The number 6 has four divisorsnamely, 1, 2, 3, and 6. List all numbers less than 20 that have exactly four divisors.

The volume of a typical neuron is about 3 10 -8 cm 3 . Write each of the numbers in Problems 1922 in fixed-point notation.

From unit-cell parameters in figures in this chapter, calculate the following shortest distances: (a) NaCl and NaNa in NaCl, (b) NiNi in NiAs, (c) CaF in CaF 2 , (d) CC in diamond, (e) TiTi in TiO 2...

The first Brillouin zone of an infinite chain of H atoms has an infinite number of crystal orbitals, each with a different value of k. (a) State the limiting values of k within the first Brillouin...

Identify the reagents necessary to accomplish each of the transformations shown below. If you are having trouble, the reagents for these transformations appear on page 444, but you should first try...

Identify the reagents that you would use to accomplish each of the following transformations: a. b. c. d. e. f. -Br OH

Draw a mechanism and predict the major product for each reaction. a. b. c. d. e. f. ? 1) LAH H. 2) H20

Identify the reagents you would use to achieve the following transformations: a. b. Br Br

The following triene reacts with excess maleic anhydride to produce a compound with molecular formula C 14 H 12 O 6 . Draw the structure of this product (ignoring stereochemistry). Maleic anhydride...

Draw the mechanism for each of the following reactions: a. b. c. NaOMe CI NaOEt. Br

The temperature of 1.75 moles of an ideal gas increases from 10.2C to 48.6C as the gas is compressed adiabatically. Calculate q, w, U, and H for this process assuming that C V ,m = 3/2 R.

In the experiment shown in Figure 2.4b, the weight drops in a very short time. How will the temperature of the water change with time? Figure 2.4b Electrical generator Mass Heating - coil (b)

Identify the reagents necessary to accomplish each of the transformations below: (a) (b)

Why is there an upper limit to the photon energy that can be observed in the emission spectrum of the hydrogen atom?

Propose an efficient synthesis for the following transformation.

Draw the structure of the product with molecular formula C 10 H 10 O that is obtained when the compound below is heated with aqueous acid. CN CN C10H100 Heat

Propose an efficient synthesis for each of the following transformations: (a) (b)

Why is the probability of finding the harmonic oscillator at its maximum extension or compression larger than that for finding it at its rest position?

A gas-phase 1 H 127 I molecule, with a bond length of 160.92 pm, rotates in three dimensional space. a. Calculate the zero point energy associated with this rotation. b. What is the smallest quantum...

Derive the ground-state term symbols for the following configurations: a. d 5 b. f 3 c. p 4

The electron affinities of He, Be, and Ne are negative, meaning that the negative ion is less stable than the neutral atom. Explain why this is so for these three elements.

Calculate the mean value of the radius r at which you would find the electron if the H atom wave function is 210 (r, , ).

Propose an efficient synthesis for each of the following compounds using the acetoacetic ester synthesis. (a) (b) (c) (d)

Show by carrying out the appropriate integration that the total energy eigenfunctions for the harmonic oscillator 0 (x) ( /) 1/4 e -(1/2)ax2 and 2 (x) ( /4) 1/4 (2x - 1) e -(1/2)ax2 are orthogonal...

Fill in the missing step in the derivation that led to the calculation of the spectral line shape in Figure 19.24. Starting from and neglecting the first term in the parentheses, show that Figure...

The Grotrian diagram in Figure 22.7 shows a number of allowed electronic transitions for He. Which of the following transitions shows multiple spectral peaks due to a splitting of terms into levels?...

Evaluate the vibrational partition function for CFCl 3 at 298 K, where the vibrational frequencies are (with degeneracy in parentheses) 1081, 847 (2), 535, 394 (2), 350., and 241(2) cm 1 .

The half-life of 238 U is 4.5 10 9 years. How many disintegrations occur in 1 minute for a 10.0-mg sample of this element?

