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/Mean; 50 Ph112 — Exam #1 l Std. Dev: 17 Name: 5'! it: ___ 1. [15 pts] Alice and Bob are equally strong swimmers — in "still" water both swim at speed c. They are, however, in a
stream that flows downstream at speed v (c is greater than v). The two start at the same point X and they both return to
point X (X is a point ﬁxed in space, relative to the land). Alice swims upstream a distance L (all distances are relative to
the land) and then downstream the same distance. Bob swims "cross stream” (moving perpendicular to the banks of
the stream). He swims out a distance L, and then back the same distance. Except for their instantaneous turns halfway
through their roundtrips, their speed is constant on each leg of their trip. When solving this problem you must write
down explicitly (and use) the proper/y labeled velocity addition formula. a) Does Alice or Bob return to point X first? To answer this, ﬁnd and compare the times they each require to complete
the trip, tA and t5. The comparison may require a bit of algebra. b) What is Bob's average speed (relative to the land) for the round trip? c) Draw a free body diagram of Bob, showing to scale, and labeling, all horizontal (xy plane) forces that realistically act
on him on the outward leg of his trip. Include in your sketch Bob’s orientation relative to the banks of the stream. V—> X 2. [20 pts] Cory is standing at the top ofa hemispherical rock of radius R. A pebble is at rest at the top of the rock. Cory
kicks the pebble, which gives it a horizontal velocity vi. What must be the minimum value of vi ifthe pebble is never to
hit the rock after it is kicked? (The algebra for this one is pretty simple, so please do it, and solve explicitly for vi.) [30 pts] In the apparatus shown at right the pulleys are massless & frictionless, but there is friction between the table and m1(uS and uk are both nonzero). a) Find the value or values of m; that will put the system on the verge of moving from rest.
b) if m2 has 1/2 the value you found in part a, what is the force of friction on m1? c) if m; has twice the value you found in part a, what is the acceleration of m2? cl) For this last part, imagine the entire apparatus has been rotated an angle a
counterclockwise, as shown in the 2nd sketch. m2 still hangs down, of course. Redo part a. Problem 3 is "setup, but do not solve.” Write all equations necessary for each part of the problem, but don’t combine these
equations. For example, you do not need to explicitly solve for m; in part a in order to find an
expression for the force of friction in part b, etc. In part b, you will simply explain what you would do differently in the case of the smaller mass. 4. [15 pts] A force F = (p §+qtj) acts on an object of mass ’m’, initially (t=0) located at the origin and moving with velocity \7 = (r 5+ sf). Note that: p, q, r, s are all constants. Where is the object at the end of ’d’ seconds? What is its velocity? Setup and solve. S. [20 pts] An Atwoods machine, shown below, consists of blocks of masses M and 3M connected by a massless string
‘ over a massless pulley. The device rests on a horizontal table. The coefﬁcient of friction between the blocks and the
1 table surfaces is pk. The pulley is pulled by a string attached to its center and accelerated to the left (relative to the
‘ table) with magnitude A. Gravity acts down, perpendicular to the plane of the table, as shown. Setup completely, but
do not solve. a) What is the horizontal acceleration of the two blocks according to an observer at rest relative to the table?
b) What is the horizontal acceleration of the two blocks according to an observer moving with the pulley?
c) What is the maximum acceleration A for which the block of mass 3M will remain stationary, relative to the table? ...
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