area = 115 m2

Question

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 2021-03-30

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 2020-12-31

The formula for the volume of a cylinder is V = πr²h. What is the radius for a cylinder that has a volume of 160π m³ and a height of 8 m? Express your answer in simplest radical form and as a decimal rounded to the nearest tenth.

asked 2021-01-31

A museum groundskeeper is creating a semicircular statuary garden with a diameter of 25 feet. There will
be a fence around the garden. The fencing costs $7.25$7.25 per linear foot. About how much will the fencing
cost altogether? Round to the nearest hundredth. Use 3.14 for ππ.
The fencing will cost about $$

asked 2021-04-23

A swimmer wears a heavy belt to make her average densityexactly equal to the density of water. Her mass, includingthe belt, is 60 kg. (a) What is the swimmer's weight innewtons? (b) What is the swimmers volume in m3? (c) At a depth of 2m below the surface ofa pond, what bouyant force acts on the swimmer? Whatnet force acts on her?

asked 2021-02-17

A square loop of copper wire is initially placed perpendiclar to the lines of a constant magnetic field of \(\displaystyle{5}\times{10}^{{3}}\) T.The area enclosed by the loop is 0.2 square meter. the loopis then turned through an angle \(\displaystyle{90}^{\circ}\) so thatthe plane of the loop is parallel to the field lines. the turntakes 0.1 second. what is the average emf induced in the loop during the turn?

asked 2021-02-11

Find the area of a circle with a radius of 5 inches. Round your answer to the nearest hundredth.

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 2021-04-26

Suppose the light bulb in the figure below is replaced with a short wire of zero resistance, and the resistance of the rails is negligible. The only resistance is from the moving rod, which is iron (resistivity \(\displaystyle={9.50}\times{10}^{{-{8}}}\) ohm.m). The rod has a cross-sectional area of \(\displaystyle{3.50}\times{10}^{{-{6}}}\)m

asked 2021-02-19

An electric heater is used to heat a room of a volume \(\displaystyle{62}{m}^{{3}}\). Air is brought into the room at \(\displaystyle{5}^{\circ}\) C and is changed completely twice per hour. Heat loss through the walls amounts to approximately 850 kcal/h. If the air is to be maintainedat \(\displaystyle{20}^{\circ}\) C, what minimum wattage must the heater have? (The specific heat of air is about 0.17 kcal/kg*Co.)