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Unformatted text preview: Spring, 2005 Name: 5 égﬁfﬂ/ﬁﬁ Signature:
Student 1]):
Email: Section Number:  You have the full class period to complete the exam. o Formulae are provided on the last page You may NOT use any other formula sheet. a When calculating numerical values, be sure to keep track of units.  You may use this exam or come up front for scratch paper.  Be sure to pet a box around your ﬁnal answers and clearly indicate your work to your
grader. a All work must be shown to get credit for the answer marked. If the answer marked does not obviously follow from the shown work, even if the answer is correct, you will not get credit for the answer. 0 Clearly erase any unwanted marks. No credit will be given if we can’t figure out which
answer you are choosing, or which answer you want us to consider.
 Partial credit can be given only if your work is clearly explained and labeled. Put your initials here after reading the above instructions: Part 1. Conceptual Questions (5 pts each)
Circle the correct answer 1. A ball is thrown up in the air. At the highest point the ball reaches,
(a) its acceleration is zero (b) its acceleration is horizontal " ts acceleration is vertically down a 7 its acceleration is verticaily up 2. If an object is in simple harmonic motion, its: Velocity is proportional to its displacement. . ' r cceleration is proportional to its displacement. Kinetic energy is proportional to its displacement.
(6) Period is proportional to its displacement. (e) Frequency is proportional to its displacement. 3. Haley’s cornet has an elliptical orbit around the sun, as shown in the figure at right. At
which ponit in its orbit does it have its greatest angular momentum with respect to the
Sun’s center? (Neglect the effect of the planets). (a) Point A
(b) Point B
(c) Point C (d Point D
(6) ts angular momentum is the same everywhere. 4. In the problem above, at which point in its orbit does it have its greatest angular velocity?  (a) Point A
) Point B
(c) Point C
(at) Point D (e) Its angular velocity is the same everywhere. 5_. When a car moves in a circle with constant speed, its acceleration is:
@ constant in magnitude and pointing towards the center (l3) constant in magnitude and pointing away from the center ((2) zero (d) constant in magnitude and direction (e) none of these Continued from part I:
6. if a body moves in such a way that its linear momentum is constant, then (a) its kinetic energy is zero. (b) the net force acting on it must be zero. (0) its acceleration must be nonzero and constant.
(ti) its center of mass must remain at rest. 0 frictional forces must be negligible. 7. You are using a wrench and trying to loosen a rusty not. Which of these arrangements wiil
be the most effective in loosening the nut? (T he diagrams are looking from below the not.)
H u Rape _E_'
W
a: I Wm“
a b. 0 Nut 8. You and your friend are riding on a merry—go—round that is turning. If your friend is twice
as far as you are from the merry~go~round’s center, and, if you and he are both of equal mass, which statement is true about your friend’s moment of inertia with respect to the axis of rotation? it is four times yours
0 It is twice yours.
6 it is the same for both of you 0 Your friend has greater moment of inertia but it is impossibie to say how much more than
yours it is. 9. The ratio of the gravitational force at an altitude 3 RE above the Earths surface (RE m the
radius of the Earth) to the gravitational force at the Earth’s surface is r
(a) 1/16 (b) 1/9
(c) 3
(d) 1/4 10. By what factor will the period of a pendulum change as you take it to an altitude 3 RE
above the surface of the earth? (a ' 1/4
(a) 1/3 Problem 2: Spacecraft in an elliptical orbit (30 points) A spacecraft of mass m in an elliptical orbit around the Earth has a low point in its orbit
(perigee) a distance from the center of the Earth; at its highest point (apogee) the
spacecraft is a distance Ra from the center of the Earth. in terms of In, RP, Ra, G, and ME (3 pts} Draw the free body diagram for the spacecraft at on of these points? {7 pts) Using conservation of angular momentum, ﬁnd the ratio of the speeds at apogee
anti perigee. (10 pts) Using conservation of energy, ﬁnd the speeé at apogee and at perigee (5 pts) What is the work necessary to escape the earth completely if we tire rockets at
apogee? (5 points) What is the work necessary to escape the earth completely if we ﬁre rockets
at perigee? Is it greater than at apogee? Problem 3: Going up a piaae (35 points)
A disk with uniform density and M and radius R is rolling Without siipping with constant speed V along a ﬂat horizontal surface. It then goes up an inclined piane of angle 6 as shown in the ﬁgure. Assume the acceleration due to gravity is given by g.
(Iaisk=(1/2)MR2) a) (10 pts) How high up the inciined plane will the ball go? In other words, What is the
height h in the ﬁgure? b) (10 pts) Draw the force diagram of the disk as it is going up the ramp. 0) (10 pts) Write down Newton’s 2mi law equations (linear and angular) of motion as the
disk is going up the ramp (1) (5 pts) What is the acceleration as the disk goes no the ramp? Problem 4: A Builet ami a Block (38 points) A bullet of mas3 m and veiocity V0 piows into a bleak of wood at rest with mass M
which is part of a pendulum and stays inside the block. Assume {hat the acceieration
due to graviiy is g. a) (5 pts) What is the veéociiy of the ﬂock/bulk: pair aﬁer the coilision? b) (7 pts) How much work is done on the block during the collision? c) (8 pts) How much energy is converted from mechanicai to non—mochanical energy?
(in, sound, heat etc.) d) (19 pts) How high, h.) does the biock ofwooé go? 8} {\ggﬁ} ig‘xéiiaﬁ; g; m gﬁﬁoﬁ o; a; ? Part 5: (30 points) ﬂ You are a stunt artist on a motorijike jumps from a ramp to the top of a building. I: is the
vertical distance from the top of the ramp to the top of the buiidiug. The ramp is a distance d away
from the buiiding. The ioitiel velocity is unknown: however the spectatoz's notice that it just so
happens that you reach the top of the building at the maximum height point during the flight, bareiy
missing the buiédiog. in this probéem yo'o shoulé igtiore air fn‘ction. Ail your answers should be in
ierms of the vaziables given. The acceleratioii of gravity is g pointing éown (g is a positive number). (5 pts) What must be ycomponent of the initial velocity so that you just barely reach the top of the
building? (10 pts) How much time does it take for you to get there? (15 pts) What is the magnitude and sogle of the initiai velocity? Again, to receive fail, or even partial, L»? credit, you must show your work that produces your answer. l $2.. Problem 6: Moving in a platform {30 points) You (mass m m) are standing at the edge ofa platform with a radius R, mass M and
=‘AMR2. i‘éeithoi you nor the platform is moving, initially and the platform can spin
without friction. You need to get the platform moving with an angular speed to. To do this you begin to walk at some constant, but unknown Speed at the outer edge of the
platform (15 points) At what speed, i‘eiative to the ground, do you need to be walking to to get the
piatform moving witii an anguiat speed a) (1g points) How much work do you need to do to accomplish this? )1 i ’2. F.
é] We. 5:5? a: 5’3??? ééfon mg} m. f {2' a a.
:: m at: jogygg a; g: éMgg a; n ...
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 Spring '06
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 mechanics

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