Forces on an incline

The Gravitational force FgFg FgFg FgFg FgFg FgFg FgFg The gravitational force on an object always points straight down and maintains a constant magnitude.

FNFN The Normal Force FNFN FNFN The normal force on an object always points perpendicular to the surface of contact. It decreases in magnitude as the angle of the incline increases. FNFN F N = 0N

Why does the Normal Force change, but gravity doesn’t? The Gravitational Force on the object is created by the mass of the object and the mass of the Earth itself. The angle of the incline has nothing to do with the Gravitational Force. The Normal Force, however, is a reactionary force from the incline’s surface on the object. As the object presses more on the surface the normal force increases. If the pressing force decreases, so does the normal force. Basically the Gravitational Force wants the object to fall straight down, but the incline’s surface gets in the way. Because of this, a Normal Force is produced. The strength of the Normal Force depends on how well the incline can oppose the Gravitational Force.

Getting a visual. FgFg On a horizontal surface the Normal Force (which is ALWAYS 90 O from the Surface) directly opposes the Gravitational Force. On a vertical surface there would be no Normal Force (which is ALWAYS 90 O from the Surface) because the object is not pressing on the surface and the surface would not create a reactionary force. FgFg FNFN If the object is not being accelerated then it is in equilibrium, and so…. F up + F down = 0 N F N + F g = 0 N F N = - F g the object in this case can never be in equilibrium. F up + F down = ma 0 N + F g = ma ma g = ma a g = a This makes sense because the object is falling.

FNFN If the object is placed on an incline which has an angle between 0 O and 90 O, then the Normal Force opposes a component of the Gravitational Force, not all of it. FgFg In this case the Gravitational Force is trying to do two things… 1)Press the object against the surface of the incline (F press ) 2) Slide the object along the surface of the incline (F slide ) F press F slide  So we can often think of the F.D.B. for an object on an incline as this: F slide

FgFg    Y X Y’ X’ FNFN

FgFg  Y’ X’ FNFN F slide F press F slide = F g *Sin  F press = F g *Cos  F N = - F press

FNFN FgFg  FNFN  F slide = F g *Sin  F press = F g *Cos 

With No friction F slide =  F (net force) FNFN  F slide = F g *Sin  F press = F g *Cos   F slide = F g *Sin  F N cancels out F press Leaving only F slide as the net force

Finding Acceleration on a smooth ramp  F slide = F g *Sin  Since F slide is the net force F slide =ma F g *Sin  ma m*a g *Sin  ma a g *Sin  a