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?

Question

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?

Isabella Alvarez · Accepted Answer

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

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

Referring to the image below:

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

Lily Adams · Answer

undefined The net force on the object can be calculated using the equation:

Net force = Force applied up the incline - Force due to gravity pulling down the incline

Force due to gravity pulling down the incline can be calculated using the formula:

Force due to gravity = mass * gravitational acceleration * sin(incline angle)

Given:
Mass (m) = 6 kg
Incline angle (θ) = π/12 radians
Gravitational acceleration (g) = 9.8 m/s²

Plugging in the values:

Force due to gravity = 6 kg * 9.8 m/s² * sin(π/12)

Calculate the force due to gravity, then subtract it from the force applied up the incline (6 N) to find the net force.