Inclined Plane Problems

Forces Acting on the Object

Fapplied Fnormal

Ffriction

WX

WWy

Note: The applied force and the force of frictioncan be in either direction as long as the friction force is opposite to the motion.

WX x

y

Remember: Weight = W = Fg=Fw=mg (different teachers

may use different symbols )

Useful Equations for Inclined Plane Problems

• Formulas• Fnet= F=ma• W=mg• Wx=mg sin θ• Wy=mg cos θ• Ff= FN

• Explanation of Symbols

• Fnet = net force

• m = mass• w = weight (force)

• Ff = friction

= coeff. of friction

• FN = normal force (perpendicular force applied by surface)

Problems With No Acceleration

Fapplied

Fnormal

Ffriction

WX

W

Wy

WXx

y

When the object on the plane does not have any acceleration, then the forces acting on the

object must be equal to zero.Fx=Fapplied-Ffriction -Wx=ma = 0 (a=0)

Fy= Fnormal-Wy=ma=0 (a=0)

Problems With Acceleration

Fapplied

Fnormal

Ffriction

WX

W

Wy

WXx

y

Fnet = maFx=Fapplied -Ffriction -Wx=ma

Fy= Fnormal-Wy=ma=0 (a=0, no motion along the y-axis)

FrictionFriction depends on the roughness of the surfaces and the force pushing them together.

The coefficient of friction (μ) is determined by the texture of the surfaces in contact.

The normal force is the force pushing the 2 surfaces together

There are 2 types of friction, static and kinetic (sliding)

Static friction is the frictional force that an object must overcome to start its motion. (μis higher for static friction)

Kinetic (or sliding) friction is the force opposing the motion of an object.

The formula for finding friction is Ff=μFN