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 2021-04-26

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 2021-03-21

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 2021-04-13

As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.

a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.

a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.

asked 2021-04-13

A slab of insulating material of uniform thickness d, lying between \(\displaystyle{\frac{{-{d}}}{{{2}}}}\) to \(\displaystyle{\frac{{{d}}}{{{2}}}}\) along the x axis, extends infinitely in the y and z directions, as shown in the figure. The slab has a uniform charge density \(\displaystyle\rho\). The electric field is zero in the middle of the slab, at x=0. Which of the following statements is true of the electric field \(\displaystyle{E}_{{{\vec}}}\) at the surface of one side of the slab?

asked 2021-02-14

The plane of a rectangular coil, 5.0-cm by 8.0-cm, is perpendicular to the direction of a magnetic field "B". If the coil has 75 turns and a total resistance of 8.0 Ohms, at what rate must the magnitude of "B" change to induce a current of 0.10 amps in the windings of the coil?

asked 2021-03-15

Three long wires (wire 1, wire 2,and wire 3) are coplanar and hang vertically. The distance betweenwire 1 and wire 2 is 16.0 cm. On theleft, wire 1 carries an upward current of 1.50 A. To the right,wire 2 carries a downward current of 3.40 A. Wire 3 is located such that when itcarries a certain current, no net force acts upon any of the wires.

(a) Find the position of wire 3, relative to wire 1.

(b) Find the magnitude and direction of the current in wire 3.

(a) Find the position of wire 3, relative to wire 1.

(b) Find the magnitude and direction of the current in wire 3.

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 2021-02-27

An alpha particle (a He nucleus, containing two protons and two neutrons and having a mass of \(\displaystyle{6.64}\cdot{10}^{{-{27}}}\) kg) traveling horizontally at 35.6 km/s enters a uniform, vertical, 1.10 T magnetic field.

A) What is the diameter of the path followed by this alpha particle?

B) What effect does the magnetic field have on the speed of the particle?

C) What are the magnitude of the acceleration of the alpha particle while it is in the magnetic field?

D) What are the direction of the acceleration of the alpha particle while it is in the magnetic field?

A) What is the diameter of the path followed by this alpha particle?

B) What effect does the magnetic field have on the speed of the particle?

C) What are the magnitude of the acceleration of the alpha particle while it is in the magnetic field?

D) What are the direction of the acceleration of the alpha particle while it is in the magnetic field?

asked 2021-03-12

A 75.0-kg man steps off a platform 3.10 m above the ground. Hekeeps his legs straight as he falls, but at the moment his feettouch the ground his knees begin to bend, and, treated as aparticle, he moves an additional 0.60 m before coming torest.

a) what is the speed at the instant his feet touch theground?

b) treating him as a particle, what is his acceleration(magnitude and direction) as he slows down, if the acceleration isassumed to be constant?

c) draw his free-body diagram (see section 4.6). in termsof forces on the diagram, what is the net force on him? usenewton's laws and the results of part (b) to calculate the averageforce his feet exert on the ground while he slows down. expressthis force in newtons and also as a multiple of his weight.

a) what is the speed at the instant his feet touch theground?

b) treating him as a particle, what is his acceleration(magnitude and direction) as he slows down, if the acceleration isassumed to be constant?

c) draw his free-body diagram (see section 4.6). in termsof forces on the diagram, what is the net force on him? usenewton's laws and the results of part (b) to calculate the averageforce his feet exert on the ground while he slows down. expressthis force in newtons and also as a multiple of his weight.