AP® Physic s C: Mechan ics
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2008 Free-Respon Questi ons
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PHYSI C S C: MECHA N ICS
SECTI O N II
Time -45 minut e s
3 Quest i ons
Direc t ions : Answe r all three quest i ons. The sugge s ted time is about 15 minut e s for answe r ing each of the quest i ons, which are worth 15 point s each. The parts withi n a quest i on may not have equal weigh t . Show all your work in the pink bookl e t in the space s provi d ed after each part , NOT in this green inr t
.
2008M 1. A skier of mass M is skiin g down a frict i onle s s hill that makes an angle θ with the horiz o ntal , as shown in the diagr a m. The skier start s from rest at time t = 0 and is subje c t to a veloc i ty-depen d ent drag force du e to air resis t ance of the form F = –bv, where v is the veloc i ty of the skier and b is a posit i ve const a nt. Expre s s all algeb r aic answe r s in terms of M, b, θ, and funda m enta l const a nts.
(a) On the dot below that repre s ents the skier , draw a free -body diagr a m indic a ting and label i ng all of the force s that act on the skier while the skier desce n ds the hill.
(b) Write a diffe r enti a l equat i on that can be ud to solve for the veloc i ty of the skier as a funct i on of
time.
(c) Deter m ine an expre s sion for the termi n al veloc i ty v T of the skier .
(d) Solve the diffe r enti a l equat i on in part (b) to deter m ine the veloc i ty of the skier as a funct i on of time, showi n g all your steps .
(e) On the axes below , sketc h a graph of the accel e rati o n a of the skier as a funct i on of time t, and indic a te the initi a l value of a. Take downh i ll as posit i ve.
t
a
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厂房租赁协议O现代教育技术
朱砂根的养殖方法和注意事项2008M2. The horizo ntalunifor m rod shownabovehas length 0.60 m and mass 2.0 kg. The left end of the rod is attach ed to a vertic al suppor t by a fricti onles s hingethat allows the rod to swingup or down. The rightend of th e rod is suppor ted by a cord that makesan angleof 30° with the rod. A spring scaleof neglig iblemass measur es the tensio n in the cord. A 0.50 kg blockis also attach ed to the rightend of the rod.
(a) On the diagra m below, draw and labelvector s to repres ent all the forces acting on the rod. Show each force
vector origin ating at its pointof applic ation.
(b)Calcul ate the readin g on the spring scale.
The rotati onalinerti a of a rod aboutits center is 1
ML2, whereM is the mass of the rod and L is its length.
12
小书迷作文Calcul ate the rotati onalinerti a of the rod-blocksystem aboutthe hinge.
(d)If the cord that suppor ts the rod is cut near the end of the rod, calcul ate the initia l angula r accele ratio n of th e
rod-blocksystem aboutthe hinge.
2008M3. In an experi mentto determ ine the spring consta n t of an elasti c cord of length 0.60 m, a studen t hangsthe cord from a rod as repres ented aboveand then attach es a variet y of weight s to the cord. For each weight, the studen t allows the weight to hang in equili brium and then measur es the entire length of the cord. The data are record ed in the tablebelow:
(a)U the data to plot a graphof weight versus length on the axes below. Sketch a best-fit straig ht line throug h
the data.
(b) U the best-fit line you sketch ed in part (a) to determ ine an experi menta l valuefor the spring consta nt k of
the cord.
The studen t now attach es an object of unknow n mass m to the cord and holdsthe object adjace nt to the pointat whichthe top of the cord is tied to the rod, as repres ented above. When the object is releas ed from rest, it falls
1.5 m before stoppi ng and turnin g around. Assume that air resist anceis neglig ible.
(c)Calcul ate the valueof the unknow n mass m of the object.
(d)i. Calcul ate how far down the object has fallen at the moment it attain s its maximu m speed.
ii.Explai n why this is the pointat whichthe object has its maximu m speed.
iii.Calcul ate the maximu m speedof the object.
