Question

asked 2021-05-05

The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with \(\displaystyle\mu={1.5}\) and \(\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}\).

(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.

(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than \(\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}\).

(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of \(\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}\)? Explain, based on theprobability of this occurring.

(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?

(e) What is the moment generating function for X?

(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.

(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than \(\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}\).

(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of \(\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}\)? Explain, based on theprobability of this occurring.

(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?

(e) What is the moment generating function for X?

asked 2021-03-30

A potential difference of 480V is established between largeparallel, metal plates. Let the potential of one plate be 480V andthe other be 0V. The plates are separated by d = 1.70cm.

a) Sketch the equipotential surfaces that correspond to 0, 120,240, 360, and 480 V.

b) In your sketch, show the electric field lines. Does yoursketch confirm that the field lines and surfaces are mutually perpendicular?

a) Sketch the equipotential surfaces that correspond to 0, 120,240, 360, and 480 V.

b) In your sketch, show the electric field lines. Does yoursketch confirm that the field lines and surfaces are mutually perpendicular?

asked 2021-04-25

The unstable nucleus uranium-236 can be regarded as auniformly charged sphere of charge Q=+92e and radius \(\displaystyle{R}={7.4}\times{10}^{{-{15}}}\) m. In nuclear fission, this can divide into twosmaller nuclei, each of 1/2 the charge and 1/2 the voume of theoriginal uranium-236 nucleus. This is one of the reactionsthat occurred n the nuclear weapon that exploded over Hiroshima, Japan in August 1945.

A. Find the radii of the two "daughter" nuclei of charge+46e.

B. In a simple model for the fission process, immediatelyafter the uranium-236 nucleus has undergone fission the "daughter"nuclei are at rest and just touching. Calculate the kineticenergy that each of the "daughter" nuclei will have when they arevery far apart.

C. In this model the sum of the kinetic energies of the two"daughter" nuclei is the energy released by the fission of oneuranium-236 nucleus. Calculate the energy released by thefission of 10.0 kg of uranium-236. The atomic mass ofuranium-236 is 236 u, where 1 u = 1 atomic mass unit \(\displaystyle={1.66}\times{10}^{{-{27}}}\) kg. Express your answer both in joules and in kilotonsof TNT (1 kiloton of TNT releases 4.18 x 10^12 J when itexplodes).

A. Find the radii of the two "daughter" nuclei of charge+46e.

B. In a simple model for the fission process, immediatelyafter the uranium-236 nucleus has undergone fission the "daughter"nuclei are at rest and just touching. Calculate the kineticenergy that each of the "daughter" nuclei will have when they arevery far apart.

C. In this model the sum of the kinetic energies of the two"daughter" nuclei is the energy released by the fission of oneuranium-236 nucleus. Calculate the energy released by thefission of 10.0 kg of uranium-236. The atomic mass ofuranium-236 is 236 u, where 1 u = 1 atomic mass unit \(\displaystyle={1.66}\times{10}^{{-{27}}}\) kg. Express your answer both in joules and in kilotonsof TNT (1 kiloton of TNT releases 4.18 x 10^12 J when itexplodes).

asked 2021-05-09

The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus

\(\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}\)

where A is the cross-sectional area of the vehicle and \(\displaystyle{C}_{{d}}\) is called the coefficient of drag.

Part A:

Consider a vehicle moving with constant velocity \(\displaystyle\vec{{{v}}}\). Find the power dissipated by form drag.

Express your answer in terms of \(\displaystyle{C}_{{d}},{A},\) and speed v.

Part B:

A certain car has an engine that provides a maximum power \(\displaystyle{P}_{{0}}\). Suppose that the maximum speed of thee car, \(\displaystyle{v}_{{0}}\), is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power \(\displaystyle{P}_{{1}}\) is 10 percent greater than the original power (\(\displaystyle{P}_{{1}}={110}\%{P}_{{0}}\)).

Assume the following:

The top speed is limited by air drag.

The magnitude of the force of air drag at these speeds is proportional to the square of the speed.

By what percentage, \(\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}\), is the top speed of the car increased?

Express the percent increase in top speed numerically to two significant figures.

\(\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}\)

where A is the cross-sectional area of the vehicle and \(\displaystyle{C}_{{d}}\) is called the coefficient of drag.

Part A:

Consider a vehicle moving with constant velocity \(\displaystyle\vec{{{v}}}\). Find the power dissipated by form drag.

Express your answer in terms of \(\displaystyle{C}_{{d}},{A},\) and speed v.

Part B:

A certain car has an engine that provides a maximum power \(\displaystyle{P}_{{0}}\). Suppose that the maximum speed of thee car, \(\displaystyle{v}_{{0}}\), is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power \(\displaystyle{P}_{{1}}\) is 10 percent greater than the original power (\(\displaystyle{P}_{{1}}={110}\%{P}_{{0}}\)).

Assume the following:

The top speed is limited by air drag.

The magnitude of the force of air drag at these speeds is proportional to the square of the speed.

By what percentage, \(\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}\), is the top speed of the car increased?

Express the percent increase in top speed numerically to two significant figures.

asked 2021-04-30

Two oppositely charged but otherwise identical conducting plates of area 2.50 square centimeters are separated by a dielectric 1.80 millimeters thick, with a dielectric constant of K=3.60. The resultant electric field in the dielectric is \(\displaystyle{1.20}\times{10}^{{6}}\) volts per meter.

Compute the magnitude of the charge per unit area \(\displaystyle\sigma\) on the conducting plate.

\(\displaystyle\sigma={\frac{{{c}}}{{{m}^{{2}}}}}\)

Compute the magnitude of the charge per unit area \(\displaystyle\sigma_{{1}}\) on the surfaces of the dielectric.

\(\displaystyle\sigma_{{1}}={\frac{{{c}}}{{{m}^{{2}}}}}\)

Find the total electric-field energy U stored in the capacitor.

u=J

Compute the magnitude of the charge per unit area \(\displaystyle\sigma\) on the conducting plate.

\(\displaystyle\sigma={\frac{{{c}}}{{{m}^{{2}}}}}\)

Compute the magnitude of the charge per unit area \(\displaystyle\sigma_{{1}}\) on the surfaces of the dielectric.

\(\displaystyle\sigma_{{1}}={\frac{{{c}}}{{{m}^{{2}}}}}\)

Find the total electric-field energy U stored in the capacitor.

u=J

asked 2021-02-08

Find the distance UV between the points U(7,−4) and V(−3,−6). Round your answer to the nearest tenth, if neces

asked 2021-03-02

asked 2020-11-30

asked 2021-02-14

asked 2020-11-24

Prove that V is a vector space. \(\displaystyle{V}={T}{\left({m},\ {n}\right)}\), the set of linear transformations \(\displaystyle{T}\ :\ {R}^{{{m}}}\ \rightarrow\ {R}^{{{n}}}\), together with the usual addition and scalar multiplication of functions.