Use the VSEPR method to predict the structures of the following: a. PCl 5 b. SO 2 c. XeF 2 d. XeF 6

One loss mechanism for ozone in the atmosphere is the reaction with the HO2 radical: HO 2 · (g) + O 3 (g) OH · (g) + 2O 2 (g) Using the following information, determine the rate law...

Determine the maximum magnitude P of the loads the beam can support if the average shear stress in each pin is not to exceed 80 MPa. All pins are in double shear, and each has a diameter of 18 mm. 6P...

The shaft is supported by a smooth thrust bearing at B and a journal bearing at C. Determine the resultant internal loadings acting on the cross section at E. - 4 ft 4 ft +4 ft- 4 ft- 400 lb 800 lb

The rectangular plate is deformed into the shape shown by the dashed lines. Determine the average normal strain along diagonal BD, and the average shear strain at corner B relative to the x, y axes....

The beam supports the triangular distributed load shown. Determine the resultant internal loadings on the cross section at point C. Assume the reactions at the supports A and B are vertical. 800...

Determine the largest load P that can be applied to the frame without causing either the average normal stress or the average shear stress at section aa to exceed Ï = 150 MPa and Ï = 60...

The rigid bar is supported by the pin-connected rod CB that has a cross-sectional area of 14 mm 2 and is made from 6061-T6 aluminum. Determine the vertical deflection of the bar at D when the...

The 2014-T6 aluminium rod has a diameter of 30 mm and supports the load shown. Determine the displacement of end A with respect to end E. Neglect the size of the couplings. 8 kN 2 kN 6 kN 4 kNY -2m-...

The 3-in.-diameter shaft is made of an elastic perfectly plastic material as shown. Determine the radius of its elastic core if it is subjected to a torque of T = 18 kip ft. If the shaft is 3 ft...

Express the internal shear and moment in the cantilevered beam as a function of x and then draw the shear and moment diagrams. 300 Ib 200 lb/ft 6 ft

Draw the shear and moment diagrams for the beam and determine the shear and moment in the beam as functions of x, where 4 ft < x < 10 ft. 150 Ib/ft 200 lb-ft 200 Ib-ft B- 4 ft ft- 6 ft 4 ft

The beam is subjected to a moment of 15 kip ft. Determine the percentage of this moment that is resisted by the web D of the beam. 1 in. 5 in. 8 in. M = 15 kip-ft- 1 in. 1 in. 3 in

The Douglas Fir beam is reinforced with A-992 steel straps at its sides. Determine the maximum stress in the wood and steel if the beam is subjected to a moment of M z = 80 kN · m. Sketch the...

Determine the shape factor for the wide-flange beam. 15 mm 20 mm 200 mm M. 15 mm 200 mm

Determine the shear stress at points B and C on the web of the beam located at section aa. 8000 lb 150 Ib/ft B. 4 ft -4 ft - 1.5 ftT1.5 ft

Determine the location e of the shear center, point O, for the thin-walled member. The member segments have the same thickness t. -- IT

The steel water pipe has an inner diameter of 12 in. and a wall thickness of 0.25 in. If the valve A is opened and the flowing water has a pressure of 250 psi as it passes point B, determine the...

Determine the normal stress developed at points A and B. Neglect the weight of the block. 6 kip 3 in. 12 kip 6 in.: D. B.

Determine the equivalent state of stress on an element at the point which represents (a) the principal stresses and (b) the maximum in-plane shear stress and the associated average normal stress....

Determine the equivalent state of stress on an element at the same point which represents (a) the principal stress, and (b) the maximum in-plane shear stress and the associated average normal stress....

Determine the equivalent state of stress if an element is oriented 60° clockwise from the element shown. 65 ksi

The wood beam is subjected to a load of 12 kN. If grains of wood in the beam at point A make an angle of 25° with the horizontal as shown, determine the normal and shear stress that act...

The box beam is subjected to the 26-kN force that is applied at the center of its width, 75 mm from each side. Determine the principal stresses at point A and show the results in an element located...

The floor of a heavy storage warehouse building is made of 6-in.-thick stone concrete. If the floor is a slab having a length of 15 ft and width of 10 ft, determine the resultant force caused by the...

