ps4c11 - Physics 111.01 September 26, 2008 PS 4c (11)...

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Physics 111.01 September 26, 2008 PS 4c (11) Problem 1. Static and Kinetic Friction on an incline: A 10 kg crate is placed at rest on an incline plane ( s = 0.7 , k = 0.5 ), whose angle can be adjusted. a.) The maximum angle of the incline for which the crate will stay at rest is: b.)-e.) If the angle of the incline were instead the two amounts shown below, please fill in the rest of the values on the chart below: angle of incline: component of weight acting along incline: (size only) friction force: (size only) (indicate static or kinetic): net force on crate: (size only) acceleration of crate: (size only) 15 o N N, N m/s 2 65 o N N, N m/s 2 f.) For the 65 o angle, find how long it would take the crate to slide down 5 m along the incline. g.) Explain why it is NOT possible for an object which is placed at rest on an inclined plane to then start sliding down with constant speed. m 10 kg θ x y mg=98 N θ N mg cos θ mg sin θ f g
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Solution. First we need a diagram and a free-body diagram. (a) From the free- body diagram we can see that, since the x and the y forces must cancel (body at rest!), ss and, for the ma e mass sliding, Nm g fm g fN cos sin θ ximum angle without th cos m g μμ = = == Setting the two expressions for f equal gives s sin cos mg mg s sin tan cos μθ = For a static coefficient of friction of 0.7, this gives 11 s tan tan 0.7 34.99 θμ −− = ° () ( ) s kk tan tan 0.7 34.99 cos 0.5 98 N cos65 20.71 N m g = ° = ° = (b-e) Now fill in the table. If the angle is equal to 15 degrees, the crate will not slide. The component of the weight along the incline is (always, in fact) equal to mg sin θ , which in the fifteen-degree case is equal to 25.36 N. The frictional force (static friction) just cancels it out. And all the forces cancel out in pairs, so the net force is zero and the acceleration is zero.
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This note was uploaded on 05/13/2010 for the course PHYSICS 111 taught by Professor Staff during the Fall '08 term at S.F. State.

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ps4c11 - Physics 111.01 September 26, 2008 PS 4c (11)...

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