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27 Nov 2019

eight grams of water initially at 100o C are pouredinto a cavity in a very large block of ice initially at0o C. How many grams of ice melt before thermalequilibrium is attained?

a) 10g

b) 100g

c) 1g

d) an unknown amount; it cannot be calculated without firstknowing the mass of the block of ice

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Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

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A cylindrical-shaped pipe can carry water from a very largeelevated container on the left to a lowe container on the right.The area of the wider portion of the pipe containing the point bhas a cross sectional area Ab=7.80 x 10^-3 m^2, and the narrowersection of the pipe containing both points c and d has a crosssectional area of Ac= 3.14 x 10^-4 m^2. Point C is at height ofy2=2m above point d. A water valve closes the elevated container atpoint a, and thus there is initially only water in the uppercontainer, and none in the pipe. The rectangular block in the lowercontainer above has dimensions 10 cm x 3cm x 3cm and mass 0.075 kg,and it rests on the bottom of the lower container before any waterenters the lower container.

a) If the pressure at the surface of the water is 1 atm, what isthe absolute pressure at point a which is at a depth of y1=2 metersbelow the surface of the water in the tank?

The valve at point a is opened to create an opening equal to thearea of the pipe containing the point b so that water flows formthe elevated container through the pipe, and into the lowercontainer.

b) Consider the pressure at pints b and c. At which of these pointsis the pressure least? Justify your answer.

c) If the speed of the water at point b is vb=6 m/s, what is thespeed of the water at point c?

d) Determine vd, the speed at which the water initially enters thelower container.

e) As the water level rises in the lower container, the blockeventually begins to float. What is the height h of the water levelat the instant the block is lifted off the bottom of the container,that is, the block just begins to float?

11) A fluid in an insulated, flexible bottle is heated by ahighresistance wire and expands. If 9 kJ of heat is
applied to the system and it does 5 kJ of work, how much doestheinternal energy change?
A) 14 kJ
B) 45 kJ
C) 4 kJ
D) -4 kJ

12) The temperature is increased from 20°C to 180°C. Bywhat factordoes the rms speed of a molecule change?
A) 1.2
B) 1.5
C) 3.0
D) 2.4

13) What is the maximum efficiency of an engine operating betweenareservoir in which ice and water coexist,
and a reservoir in which water and steam coexist? The pressureisconstant at 1.0 atmosphere for both
reservoirs.
A) 0.27%
B) 1.0%
C) 27%
D) 100%

6) A child does 350 J of work while pulling a box from the groundupto his tree house with a rope. The tree
house is 8.4 m above the ground. What is the mass of the box?
A) 2.6 kg
B) 3.2 kg
C) 4.3 kg
D) 3.9 kg
7) 4.00 × 105 J of work are done on a 1110 kg car whileitaccelerates from 10.0 m/s to some final velocity. Find
this final velocity.
A) 25.7 m/s
B) 22.9 m/s
C) 28.6 m/s
D) 31.5 m/s
8) A block starts from rest at the top of a 31.0° inclinedplane andencounters a spring, of constant 3.4 kN/m,
rigidly attached to the plane. If the block's mass is 33.0 kg anditcompresses the spring by 37.0 cm, find the
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A playground ride consists of a disk of mass M = 56 kg and radius R= 2.0 m mounted on a low-friction axle. A child of mass m = 21 kgruns at speed v = 2.8 m/s on a line tangential to the disk andjumps onto the outer edge of the disk.



ANGULAR MOMENTUM
(a) Consider the system consisting of the child and the disk, butnot including the axle. Which of the following statements are true,from just before to just after the collision?
The momentum of the system doesn't change.
The momentum of the system changes.
The axle exerts a force on the system but nearly zero torque.
The torque exerted by the axle is zero because the force exerted bythe axle is very small.
The angular momentum of the system about the axle changes.
The angular momentum of the system about the axle hardlychanges.
The torque exerted by the axle is nearly zero even though the forceis large, because || is nearly zero.



(b) Relative to the axle, what was the magnitude of the angularmomentum of the child before the collision?
|C| = kg·m2/s
(c) Relative to the axle, what was the angular momentum of thesystem of child plus disk just after the collision?
|C| = kg·m2/s
(d) If the disk was initially at rest, now how fast is it rotating?That is, what is its angular speed? (The moment of inertia of auniform disk is ½MR2.)
= radians/s
(e) How long does it take for the disk to go around once?
Time to go around once = s
ENERGY
(f) If you were to do a lot of algebra to calculate the kineticenergies before and after the collision, you would find that thetotal kinetic energy just after the collision is less than thetotal kinetic energy just before the collision. Where has most ofthis energy gone?
Increased chemical energy in the child.
Increased thermal energy of the disk and child.
Increased translational kinetic energy of the disk.



MOMENTUM
(g) What was the speed of the child just after the collision?
v = m/s
(h) What was the speed of the center of mass of the disk just afterthe collision?
vcm = m/s
(i) What was the magnitude of the linear momentum of the disk justafter the collision?
|p| = kg·m/s
(j) Calculate the change in linear momentum of the systemconsisting of the child plus the disk (but not including the axle),from just before to just after impact, due to the impulse appliedby the axle. Take the x axis to be in the direction of the initialvelocity of the child.
px = px,f - px,i = kg·m/s

ANGULAR MOMENTUM
(k) The child on the disk walks inward on the disk and ends upstanding at a new location a distance R/2 = 1 m from the axle. Nowwhat is the angular speed? (It helps to do this analysisalgebraically and plug in numbers at the end.)
= radians/s
ENERGY
(l) If you were to do a lot of algebra to calculate the kineticenergies in part (k), you would find that the total kinetic energyafter the move is greater than the total kinetic energy before themove. Where has this energy come from?
Decreased chemical energy in the child.
Decreased momentum of the disk.
Decreased thermal energy of the disk and child.

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