1 / 10

Motion on Inclined Planes

Motion on Inclined Planes. A tilted coordinate system is convenient, but not necessary!. Inclined Plane Problems. a. Its important to understand ∑ F = ma & How to resolve it into x,y components in the tilted coordinate system!!. You MUST understand this case to understand

myrnam
Download Presentation

Motion on Inclined Planes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Motion on Inclined Planes

  2. A tilted coordinate systemis convenient, but not necessary! Inclined Plane Problems a • Its important to understand∑F = ma& How to resolve it into x,y components in the tilted coordinate system!!

  3. You MUSTunderstand • this case to understand • the case with friction!! • By geometry, the 2 • angles marked θ are • the same! a By Trigonometry: FGx= FGsin(θ) = mgsin(θ) FGy= -FGcos(θ) = -mgcos(θ) FG = mg Both Angles = !

  4. Example: Sliding Down Incline • A box of mass m is placed on a smooth (frictionless!) • incline that makes an angle θwith the horizontal. • Calculate: a)The normal force on the box. • b) The box’s acceleration. • c) Evaluate both for m = 10 kg & θ = 30º Free Body Diagram

  5. Example: The Skier • A skier descends a 30° slope, at constant • speed. What can you say about the • coefficient of kinetic friction? Is the normal force FNequal & opposite to the weight??? NO!!!!!!!

  6. Summary of Inclines:An object sliding down an • incline has 3 forces actingon it: the normal forceFN, • gravity FG = mg, & friction Ffr. FN is always • perpendicular to the surface & is NOTequal & • opposite to the weightmg. The friction force Ffris • parallel to the surface. Gravity FG = mg points down. • If the object is at rest, the • forces are the same except • that we use the static • frictional force, & the • sum of the forces is zero.

  7. Problem FN Ff Newton’s 2nd Law ∑F = ma x: mgsinθ – Ff = ma y: FN - mgcosθ = 0 Friction: Ff = μkFN NOTE!!!  FN = mgcosθ FN  mg mg sinθ mg cosθ FG = mg THE NORMAL FORCE IS NOT EQUAL TO THE WEIGHT!!!

  8. Example: A ramp, a pulley, & two boxes • Box A, mass mA = 10 kg, rests on a surface inclined at • θ = 37°to the horizontal. It’s connected by a light cord, • passing over a massless, frictionless pulley, to Box B, which • hangs freely.(a) If the coefficient of static friction is s= 0.4, • find the range of values for mass B which will keep the • system at rest. (b) If the coefficient of kinetic friction is k= • 0.3, and mB = 10 kg, find the acceleration of the system.

  9. Example: A ramp, a pulley, & two boxes • (a) Coefficient of static friction s= 0.4, find the range of values • for mass B which will keep the system at rest. • Static Case (i): Small mB << mA: mAslides down the incline, so • friction acts up the incline. • Static Case (ii): Larger mB > mA: mAslides up the incline, so • friction acts down the incline. Static Case (ii): Larger mB > mA mAslides up incline Ffr acts down incline Static Case (i): mB << mA mAslides down incline Ffr acts up incline

  10. Example: A ramp, a pulley, & two boxes (b) The coefficient of kinetic friction is k= 0.3, & mB = 10 kg. find the acceleration of the system & the tension in the cord. Motion: mB = 10 kg mAslides up incline Ffr acts down incline

More Related