Test 2 phy a) How is the velocity of a particle defined? b) What is an inertial reference frame? c) Describe friction.

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1 Tet phy a) How i the velocity of a paticle defined? b) What i an inetial efeence fae? c) Decibe fiction. phyic dealt otly with falling bodie. d) Copae the acceleation of a paticle in efeence fae elated by the Galilean tanfoation.. Identifying the foce (indicate the object, the ouce and the type of each foce), daw the fee body diaga fo a) a van paked on a hill b) a bucket hanging unde a helicopte oving with contant velocity. (Make ue that the net foce i conitent with the indicated otion.) 3. Conide a atellite of a oving aound a planet of a M and adiu R, at an altitude h above the planet uface, a illutated in the figue. Relate the peed of the atellite to the given infoation (, M, R, and h). (Hint. Aue you know the gavitational contant G.) 4. An object ( paticle ) ha a velocity of [3,0] / at one intant. Five econd late, it velocity ha changed to [8,10] /. Auing that the object wa ubject to a contant net foce, a) find the aveage acceleation of the object (duing thi tie inteval) b) and the diplaceent of the object (in the ae tie). c) Deteine the agnitude of the net foce.

2 - 1 - a) The ate, at which a paticle i changing it poition (vecto), i called the velocity (vecto) of the paticle. v ( t) d dt b) If a paticle doe not inteact with othe bodie being conideed (we ay that all bodie exet a zeo (vecto) foce on the paticle), it i poible to find a efeence fae in which that paticle ha zeo acceleation. Thi efeence fae i called an inetial efeence fae. c) Within cetain liit (of the extenal foce) the tatic fiction (inteaction) pevent the object' uface fo oving along the igid uface. The axiu agnitude of thi foce i popotional to the agnitude of the noal foce f µ N. When the extenal foce exeted the liit, the object begin to lide on the uface, while the kinetic fictional foce ha a value fk µ kn in the diection oppoite to the elative velocity of the liding uface. d) In a efeence fae elated by the Galilean tanfoation the acceleation ae identical at any intant a ( t) a' ( t)

3 - D T W W gavitational foce exeted by the eath on the bucket. T tenion foce exeted by the ope on the bucket. D dag foce exeted by the ai on the bucket. W gavitational foce exeted by the eath on the van. N N tenion foce exeted by the oad on the van. f f (tatic) fictional foce exeted by oad on the van. W

4 - 3 - R F G h The atellite i ubjected only to gavitational foce exeted by the planet. Fo the univeal law of gavity, the agnitude of that foce i 1) F net F G G M ( R + h) The ybol ae conitent with the figue. Becaue of the lage a of the planet (in copaion with the atellite) one can aue that the planet efeence fae i inetial. In thi fae the net foce exeted on the object and it acceleation ae elated by Newton econd law of otion. In te of the agnitude ) F net a c whee i the a of the atellite and a c it centipetal acceleation. In a unifo cicula otion, the angula velocity w i contant leading to a contant peed of the atellite 3) v w ω ω (R+h) fo which the agnitude of the centipetal acceleation can be elated to the peed of the atellite 4) a c w w (w ) ω The et i algeba. By ubtitution v ω a c Fnet GM GM GM R + h

5 - 4 - y a) Fo the definition of the aveage value of a function a av ( t) t f i a t dt 5 v v t [ 8,10] [ 3,0] [ 1,] v i a v f x b) Since the net foce i tie independent the paticle ove with a contant acceleation. In uch a cae the aveage acceleation i equal to the acceleation. Fo the given initial (o final) velocity and the acceleation function one can deteine velocity at an abitay intant v t i i + 0 ( t) v + adt v at t i (Note. Uing the final velocity i alo coect although oe coplicated t f t 8 ( t) v + adt v + a( t t ) v i ) f f With the oigin of the coodinate yte at the initial location of the object the poition vecto can be deteined fo the velocity function t t i i i i i + t 0 t 0 ( t) + vdt + v + atdt + v t at i The diplaceent (fo it definition) i theefoe f i v i t + 1 at i 1 [ 3,0] 5 + [ 1,] ( 5) [ 7.5,5.0] c) The net foce and acceleation ae elated by Newton econd law, which equie the a of the object to be given. Thee i no infoation leading to it value theefoe it i not poible to find the net foce. 1

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