PIlYS 1200 BB 8 L, Aa isuk level wad Th car mainas cs speed r. the radius of the
ID: 1790561 • Letter: P
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PIlYS 1200 BB 8 L, Aa isuk level wad Th car mainas cs speed r. the radius of the 11111, is , . nnd 114° l'In-flicielll of slitic lintion be1wcc" thc car's tires and the road is us. Using an l'Ill ) iind N21. Vi1 l'It" detive the li,llowing "wdel tor the mininnm coet icient of static lì iction (IN 14°edell to kvel' lltar {11,111 skidding during a lutt1: lon've N(Ol asked to derive this model. vut it would be ^oipructice'Just nopractice work in n way to tikts ent is as a measure ol the hw e ees can "grip" the 1ncl 1"vl new 1 ircs on a diy 1 liul, ll.is high (closer to 1). Illaking it easier for the car to avoid skidling. Il te a bald, is wet or icy. thentt will be low (lser to 0). and the 111 is 131(H(' likelv 10 skill In those te, e dl's ls is tlhe miniun "^rip" tie tites need to make the tui without skidng. "Giip" olcouso is a elnical term. and it is't a toe.) a) 'tove that delpasss tho smell test. Show all algcbra. b) Imi1gnle illHXpetinlent ill whi11 you try laking the sane tulll at vartous speeds. Does the model pediet that yo'ro mo likely to skid aigher speeds or lower specds? Explain. Deus lhu 1110(1'l's Prcdictio11 111atch what vu)u'd expect? Explain. Now imagine you'v taking diltercnt tuns: some sharp, some wide. but all at the sane speed. Does the tuodel Predict tltat you'd bei wre likely to skid on a wide tun! or a sharp tutn? Explnin Dos tis prediction match common sense or expcrience? Explain. 2. Acilse of soda is launched lion! Ihe bottonl of the iamp with an initial speed v, and slides up along 'he lamp. traveling a distance d before stopping. The ranp is nclined at an angle above hoiontal, and the coeflice of statie riction between the ramp and the case is Using the ìdeas ol wrk and entrity allows us to derive tis 111odel for predicting d: 2 y(14x cost, + sin(, ) Not sprisingly, since l speed appears in tentor, the faster the case's speed at launch, the ather it w slide,so the model agrees with common sense on that score. A more interesting aspect of the model is the ramp's angle oncretely, what would it mean to set the ra' ale o real life?Orto set it to 90*? b) Substitute@-0° into lhe odel and simplify. Show all work.Explanation / Answer
1. speed of car = v
radius of turn = r
coefficient of static friciotn = k
so for equilibrium from fore balance
mv^2/r = k*mg
k = v^2/rg
b. for a constant k value
one is more likely to skid at higher speeds
because let skidding force be F
then
mv^2/r - kmg = F
dF/dv = 2mv/r
so rate of change of skidding force is directly proportional to speed
hence car would skid easily at higher speeds
c. again
mv^2/r - kmg = F
dF/dr = -mv^2/r^2
hence, the car will skid more at lower values of r
so sharper turns lead to more skidding
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