ottcomn

Answered 2021-02-18
Author has **22230** answers

content_user

Answered 2021-09-09
Author has **10829** answers

Given that

thermal conductivity of plaster board, \(k_p=0.30\ J/(s\cdot m\cdot C)\)

thermal conductivity of brick, \(k_b=0.60\ J/(s\cdot m\cdot C)\)

thermal conductivity of wood, \(k_w=0.10\ J/(s\cdot m\cdot C)\)

The inside temperature, \(T_i=25.5^\circ C\)

The outside temperature, \(T_0=0^\circ\ C\)

a) The rate of heart transfer is the same for all three materials, so

\(\frac{Q}{t}=\frac{k_pA\triangle T_b}{L}=\frac{k_bA\triangle T_b}{L}=\frac{k_wA\triangle T_w}{L}\)

Let \(T_1\) be the temperature at the plasterboard-brick interface, \(T_2\) be the temperature at the brick-wood interface.

For plaster-board interface,

\(\frac{k_pA\triangle T_p}{L}=\frac{k_bA\triangle T_b}{L}\)

\(k_p(T_i-T_1)=k_b(T_1-T_2)\)

\(k_pT_i-k_pT_1=k_bT_1-k_bT_2\)

\(T_2=(\frac{k_p+k_b}{k_b})T_1-(\frac{k_p}{k_b})T_i\)

Hence, for brick-wood interface

\(\frac{k_bA\triangle T_b}{L}=\frac{k_wA\triangle T_w}{L}\)

\(k_b(T_1-T_2)=k_w(T_2-T_0)\)

\(k_bT_1=(k_w+k_b)T_2-k_wT_0\)

\(k_bT_1=(k_w+k_b)\{(\frac{k_p+k_b}{k_b})T_1-(\frac{k_p}{k_b}T_i)\}-k_wT_0\)

Therefore, the tempaerature at the plasterboard-brick interface is \(=19.83^\circ C\)

asked 2021-03-30

A long, straight, copper wire with a circular cross-sectional area of \(\displaystyle{2.1}{m}{m}^{{2}}\) carries a current of 16 A. The resistivity of the material is \(\displaystyle{2.0}\times{10}^{{-{8}}}\) Om.

a) What is the uniform electric field in the material?

b) If the current is changing at the rate of 4000 A/s, at whatrate is the electric field in the material changing?

c) What is the displacement current density in the material in part (b)?

d) If the current is changing as in part (b), what is the magnitude of the magnetic field 6.0cm from the center of the wire? Note that both the conduction current and the displacement currentshould be included in the calculation of B. Is the contribution from the displacement current significant?

a) What is the uniform electric field in the material?

b) If the current is changing at the rate of 4000 A/s, at whatrate is the electric field in the material changing?

c) What is the displacement current density in the material in part (b)?

d) If the current is changing as in part (b), what is the magnitude of the magnetic field 6.0cm from the center of the wire? Note that both the conduction current and the displacement currentshould be included in the calculation of B. Is the contribution from the displacement current significant?

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 2021-04-14

A medical technician is trying to determine what percentage of apatient's artery is blocked by plaque. To do this, she measures theblood pressure just before the region of blockage and finds that itis \(\displaystyle{1.20}\times{10}^{{{4}}}{P}{a}\), while in the region of blockage it is \(\displaystyle{1.15}\times{10}^{{{4}}}{P}{a}\). Furthermore, she knows that blood flowingthrough the normal artery just before the point of blockage istraveling at 30.0 cm/s, and the specific gravity of this patient'sblood is 1.06. What percentage of the cross-sectional area of thepatient's artery is blocked by the plaque?

asked 2021-05-16

A toaster rated at 1050 W operates on a 120V household circuitand a 4.00 m length of a nichrome wire as its heatingelement. The operating temperature of this element is 320degrees celsius.

What is the cross-sectional area of the wire?

What is the cross-sectional area of the wire?

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 2021-02-23

A 0.30 kg ladle sliding on a horizontal frictionless surface isattached to one end of a horizontal spring (k = 500 N/m) whoseother end is fixed. The ladle has a kinetic energy of 10 J as itpasses through its equilibrium position (the point at which thespring force is zero).

(a) At what rate is the spring doing work on the ladle as the ladlepasses through its equilibrium position?

(b) At what rate is the spring doing work on the ladle when thespring is compressed 0.10 m and the ladle is moving away from theequilibrium position?

(a) At what rate is the spring doing work on the ladle as the ladlepasses through its equilibrium position?

(b) At what rate is the spring doing work on the ladle when thespring is compressed 0.10 m and the ladle is moving away from theequilibrium position?

asked 2021-06-10

Water flows through a water hose at a rate of \(Q_{1}=680cm^{3}/s\), the diameter of the hose is \(d_{1}=2.2cm\). A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of \(v_{2}=9.2m/s\).

a) Enter an expression for the cross-sectional area of the hose, \(A_{1}\), in terms of its diameter, \(d_{1}\)

b) Calculate the numerical value of \(A_{1},\) in square centimeters.

c) Enter an expression for the speed of the water in the hose, \(v_{1}\), in terms of the volume floe rate \(Q_{1}\) and cross-sectional area \(A_{1}\)

d) Calculate the speed of the water in the hose, \(v_{1}\) in meters per second.

e) Enter an expression for the cross-sectional area of the nozzle, \(A_{2}\), in terms of \(v_{1},v_{2}\) and \(A_{1}\)

f) Calculate the cross-sectional area of the nozzle, \(A_{2}\) in square centimeters.

a) Enter an expression for the cross-sectional area of the hose, \(A_{1}\), in terms of its diameter, \(d_{1}\)

b) Calculate the numerical value of \(A_{1},\) in square centimeters.

c) Enter an expression for the speed of the water in the hose, \(v_{1}\), in terms of the volume floe rate \(Q_{1}\) and cross-sectional area \(A_{1}\)

d) Calculate the speed of the water in the hose, \(v_{1}\) in meters per second.

e) Enter an expression for the cross-sectional area of the nozzle, \(A_{2}\), in terms of \(v_{1},v_{2}\) and \(A_{1}\)

f) Calculate the cross-sectional area of the nozzle, \(A_{2}\) in square centimeters.