Question

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 2021-03-21

In the figure below, the rolling axle, 1.43 m long, is pushed along horizontal rails at a constant speed v = 3.36 m/s.

A resistor R = 0.325 ohm is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, and so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R.) There is a uniform magnetic field B = 0.0850 T vertically downward. Calculate the induced current I in the resistor and what horizontal force F is required to keep the axle rolling at constant speed?

A resistor R = 0.325 ohm is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, and so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R.) There is a uniform magnetic field B = 0.0850 T vertically downward. Calculate the induced current I in the resistor and what horizontal force F is required to keep the axle rolling at constant speed?

asked 2021-04-24

Problem: From what maximum height can a 75 kg person jump w/obreaking the lower leg bone on either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60m from the standing to the seat position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is \(\displaystyle{170}\times{10}^{{6}}\ \frac{{N}}{{m}^{{2}}}\) and its smallest cross sectional areais \(\displaystyle{2.5}\times{10}^{{-{4}}}\)

asked 2021-05-09

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

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 2021-05-18

The student engineer of a campus radio station wishes to verify the effectivencess of the lightning rod on the antenna mast. The unknown resistance \(\displaystyle{R}_{{x}}\) is between points C and E. Point E is a "true ground", but is inaccessible for direct measurement because the stratum in which it is located is several meters below Earth's surface. Two identical rods are driven into the ground at A and B, introducing an unknown resistance \(\displaystyle{R}_{{y}}\). The procedure for finding the unknown resistance \(\displaystyle{R}_{{x}}\) is as follows. Measure resistance \(\displaystyle{R}_{{1}}\) between points A and B. Then connect A and B with a heavy conducting wire and measure resistance \(\displaystyle{R}_{{2}}\) between points A and C.Derive a formula for \(\displaystyle{R}_{{x}}\) in terms of the observable resistances \(\displaystyle{R}_{{1}}\) and \(\displaystyle{R}_{{2}}\). A satisfactory ground resistance would be \(\displaystyle{R}_{{x}}{<}{2.0}\) Ohms. Is the grounding of the station adequate if measurments give \(\displaystyle{R}_{{1}}={13}{O}{h}{m}{s}\) and R_2=6.0 Ohms?

asked 2021-02-23

A block of mass m=3.6 kg, moving on africtionless surface with a speed \(\displaystyle{v}_{{1}}={9.3}\) m/s makes a perfectly elastic collision with a block of mass Mat rest. After the collision, the 3.6 kg block recoils with a speed of \(\displaystyle{v}_{{1}}={2.7}\) m/s in figure, the speed of the vlock of mass M after the collision is closest to:

a. 9.3 m/s

b. 6.6 m/s

c. 8.0 m/s

d. 10.7 m/s

e. 12.0 m/s

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 2021-02-13

A vertical cylinder of cross-sectional area \(\displaystyle{0.050}{m}^{{2}}\) is fitted with a tight-fitting, frictionless pistionof mass 5.0 kg. If there are 3.0 mol of ideal gas in the cylinderat 500 K, determine the height "h" at which the postion will be inequilibrium.

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 2021-02-23

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?