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Ch4 HW2

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WebAssign Ch4 HW2 (Homework) BLAKE T BREDBENNER PHYS 2211, section N, Spring 2009 Instructor: Edwin Greco Due: Monday, February 2, 2009 09:00 AM EST About this Assignment Ask Your Teacher Extension Requests Question Points 12345 6 7 8 6 3 2 6 3 0/4 0/2 1 Total 21/27 Description Ball-spring model of a solid; tension forces; length of interatomic bond. Instructions Reading: Sec. 4.1-4.4

The due date for this assignment is past. Your work can be viewed below, but no changes can be made. 1.

6/6 points

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Question: MI2 04.X.00

A climber whose mass is 50 kg hangs motionless from a rope. What is the tension in the rope? tension = 490

490 N

Later, a different climber whose mass is 80 kg hangs from the same rope. Now what is the tension in the rope? tension = 784

784 N

Compare the physical state of the rope when it s the heavier climber to the state of the rope when it s the lighter climber. Which statements about the physical state of the rope are true? Check all that apply. The interatomic bonds in the rope are stretched more when the rope s the haevier climber than when the rope s the lighter climber.

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The rope is slightly longer when it s the heavier climber than when it s the lighter climber. Because the same rope is used, the tension in the rope must be the same in both cases.

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3/3 points

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Question: MI2 04.X.00.01

Why are two balls connected by a spring a good model for two atoms connected by a chemical bond? If the two atoms get farther apart than the equilibrium interatomic distance, they attract each other. If the two atoms get closer together than the equilibrium interatomic distance, they repel each other. The magnitude of the force one atom exerts on another is proportional to the stretch or compression of the bond between them. Each spring represents a real microscopic coiled metal wire that connects two adjacent atoms.

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2/2 points

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Question: MI2 04.X.00.02

Consider a 3 kg block of magnesium modeled as an array of balls connected by springs, as shown in Figure 4.6 on page 107. What is the mass in kg of a single "ball" in the ball-spring model? One mole (6.02 1023 atoms) of magnesium has a mass of 24 grams, as shown in the periodic table on the inside front cover of the textbook. 3.99 10-26 kg 0.024 kg 4.98 10-24 kg 3 kg 125.0 kg 6.02

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6/6 points

1023 kg

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Question: MI2 04.X.00.03

The diameter of a copper atom is approximately 2.28e-10 m. The mass of one mole of copper is 64

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grams. Assume that the atoms are arranged in a simple cubic array, as shown in Figure 4.10, on p. 109. to convert to S.I. units. What is the mass of one copper atom, in kg? mass = 1.06e-25 1.06e-25 kg How many copper atoms are there in a cubical block of copper that is 3 cm on each side? 2.28e+24 number of atoms = 2.28e24 What is the mass of the cubical block of copper, in kg? mass of block = .242 0.242 kg

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3/3 points

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Question: MI2 04.X.01

One mole of magnesium (6 1023 atoms) has a mass of 24 grams, as shown in the periodic table on the inside front cover of the textbook. The density of magnesium is 1.7 grams/cm3. What is the approximate diameter of a magnesium atom (length of a bond) in a solid block of the material? Make the simplifying assumption that the atoms are arranged in a "cubic" array, as shown in Figure 4.10 on page 109. to convert to SI units. d = 2.86e-10

2.87e-10 m

Solution or Explanation See the example on pages 108-109.

6.

0/4 points

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One mole of iron (6

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Question: MI2 04.X.04.02

1023 atoms) has a mass of 56 grams, and its density is 7.87 grams per cubic

centimeter, so the center-to-center distance between atoms is 2.28 10-10 m. You have a long thin bar of iron, 2.0 m long, with a square cross section, 0.12 cm on a side. You hang the rod vertically and attach a 148 kg mass to the bottom, and you observe that the bar becomes 1.01 cm longer. From these measurements, it is possible to determine the stiffness of one interatomic bond in iron. 1) What is the spring stiffness of the entire wire, considered as a single macroscopic (large scale), very stiff spring? ks = 1.4e5 1.44e+05 N/m

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2) How many side-by-side atomic chains (long springs) are there in this wire? This is the same as the number of atoms on the bottom surface of the iron wire. Note that the cross-sectional area of one iron atom is (2.28 10-10)2 m2. Number of side-by-side long chains of atoms = (No Response) 2.77e+13 3) How many interatomic bonds are there in one atomic chain running the length of the wire? Number of bonds in total length = (No Response) 8.77e+09 4) What is the stiffness of a single interatomic "spring"? 45.6 N/m ks,i = (No Response) An interatomic bond in iron is stiffer than a slinky, but less stiff than a pogo stick. The stiffness of a single interatomic bond is very much smaller than the stiffness of the entire wire.

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0/2 points

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Question: MI2 04.P.78.alt03

A hanging wire made of an alloy of titanium with diameter 0.06 cm is initially 3.0 m long. When a 20 kg mass is hung from it, the wire stretches an amount 1.73 cm. A mole of titanium has a mass of 48 grams, and its density is 4.54 g/cm3. Based on these experimental measurements, what is Young's modulus for this alloy of titanium? Y = 6.01e10

1.20e+11 N/m2

As you've done before, from the mass of one mole and the density you can find the length of the interatomic bond (diameter of one atom). This is 2.60 10-10 m for titanium. As shown in the textbook, the micro quantity ks,i (the stiffness of one interatomic bond) can be related to the macro property Y: ks,i = (No Response) 31.2 N/m

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1/1 points

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Question: MI2 04.X.05.02

Two wires are made of the same kind of metal. Wire A has a diameter of 3.2 mm and is initially 2.4 m long. You hang a 11 kg mass from wire A, measure the amount of stretch, and determine Young's modulus to be YA = 1.39

1012 N/m2.

Wire B, which is made of the same kind of metal as wire A, has the same length as wire A but twice

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the diameter. You hang the same 11 kg mass from wire B, measure the amount of stretch, and determine Young's modulus, YB. Which of the following is true? YB < YA YB = YA YB > YA

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