Download General Physics Contest 2010 May 22, 2010 (9:10

General Physics Contest 2010
May 22, 2010 (9:10-10:50), Total 5 pages
Part I : Choice Questions (20 single-choice questions of 3% each. Use 2B pencil to mark the answer.)
1.
A particle moving along the x-axis has a position function given by x(t) = (4.00 m/s3) t3-(5.00
m/s) t + (6.00 m). What is the average acceleration of the particle between t = 1.00 s and
t = 2.00 s. (A) 24 m/s2 (B )12 m/s2 (C) 36 m/s2 (D)18 m/s2 (E)30 m/s2.
2.
Two planets have masses M and m, and the ratio M/m = 25. The
distance between the planets is R. The point P is between the
planets as shown, and the distance between M and P is x. At P, the
gravitational force on an object due to M and m are equal in
magnitude. The value of x is (A) 5R/6 (B) 25R/36 (C) R/25
(D) 6R/5 (E) none of these.
3.
Two masses are connected by a heavy (1.00 kg) cable.
The two masses are pulled along a smooth horizontal
surface by an external force P = 22.0 N as shown in figure.
Calculate the tension in the cable at its midpoint.
(A) 11.0 N
4.
(C) 8.0 N (D) 9.0 N
(E) 22.0 N.
A lamp with a mass m is suspended from the ceiling by two
cords as shown. The ratio of the magnitude of the vertical
component of the tension in T2 to that in T3 is
(A) 1：1
5.
(B) 10.0 N
(B) 1：2
(C)
3 ：3
(D) 3：2
P=22N
6kg
4kg
T2
T3
T1
(E) 3：1.
A mass m2 = 1.5 kg rests on a horizontal table. The static and
kinetic coefficients of friction between m2 and the table are
m2
s = 0.3 and k = 0.25, respectively. The mass m2 is attached
m1
by strings to masses m1 = 2.5 kg and m3 = 4.5 kg as shown.
Masses m1 and m3 hang freely. The system is initially held at
rest. After it is released, the acceleration of m2 is
approximately (A) 1.9 m/s2 (B) 2.4 m/s2 (C) 3.0 m/s2 (D) zero (E) 13 m/s2.
1
m3
6.
The balls shown in the figure are strung on a taut wire and slide without friction. If the balls are
of equal mass, the diagram that best represents an elastic collision is:
After collision
(A)
(B)
After
collision
(C)
(D)
(E)
7.
A cube of side 2a and mass M is sliding on a
frictionless surface with uniform velocity v0, as
shown in the Figure. It hits a small obstacle at
the end of the table, which causes the cube to
tilt as in Fig. b. Find the minimum value of v0
such that the cube will fall off the table (g is the
gravitational acceleration constant on earth). (A)
(C)
8.
16
3
ag ( 2  1)
(D)
4
ag ( 2  1)
3
3
v0
h=a
F=Mg
Fig. b
Fig. a
2ag ( 2  1)
(B)
4ag ( 2  1)
ag ( 2  1) .
A wooden rod of uniform cross section and of length l is hinged
at the bottom of a tank which is filled with water to a height
h =l/3. If the density of wood is 0.45 g/cm3, find the angle 
from the vertical at which the rod is in equilibrium.
(A)   60 (B)   30 (C)   45
9.
8
(E)
2a
h=l/3 θ
(D)   37 (E)   53
One source of sound is at A and another is at B. The two sources
are in phase. The distance AB =10.0 m. The frequency of the
sound wave from both sources is 1000 Hz and both the same
amplitude. The speed of sound in air is 330 m/s. A receiver is at
point C, and AB is perpendicular to AC . The greatest distance
AC for which the signal at C is a minimum is
(A) 330 cm (B) 152 m (C) 330 m (D) 303 m (E) 100 m.
2
A
B
C
10. A speedboat moving at 20.6 m/s sounds a signal on its horn, producing a tone of 320 Hz. There
is no wind, and the speed of sound in air is 329 m/s. The apparent frequency of the sound heard
by an observer in another boat moving in the opposite direction and approaching the first at a
speed of 15.4 m/s is (A) 282 Hz (B) 287 Hz (C) 316 Hz (D) 357 Hz (E) 369 Hz.
11. The specific heat of a substance is:
(A) the amount of heat energy to change the state of one gram of the substance.
(B) the amount of heat energy per unit mass emitted by oxidizing the substance.
(C) the amount of heat energy per unit mass to raise the substance from its freezing to its
boiling point.
(D) the amount of heat energy per unit mass to raise the temperature of the substance by 1˚C.
(E) the temperature of the object divided by its mass.
12. Two ideal gases, each consisting of N monatomic molecules, are in thermal equilibrium with
each other and equilibrium is maintained as the temperature is increased. A molecule of the first
gas has mass m and a molecule of the second has mass 4m. The ratio of the changes in the
internal energies ΔE4m/ΔEm is: (A) 1/4 (B) 1/2 (C) 1 (D) 2 (E) 4.
13. The temperatures TC of the cold reservoirs and the temperatures TH of the hot reservoirs for
four Carnot heat engines are
engine 1: TC = 400K and TH = 500K
engine 2: TC = 500K and TH = 600K
engine 3: TC = 400K and TH = 600K
engine 4: TC = 600K and TH = 800K
Rank these engines according to their efficiencies, least to greatest
(A) 1, 2, 3, 4 (B) 1 and 2 tie, then 3 and 4 tie (C) 2, 1, 3, 4 (D) 1, 2, 4, 3 (E) 2, 1, 4, 3
14. Consider the following procedural steps:
1. ground an electroscope.
2. remove the ground from the electroscope.
3. touch a charged rod to the electroscope.
4. bring a charged rod near, but not touching, the electroscope.
5. remove the charged rod.
To charge an electroscope by induction, use the sequence:
(A) 1, 4, 5, 2 (B) 4, 1, 2, 5 (C) 3, 1, 2, 5 (D) 4, 1, 5, 2 (E) 3, 5
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15. Two charged point particles are located at two vertices of an equilateral triangle and the electric
field is zero at the third vertex. We conclude:
(A) the two particles have charges with opposite signs and the same magnitude.
(B) the two particles have charges with opposite signs and different magnitudes.
(C) the two particles have identical charges.
(D) the two particles have charges with the same sign but different magnitudes.
(E) at least one other charged particle is present.
16. 10C (Coulomb) of charge are placed on a spherical conducting shell. A particle with a charge of
−3C is placed at the center of the cavity. The net charge on the outer surface of the shell is:
(A) −7C
(B) −3C
(C) 0C
(D) +3C
(E) +7C
17. Two conducting spheres are far apart. The smaller sphere carries a total charge Q. The larger
sphere has a radius that is twice that of the smaller and is neutral. After the two spheres are
connected by a conducting wire, the charges on the smaller and larger spheres, respectively, are:
(A) Q/2 and Q/2 (B) Q/3 and 2Q/3 (C) 2Q/3 and Q/3 (D) zero and Q (E) 2Q and –Q
18. Capacitors C1 and C2 are connected in parallel. The equivalent capacitance is given by:
(A) C1C2/(C1 + C2) (B) (C1 + C2)/C1C2
(C)1/(C1 + C2) (D) C1/C2
(E) C1 + C2
19. The current is from left to right in the conductor shown. The
magnetic field B is into the page and point S is at a higher
potential than point T. The charge carriers are:
(A) positive (B) negative (C) neutral (D) absent
(E) moving near the speed of light
B 
20. A constant current is sent through a helical coil. The coil:
(A) tends to get shorter (B) tends to get longer (C) tends to rotate about its axis
(D) produces zero magnetic field at its center (E) none of the above
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Part II: Problems (4 problems of 10% each. Answer the questions as clear as possible.)
1.
A person stands on a platform that can rotate
about a vertical axis. The person holds a heavy
weight of mass M in each of his hands which
are stretched out as shown in Fig1-a. The
platform was set in uniform circular motion
Axis of rotation

