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Unformatted text preview: Name: ................................. SID .............................. l. A mass m., initially moving with velocity v0 to the right, undergoes an elastic collision
with an initially stationary mass m. After the collision, both masses are moving to the
right, and the velocity of mass m. is one fourth the velocity of m; (V1 = i—Vz). What is the ratio ofthe two masses, ml/mg? Hint: It may be convenient to set m1 = ymg and solve for 7/. Initially your solution may appear to involve a quadratic, but in the end, it
does not. Explain your work; substantial partial credit will be given if your steps are
correct even if your algebra is wrong. (Dvlaé/mpﬁ V141) (OllﬂClTﬁlﬂpt, _\‘t.tl'W\S/ aka WMLJHPJAW Eod‘l'om e714, This page intentionally left blank. New gelm “HM— 'Fj “9* V2.3 vL :OlwO
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zvBL 5‘— 2. 2. Kate, a bungeejumper, wants tojump off the edge ofa bridge that spans a river below.
Kate has a mass m, and the surface of the bridge is a height h above the water. The bungee cord, which has length L when unstretched, will ﬁrst straighten and then stretch
as Kate falls. Assume the following: . The bungee cord behaves as an ideal spring once it begins to stretch, with spring
constant k. . Kate doesn't actually jump but simply steps off the edge of the bridge and falls straight
downward. . Kate's height is negligible compared to the length ofthe bungee cord. Hence, she can be
treated as a point particle. a. How far below the bridge will Kate eventually be hanging, once she stops
oscillating and comes finally to rest? Assume that she doesn‘t touch the water. b. What is the spring constant I? for displacements around the equilibrium position
found in part a)? In other words, if Ax is the displacement from the equilibrium found in a), what is the proper value of E in the equation Fnet = 4—ch ‘? A
“proof" is required here; very little credit will be give for simply stating the
answer. c. What is the spring constant k which will result in Katejust touching the water in
the river? 00 m?”l4%eco:o H6292. VELHQ
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3— r——. 3. A very thinwall hoop rolls without slipping down the ramp shown in the picture below. At
the very end ofthe ramp, there is a lip which launches the hoop straight up into the air. The
distance from the tOp ofthe ramp to the top ofthe lip is h. How high does the hoop rise after it is launched offthe lip? I h v a. r
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‘3 l /r' 4. What is the maximum acceleration a with which a forklift can lift a mass m without
tipping? Assume the forklift has mass M evenly distributed throughout its body, and
that the length ofthe forklift is L. (Ignore the mass ofthe fork and fork support itself.)
The mass m is a distance x in front of the front wheel of the forklift. ...
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 Spring '10
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