Two loudspeakers on a concert stage are vibrating in phase. A listener is 45.9 m from the left speaker and 34.7 m from the right one. The listener can respond to all frequencies from 20 to 20 000 Hz, and the speed of sound is 343 m/s. What is the lowest frequency that can be heard loudly due to constructive interference?

A proton is traveling horizontally to the right at 4.20×10⁶ m/s.

A) Find the magnitude of the weakest electric field that can bring the proton uniformly to rest over a distance of 3.50 cm. E=___ N/C

B) What is the direction of this electric field?

C) How much time does it take the proton to stop after entering the field? t=____ s

D) What minimum field magnitude would be needed to stop an electron under the conditions of part A? E=___ N/C

E) What is the direction of the field in part D?

If the coefficient of kinetic friction between tires and dry pavement is 0.90, what is the shortest distance in which you can stop an automobile by locking the brakes when traveling at 22.9m/s ?

On wet pavement, the coefficient of kinetic friction may be only 0.25. How fast should you drive on wet pavement in order to be able to stop in the same distance as in part A? (Note: Locking the brakes is notthe safest way to stop.)

If the coefficient of kinetic friction between tires and dry pavement is 0.90, what is the shortest distance in which you can stop an automobile by locking the brakes when traveling at 22.9m/s ?

Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide with a glancing blow. Asteroid A, which was initially traveling at vA1 = 40.0 m/s with respect to an inertial frame in which asteroid B was at rest, is deflected 30.0 ? from its original direction, while asteroid B travels at 45.0 ? to the original direction of A, as shown in (Figure 1).

a: Find the speed of asteroid A after the collision.

b: Find the speed of asteroid B after the collision.

c: What fraction of the original kinetic energy of asteroid A dissipates during this collision?

A tube 12 cm in diameter is carrying engine oil a distance of 4 meters from barrel to outlet. If the pressure difference between the ends of the tube is 1064.28 atm , what is the oil flow rate?

3.19 A gas with adiabatic exponent γ is compressed adiabatically from an initial state (Pi, Vi) to final state (Pf, Vf). (a) Show that the work done in this process is

W=((ViPi)/y-1)*[(Vi/Vf)^(y-1) -1]

(b) Evaluate the result numerically for one mole of helium gas initially
at P = 1.0 atm and T = 300 K compressed to half its initial volume.
(c) Compute the work done in an isothermal compression from the same
initial point to half the initial volume. Explain the difference between
the numerical results for work done in adiabatic and isothermal
compression.

A frictionless vertical post is inserted into a bowling ball with a hole drilled through its center. The ball has a mass of 10.5 kg. A rope is attached to a ring that has been affixed to the ball. Kurt pulls on the rope at an angle of 0 = 24.5° with respect to the vertical with a constant force of magnitude |F| = 134 N .

(a) How much work does Kurt do on the bowling ball by raising it through a vertical distance of 1.08 m at a constant velocity?

(b) How much work does the Earth do on the ball while it is being raised through a distance of 1.08 m?

(c) Kurt is lazy and would like to be able to raise the ball through the same vertical distance with a minimum effort. What two changes in his actions would you recommend to her?

(d) What is the net work done on the ball by the two forces acting on it?

(e) If Kurt raises the mass in a time of 0.56 s what is his horse power?

In this problem we want to calculate the electric field due to several charge linear distributions .a) Consider a thin rod of length L. The rod carries a uniform charge density, λ, and total charge Q. Calculate the electric field at a point p that is on the rod’s cylindrical axis of symmetry and a distance d away from the end of the rod. Do this by direct integration. How does your expression be have as L→∞?b) Repeat, with the rod’s charge density being λ=αx, whereαhas a numerical value of 0.25 (what are the dimensions and units of α?)?

Two very long wires run in the z direction, one at (1,0) cm, the other at (-1,0) cm. (a) If both wires are carrying a positive current of 0.6 A upwards in z, calculate the force each wire exerts on the other. Is it repulsive or attractive? (b) Do the same problem, but with the wire at (-1,0) cm carrying 0.6 A downwards. Hint: you shouldn’t have to do any more math for this part

Compute the equivalent focal length of the following thick lens combination:

Lens A: R1 = 16.28mm, R2 = -275.7mm, n = 1.6116 , d = 3.57mm

Distance: 1.89 mm

Lens B: R1 = -34.57mm, R2 = 15.82mm, n = 1.6053, d = 0.81mm

Distance: 3.25mm

Lens C: R1 = inf, R2 = 19.20mm, n = 1.5123, d = 2.17mm

In contact with,

Lens D: R1 = 19.20mm, R2=-24mm, n=1.6116, d=3.96mm

Three spheres are arranged in the xy plane as in the figure below. The first sphere, of mass

m₁ = 15.6 kg,

is located at the origin; the second sphere, of mass

m₂ = 4.47 kg

is located at (−6.00, 0.00) m; and the third sphere, of mass

m₃ = 2.00 kg

is located at (0.00, 5.00) m.Assuming an isolated system, what is the net gravitational force on the sphere located at the origin?

A roller-coaster car speeds down a hill past point A where R1 = 11.6 m and then rolls up a hill past point B where R2 = 15.2 m, as shown below.

(a) The car has a speed of 20.0 m/s at point A. if the track exerts a normal force on the car of 2.08 104 N at this point, what is the mass of the car?

(b) What is the maximum speed the car can have at point B for the gravitational force to hold it on the track?

Discuss how Maxwell's predictions were confirmed by the experiments carried out by Hertz. Please use own words at least 2 paragraphs.

A thick lens has an index of refraction of 1.60. It is 4-cm thick and is surrounded by air. The radius of curvature of the front surface is 5 cm, and the radius of curvature of the back surface is 12 cm. A 1-cm tall object is placed to the left of the first surface. At what angle above the optic axis should a ray strike the front side of the lens 0.5 cm above the optical axis so that it emerges from the back side of the lens traveling parallel to the optical axis? Use matrix techniques.

A proton with an initial velocity of 3.9 106 m/s enters a parallel-plate capacitor at an angle of 46° through a small hole in the bottom plate as shown in the figure below. If the plates are separated by a distance
d = 2.1 cm,
what is the magnitude of the minimum electric field to prevent the proton from hitting the top plate?
___ N/C

Compare your answer with the results obtained if the proton was replaced with an electron and choose an answer:

A. The magnitude of the electric field needed for a proton is larger than what is needed for an electron.

B. The magnitude of the electric field needed for a proton is smaller than what is needed for an electron.   

C. The magnitude of the electric field needed for a proton is the same as what is needed for an electron.