R

R
R
2
M
M
M
R
2
M
F=mg(external)
with angular velocity 1. At same time, the
person brings his arms closed to his body so
that the distance of each mass to the rotation
axis is reduced from R to R/2, as shown in
Fig1-b. The rotational inertias of the person
and the platform are negligible. Find:
Fig. 1-a.
(a) the gain of rotation energy;
(b) the work done by hands when the weights were pulled in.
2. A cart consists of a body of mass m and two wheels,
each of mass M and radius R. The cart is attached to a
spring of constant k. The other end of the spring is fixed
to a wall as shown in Fig. 2. Find an expression for the
horizontal oscillatory motion of the cart.
Fig. 1-b.
k
m
R
Fig. 2.
5
M
3. The cycle in Fig. 3 represents the operation of a gasoline internal
combustion engine. Assume the gasoline-air intake mixture is an
ideal gas with  = 1.30. What are the ratios
(a) T2/T1, T3/T1 and T4/T1, (b) p3/p1 and p4/p1?
(c) What is the engine efficiency?
Fig. 3.
4.
Figure 4 shows a parallel-plate capacitor of plate area
A and plate separation d. A potential difference V0 is
applied between the plates. The battery is then
disconnected, and a dielectric slab of thickness b and
dielectric constant  is placed between the plates as
shown. Assume A= 115 cm2, d = 1.24 cm, V0 = 85.5 V,
b = 0.780 cm, and  = 2.61. (Permittivity constant 0 =
Fig. 4.
8.85 x 10-12 F/m)
(a) What is the capacitance C0 before the dielectric slab is inserted? What free charge appears
on the plates?
(b) What is the electric field E0 in the gaps between the plates and the dielectric slab?
(c) What is the electric field E1 in the dielectric slab?
(d) What is the potential difference V between the plates after the slab has been introduced?
(e) What is the capacitance with the slab in place between the plates of the capacitor?
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