Physics 218 Honors Final Exam; Secs. 201,202,203; Fall-lO
Name:
Section. No:
NOTE: Points are noted on each problem
1 .(1O pts) The upper surface of water in a standpipe is a height H above the level ground
a) At what depth h from the upper surface should a small hole be put to make the emerging horizontal
water stream strike the ground at the maximum distance from the base of the standpipe?
b) What is this maximum distance?
Express your answers in terms of H.
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2.(1O pts) A convex object floating on mercury has ¼ of its volume submerged. If enough water is added to
cover the object (specific gravity of mercury is 13.6 and the density of water is p = 3
1000kg/rn
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a) What fraction of its volume will remain immersed in mercury?
b) Does the answer depend on the shape of the body
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3.(12 pts) Two stars of masses M and m, separated by a distance d, revolve in circular orbits about their center
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a) What condition does the center of mass impose on ri and r2 in terms of M and m.
b) Find the period T of each star in terms of M, m, G, and d.
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4.(12 pts) A yo-yo is made from two uniform disks of radius R and combined mass M (Idisk MR
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The short shaft connecting the disks has a small radius r and negligible mass. A string of length L+R is
wrapped around the shaft several times by an expert yo-yo operator, who releases it with zero speed.
Assume the string is vertical at all times. NOTE: express all answers in terms of M, r, R, L, and g
a) What is the tension in the string during the descent of the yo-yo?
b) What is the acceleration of the CM of the yo-yo?
c) How long does it take the yo-yo to reach its maximum vertical distance before turning around and
climbing back up the string?
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5.(l0 pts) When a massive aluminum sculpture is hung from a steel wire, the fundamental frequency for
transverse standing waves on the wire is 250.0 Hz. The sculpture (but not the wire) is then completely
submerged in water. What is the new fundamental frequency? NOTE: The density of aluminum is 2.7 x
3 Kg/rn
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6. (12 pts) Energy is released by the Crab Nebula at a rate of 5 x i’ W., about i0
5 times the rate which
the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a
rapidly spinning neutron star at its center. This object rotates once every 0.0331 s and this period is
increasing by 4.22 x
s for each second of time that elapses.
a) If the rate at which energy is lost by the neutron star is equal to the rate at which energy is released by
the nebula, fmd the moment of inertia of the neutron star.
b) We think this neutron star has a mass about 1.4 times the mass of the sun. Modeling the neutron star
as a solid unifçrm sphere (I 2MR
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2
1030 kg
c) Assume the neutron star is uniform and calculate its density
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7. (12 pts) A fireworks rocket is fired vertically upward. At its maximum height of 80.0 m, it explodes
and breaks into two pieces, one with mass 1.40 kg and the other with mass 0.28 kg. In the explosion,
860 J of chemical energy is converted into kinetic energy of the two fragments.
a) What is the speed of each fragment just after the explosion?
b) It is observed that that the two fragments hit the ground at the same time. What is the distance
between the points on the ground where they land? Assume the ground is level and air friction is
ignored.
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8.(10 pts) In a shipping company, an open cart of mass 50.0 kg is rolling to the left at a speed of 5.00
mis (see Fig. below). You can ignore friction between the cart and the floor. A 15.0 kg package slides
down a chute that is inclined at 37° from the horizontal and leaves the end of the chute with a speed of
3.00 mis. The package lands in the cart and they roll off together. If the lower end of the chute is a
vertical distance of 4.00 m above the bottom of the cart, what are
a) the speed of the package just before it lands in the cart?
b) the final speed of the cart?
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9. (12 pts) A small block with mass m is placed inside an inverted cone that is rotating about a vertical
axis such that the time for one revolution of the cone is T (this the period). The walls of the cone make
an angle 13 with the vertical. The coefficient of static friction between the block and the cone is j.t
. If
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the block is to remain at a constant height h above the apex of the cone, what are the minimum and
maximum values ofT?
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