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Physics 218 Honors Final Exam; Secs. 201,202,203; Fal
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Name:
Section. No:
NOTE: Points are noted on each problem
1 .( 12 pts) A certain quaternary star system consists of three stars
each of mass m moving in the same
circular orbit of radius R about a central star of mass M. The stars
orbit in the same sense and are
positioned one-third of a revolution apart from one another.
a) Compute the net centripetal force on one of the stars of mass m.
(HINT: do not forget the
gravitational force exerted on each mass m due to the othe two
r
identical masses in addition to the large
mass M)
,
b) Compute the period of the three stars in terms of G, M, m, and
R
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2.(10 pts) How many cubic meters of helium, are required to lift a balloon with a 400 kg payload
to a height of
8,000 m? (Take PHC 0.180 kg/m
.) Assume the balloon maintains a constant volume and the density of air
3
decreases with the altitude according to the expression Pair = Po ,
000 where z is in meters and
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3.(lO pts) A flexible cable of weight W hangs between the
two pegs located at the same height. At each peg,
the tangent to the cable makes an angle 0 with the horizonta
l.
a) Find the magnitude of the force that each peg exerts on
the cable. Draw a free body diagram for the cable
b) Find the tension in the chain at its midpoint. Draw a
free body diagram for the half-cable
Express your answers in terms of W and 0.
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4.(12 pts) A spool of thread consists of a cylinder of radiu
sR
1 with end caps of radius R
2 as shown
below. The mass of the spool, including the thread, is
m,and its moment of inertia about an axis
through its center is I. The spool is placed on a rough horiz
ontal surface so that it rolls without slipping
when a force T acting to the right is applied to the free
end of the thread.
a) Find the direction of the friction force. Explain.
b) Find the magnitude of the friction force exerted by the
surface on the spool in terms of T, R
,R
1
, m,
2
and 1.
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5.( 10 pts) A 0.500-kg sphere moving with a velocity
given by (2.001—3.003+1.00 k) mIs strikes
another sphere of mass 1.5 kg that is moving with
a velocity of (—1.001 + 2.003 3.00 k) rn/s. The
velocity of the 0.500 kg sphere after the collision
is given by (—1.001+3.003 8.00k) mIs.
a) Find the final velocity of the 1.50 kg sphere
b) Is the collision elastic, inelastic, or perfectly inela
stic? Justify your answer
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6. (12 pts) A 5.00 g bullet moving with an initial speed of 400
mIs is fired into and passes through a
1.00 kg block as shown below. The block, initially at rest
on a frictionless horizontal surface, is
connected to a spring with force constant 900 N/rn. The bloc
k moves 5.00 cm to the right after impact
before stopping.
a) Find the speed at which the bullet emerges from the bloc
k
b) Find the mechanical energy converted into internal ener
gy in the collision.
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7. (12 pts) A toy cannon uses a spring to project a 5.30-g
soft rubber ball. The spring is originally
compressed by 5.00 cm and has a force constant of 8.00
N/rn. When the cannon is fired, the ball moves
15.0 cm through the horizontal barrel of the cannon and the
barrel exerts a constant force of 0.0320 N on
the ball.
a) With what speed does the ball leave the barrel of the cannon
b) At what point along the barrel does the ball have maxim
um speed?
c) What is this maximum speed?
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8.(12 pts) A string on a musical instrument is held under tension
T and extends from the point x 0 to
the point x = L. The string is overwound with wire in such a way
that its mass per unit length jL(x)
increases uniformly from jio at x =0 to IlL at x = L.
a) Find an expression for ji(x) as a function of x over the range
0 x L.
b) Find the time interval required for a transverse pulse to travel
the length of the string.
Express your answer in terms of T, L, IlL, and
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9. (10 pts) Two wires are welded together end-to-end. The wires are made of the same materi
al, but the
diameter of one is twice that of the other. They are subjected to a tension of 4.60 N.
The thin wire has a
length of 40.0 cm and a linear density of 2.00 g/m. The combination is fixed at both
ends and vibrated
in such a way that two antinodes are present, with the node between them being precise
ly at the weld.
a) What is the frequency of vibration
b) What is the length of the thick wire?
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