The bolt is fixed to its support at C. If a force of 18 lb is applied to the wrench to tighten it, determine the principal stresses and the absolute maximum shear stress in the bolt shank at point A....

Classify each of the structures as statically determinate, statically indeterminate, stable, or unstable. If indeterminate, specify the degree of indeterminacy. The supports or connections are to be...

Classify each of the structures as statically determinate, statically indeterminate, stable, or unstable. If indeterminate, specify the degree of indeterminacy. a. b. c. d.

The beams AB and BC are supported by the cable that has a parabolic shape. Determine the tension in the cable at points D, F, and E, and the force in each of the equally spaced hangers. 3'm 9 m A B 5...

Draw the shear and moment diagrams for each member of the frame. The joints at A, B, and C are pin connected. 250 lb/ft B 120 lb/ft JA 6 ft- 6 ft 8 ft 60

Draw the shear and moment diagrams for each member of the frame.The members are pin connected at A, B, and C. 15 kN 10 kN -2 m -2 m -2 m A 4 kN/m 6 m 45%

Draw the shear and moment diagrams for each member of the frame. Assume A is fixed, the joint at B is a pin, and support C is a roller. 20 k 0.5 k/ft B 8 ft |A - 6 ft- 6 ft

The compound beam is subjected to a uniform dead load of 1.5 kN/m and a single live load of 10 kN. Determine (a) The maximum negative moment created by these loads at A, and (b) The maximum positive...

Determine the absolute maximum moment in the beam due to the loading shown. 20 kN 40 kN 25 kN 15 mo -12 m-

Use the cantilever method and determine (approximately) the reactions at supports A, B, C, and D. All columns have the same cross-sectional area. K 9 kN 4 m 12 kN 4 m 5 m 5 m 5 m -

Determine the displacement at C. Assume A is a fixed support,Bis a pin, and Dis a roller. EI is constant. Use the conjugate-beam method. 25 kN -3 m -3 m 3 m

Determine the equations of the elastic curve using the coordinates x 1 and x 3 , and specify the slope and deflection at point B. EI is constant. X2 L -

Use the method of virtual work and determine the horizontal deflection at C. EI is constant. There is a pin at A. Assume C is a roller and B is a fixed joint. 400 lb/ft 6 ft 10 ft 45

Convert 3.65 10 3 cubic millimeters to cubic meters.

The fuel tank of an automobile holds 0.095 m 3 . If it is full of gasoline having a specific gravity of 0.68, calculate the weight of the gasoline.

Which would have the greater dynamic viscosity, a cold lubricating oil or fresh water? Why?

Calculate the mass of a body in kg if it has a kinetic energy of 38.6 Nm when moving at 31.5 km/h. The formula for kinetic energy is KE = mv 2 , where m = mass and v = velocity.

The maximum pressure that can be developed for a certain fluid power cylinder is 15.0 MPa. Compute the required diameter for the piston if the cylinder must exert a force of 30 kN.

Determine which of the following describe traveling waves: (a) (b) (c) (d) Where appropriate, draw the profile and find the speed and direction of motion. (y, t) = ea*y+br2abty) | V(z, t) = A sin (az...

Show that the function is a solution of the differential wave equation. In what direction does it travel? (y, t) = (y 41)

Write the expression relating gage pressure, absolute pressure, and atmospheric pressure.

If milk has a specific gravity of 1.08, what is the pressure at the bottom of a milk can 550 mm deep?

A water storage tank is on the roof of a factory building and the surface of the water is 50.0 ft above the floor of the factory. If a pipe connects the storage tank to the floor level and the pipe...

For the tank shown in Fig. 3.21, determine the reading of the bottom pressure gage in psig if the top of the tank is sealed, the top gage reads 50.0 psig, and the depth of the oil h is 28.50 ft. Air...

