Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of -0.8803 N when separated by 50 cm, center-to-center. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0921 N. What were the initial charges on the spheres? Since one is negative and you cannot tell which is positive or negative, there are two solutions. Take the absolute value of the charges and enter the smaller value here. Enter the larger value here.

A 26-turn circular coil has a diameter of 0.60 m. It is placed with its axis along the direction of a 50.0-?T magnetic field and then flipped through an angle of 180° in 0.170 s. Determine the average emf generated in the coil, and the magnitude of the emf at 0.085 s. [4.3 x 10-3 V, 6.8 x 10-3 V] (Note: Very few students got the second part correct, you need to find the function for emf with respect to time and plug in time t.)

An electron and a 0.0500-kg bullet each have a velocity of magnitude 510 m/s, accurate to within 0.0100%. Within what lower limit could we determine the position of each object along the direction of the velocity? electron mm bullet m

An unknown mass of water (m1) of temperature 3.4°C is mixed with another unknown mass of water (m2) of 55.6°C. The combined mixture of water (m3) has a temperature of 26.1°C and a mass of 154 grams. Determine the mass of (m1) and (m2) WITHOUT using c_water= 4184 J/kg°C.

2. What are the differences between standing and traveling waves?

A block of mass m1 = 2.3 kg initially moving to the right with a speed of 4.8 m/s on a frictionless, horizontal track collides with a spring attached to a second block of mass m2 = 3.5 kg initially moving to the left with a speed of 2.7 m/s. The spring constant is 580N/m. What if m1 is initially moving at 3.6 m/s while m2 is initially at rest? (a) Find the maximum spring compression in this case. x = 0.176 m (b) What will be the individual velocities of the two masses (v1 and v2) after the spring extended fully again? (That is, when the two masses separate from each other after the collision is complete.) v1=? v2=?

Galileo's great-great-great grandchild stands at the top of a vertical tower 57.8 m tall with a Chianti bottle. How long does it take for the bottle to fall to the ground, if it was just dropped from the tower? How far does the bottle land from a point on the ground directly beneath the point from which it was launched, if the bottle was thrown straight out horizontally from the tower with a speed of 12.9 m/s? What is the bottle's horizontal component of velocity, if the bottle was thrown straight out horizontally from the tower with a speed of 12.9 m/s? What is the magnitude of its velocity just before it strikes the ground, if the bottle was thrown straight out horizontally from the tower with a speed of 12.9 m/s?

7.1.2. A pulsating sphere of radius a vibrates with a surface velocity amplitude U₀ and at such a high frequency that ka _>> 1. Derive expressions for the pressure amplitude, the particle velocity amplitude, the intensity, and the total acoustic power radiated in the resulting acoustic wave.

Now that the satellite has been launched (i.e. Ch. 12 Lab), Earth is hopeful to get a more reliable eye on space anomalies. Shortly after the satellite's course around Jupiter, communication started to get more and more sporadic and weaker in signal. To counter this, a new satellite dish will be designed, specifically targeting the new satellite. Satellite dishes follow the shape of a paraboloid. The equation of a paraboloid is as follows: z=x^2/a^2+y^2/b^2 Where a and b could be the same number (depending on the desired shape). When you are designing this dish, where should you place the receiver? The receiver is like the ‘antenna’, receiving the data signals. Could the effectiveness of the receiver be changed if the ratio a/b is changed? A preliminary design is started with the dish’s circular radius of 20 feet, and a depth of 5 feet. What is the equation for this paraboloid? Hint: a = b, for this design. When the dish is a circular paraboloid (again a = b), a two-dimensional model could be viewed with the equation: x^2=4py , where p is the distance from the parabola's vertex to its focus. This equation can be revolved around the y-axis to form the shape of the satellite dish. Using the dimensions of the dish in #2, find the equation of the parabola in two-dimensions. Where should the receiver be placed? If the graph is revolved around the y-axis, what is the surface area of the satellite dish? From #3, find the cost of the dish itself when the material to make the dish costs $1,500 per square foot (it is a high quality satellite dish!). Many satellite dishes today are elliptic paraboloids (now a ≠ b), for reasons of reducing interference. But, would this change of shape also change where to place the receiver? Let’s use a satellite dish which has a 20-foot radius in the x-direction, and has a 10-foot radius in the y-direction. If a single receiver is placed at 10 feet from the vertex, what must the depth be in the x-direction and y-direction, separately, in order that the signal is maximized? What would a function look like for the depth of the dish at any particular place on the rim? Is there any theoretical reason to use an elliptic paraboloid vs. a circular paraboloid? Explain your reasoning. Thank you.

1. How does the brightness of the refracted ray change when the incident angle (from glass to air) changes from less than critical angle to greater than critical angle?

a. brighter

b. dimmer

c. unchanged

d. dimmer and then disappear

2. Trying to picture an electroscope you made in the lab, on rubbing an rubber rod with fur, the electrons from the fur get transferred to the rubber rod. While holding the rubber rod near the electroscope (not touching the top paper clip), the foil leaves separate. At the same time, someone rubs a Styrofoam cup on a piece of cloth and also brings it to the electroscope, the leaves close a bit. What is the type of charge the Styrofoam cup carrying?

A. positive

b. negative

c. cannot decide

3. What would be the correct description of how an image in a plane mirror compares to the original object?

4. If the distance between the object and the screen is 1meter, a thin lens is put in between and moving, when the lens is 30 cm away from the object, a clear image is formed on the screen. How much is the focal length of this thin lens?

a. 0.048 m

b. 21 cm

c. 0.019 m

d. 52.5

A playground is on the flat roof of a city school, 6.00 m above the street below. The vertical wall of the building is 7.00 m high, forming a 1.00 m high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of 53.0° above the horizontal at a point 28.0 m from the base of the building wall. The ball takes 2.10 s to reach a point vertically above the wall.

(a) Find the speed at which the ball was launched.
m/s

(b) Find the vertical distance by which the ball clears the wall.
m

(c) Find the distance from the wall to the point on the roof where the ball lands.
m

1. In "magnetic force on a current carrying wire" experiment, using the data for force(y-axis, in Newton) versus length (in meters), someone obtained a linear curve fit equation: y=0.1x+2. If in the experiment, the wire carrying a current I=2.0 A, how strong is the magnetic field?

A. 0.1 T

B. 0.05 T

C. 2 T

D. 0.2 T

2. If the distance between the object and the screen is 1meter, a thin lens is put in between and moving, when the lens is 30 cm away from the object, a clear image is formed on the screen. How much is the focal length of this thin lens?

A. 0.048 m

B. 21 cm

C. 0.019 m

D. 52.5 cm

3. When light, starting in air, is shone on a piece of glass, what effects should you likely to observe?

A.Reflection

B. Refraction

C. Both reflection and refraction

D. Inversion

E. Conversion

I have recently been intrigued by the following question: What is the difference between the pitch of the noise of dripping water between hot and cold water? For example, would cold water create a higher pitched noise while dripping into a pot of water? Or vice versa?

Solve the quantum simple harmonic oscillator in three dimensions i.e. find the energy and eigenkets. It's solution will include hermite polynomials.

Give a definition for the golf ball event horizon and the photon event horizon.