravitation force, equal to #mgsintheta# (directed down the incline)

  • applied force, equal to #6# #"N"# (directed up the incline)

We need to find the quantity #mgsintheta# by knowing

  • #m = 6# #"kg"#

  • #g = 9.81# #"m/s"^2#

  • #theta = pi/12#

Therefore,

#mgsintheta = (6color(white)(l)"kg")(9.81color(white)(l)"m/s"^2)sin(pi/12) = 15.2# #"N"#

The net horizontal force #sumF_x# is given by

#sumF_x = mgsintheta - F_"applied" = 15.2# #"N"# #-6# #"N"#

#= color(red)(9.23# #color(red)("N"#

directed down the plane