For the tank in Fig. 3.22, compute the depth of the water if the depth of the oil is 6.90 m and the gage at the bottom of the tank reads 125.3 kPa(gage). Vent Oil (sg = 0.86) h2 Water

For the water tank shown in Fig. 4.43, compute the magnitude and location of the total force on the vertical back wall. 8 ft Water 60 15 ft 10 ft

Prove that for a vacuum-dielectric interface at glancing incidence r ¥ -1, as in Fig. 4.49. Fig. 4.49. 1.0 0.5 -0.5 56.3 -1.0 30 90 0; (degrees) Amplitude coefficients

A concrete block with a specific weight of 23.6 kN/m 3 is suspended by a rope in a solution with a specific gravity of 1.15. What is the volume of the concrete block if the tension in the rope is...

A steel cube 100 mm on a side weighs 80 N. We want to hold the cube in equilibrium under water by attaching a light foam buoy to it. If the foam weighs 470 N/m 3 , what is the minimum required volume...

A certain deep-well pump for a residence is rated to deliver 745 gal/h of water. Express this flow rate in ft 3 /s.

The recommended velocity of flow in the discharge line of an oil hydraulic system is in the range of 8.0 to 25.0 ft/s. If the pump delivers 30 gal/min of oil, specify the smallest and largest...

A spacecraft that is initially at rest turns on its engine at t - 0. If its mass is m - 3000 kg and the force from the engine is 45 N, what is the acceleration of the spacecraft?

A rock is dropped from a very tall tower. If it takes 4.5 s for the rock to reach the ground, what is the height of the tower?

A spa tub is to be designed to replace bath tubs in renovations. There are to be 6 outlet nozzles, each with a diameter of 12 mm, and each should have an outlet velocity of 12 m/s. What is the...

Solve Problem 6.88 using the direct application of torricelli's theorem. What depth of fluid above the outlet nozzle is required to deliver 200 gal/min of water from the tank shown in Fig. 6.37? The...

For the tank shown in Fig. 6.38, compute the velocity of flow from the outlet nozzle at varying depths from 10.0 ft to 2.0 ft in 2.0-ft increments. Then, use increments of 0.5 ft to zero. Plot the...

Figure 6.37 shows a venturi meter with a U-tube manometer to measure the velocity of flow. When no flow occurs, the mercury column is balanced and its top is 300 mm below throat. Compute the volume...

Figure 6.36 shows a system in which water flows from a tank through a pipe system having several sizes and elevations. For points A-G, compute the elevation head, the pressure had, the velocity head,...

For the venturi meter shown in Fig. 6.30, calculate the manometer deflection h if the velocity of flow of water in the 25-mm-diameter section is 10 m/s. Direction of flow 25-mm diameter 50-mm...

In the fabricated enlargement shown in Fig. 6.29, the pressure at A is 25.6 psig and the pressure at B is 28.2 psig. Calculate the volume flow rate of oil (sg = 0.90). Direction of flow 5-in inside...

A standard 6-in Schedule 40 steel pipe is carrying 95 gal/min of water. The pipe then branches into two standard 3-in pipes. If the flow divides evenly between the branches, calculate the velocity of...

Repeat Problem 6.51 for a 4-in Schedule 80 pipe. Repeat Problem Compute the resulting velocity of flow if 400 gal/min of fluid flows through a 4-in Schedule 40 pipe.

A standard steel tube, 1.5 25-mm OD 1.5-mm wall (Appendix G.2), is carrying 19.7 L/min of oil. Calculate the velocity of flow.

Oil with a specific weight of 55.0 lb / ft 3 flows from A to B through the system shown in Fig. 6.35. Calculate the volume flow rate of the oil.

A 4-in-ductile iron pipe carries 0.20 ft 3 /s of glycerin (sg = 1.26) at 100F. Is the flow laminar or turbulent?

Calculate the maximum volume flow rate of fuel oil at 45C at which the flow will remain laminar in a DN 100 Schedule 80 steel pipe. For the fuel oil, use sg = 0.895 and dynamic viscosity = 4.0 10 -2...

In a dairy, milk at 100F is reported to have a kinematic viscosity of 1.30 centistokes. Compute the Reynolds number for the flow of the milk at 45 gal/min through a 1-in steel tube with a wall...