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Unformatted text preview: Physics 1A Sgring 2009 FINAL PRACTICE TEST  Tu., June 2, 2009
Notice that this is a practice exam only for the sub jects not covered in the midterm
exams. The. actual ﬁnal exam will cover everything we have seen in the course. This exam is closed book. One usual sheet (8.5 inches. x 11 inches) with formulas (two sides) is
allowed. ' Write all units for all numerical results. For full credit on a calculation, always show your work to
get your answer. PLe‘ase put a box around your ﬁnal answer to each questiOn. This practice exam consists of a set of 2 short questions and 3 longer problems (with increasing
difﬁculty). Good luck! NAME: ————————————————————————————————————— STUDENT I.D.: —————————————————————————————— SIGNATURE: _________________________________ (1.) Short question (5 points)
A 1.00 m long rod weighing 4.00 kg is horizontally attached to a vertical wall on one side and
to a string forming an angle of 30 degrees with the rod on the other end as shown. A 10.00
kg mass is hanging from the rod at '20 cm from the the wall. Calculate the tension in the string. (2.) Short question (5 points)
A rubber ball with a. small hollowed out hole on the left side is dropped vertically down, as Shown. Before the impact with the ﬂoor the ball is not rotating. The collision is perfectly
elastic. Just after the impact will the ball rotate counterclockwise, or clockwise, or not rotate at all?
Explain brieﬂy. (3) A problem (20 points total10 each question)
An homogeneous bar of length L and mass M can rotate on a horizontal frictionless plane
around a vertical aids passing through one of its ends (the moment of inertia of the bar with
respect to its center of mass is I = ML2/12). The bar is at rest until a small ball of mass m
width velocity '5’ perpendicular to the bar hits it in the mid point, bouncing back with velocity
n" = mil/3. The mass of the bar is 9 times the mass of the ball, i.e. M = 9m. What is the angular velocity of the bar after the collision?
31:) Find the kinetic energy of the bar plus ball system just before and just after the collision. Is
the collision elastic? (Note: I could have asked you instead to compute the. initial and and final linear momentum instead and ask you if the linear momentum is conserved. You may think which would have
been your answer in this case) Vertical
got 1‘ S KL}
E %O (4) Problem (20 points) A uniform solid cylinder with mass M and radius ZR rests on a horizontal tabletop. A string
is attached by a yoke to a frictionless axle that paSses horizontally through the center of the
cylinder, so that the cylinder can rotate about the axle. The string runs over a diskshaped
pulley with mass M and radius R that is mounted on a frictionless, axle through its center. A
block also of mass M is suspended from the end of the string (see the ﬁgure). The string does
not slip over the pulley surface and the cylinder rolls without slipping on the tabletop. (The
rotational inertia of an homogenous solid cylinder or homogeneous disk of mass M and radius
r with respect to an axis perpendicular to the circular surfaces of any of them and passing
through the center of mass is I = M r2 /2) Find the magnitude of the acceleration of the block after the system is released from rest. (5) A problem (30 points total)
On a spherical asteroid of radius 525 km the gravitational acceleration at the surface is 2.7
111/32. The asteroid has no atmosphere. (G: 6.6? ><10‘11 N 1212/ kg) 5a (5 points)
What is the mass of the asteroid? 51:) (5 points)
What is the (minimum) escape speed on the surface of the asteroid? (Derive the expression
for the escape speed starting from the conservation of energy before computing it) 5c (10 points) With what speed will an object hit the asteroid if it is dropped from 1000 km above the
surface? 5—d (10 points) How far from the surface of the asteroid will a particle go if it leaves the surface. of the. asteroid
moving radially outwards with a speed of 1000 m/s? ...
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 Fall '10
 Musumeci
 Physics

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