A baseball is thrown from the roof of 23.5 m -tall building with an initial velocity of magnitude 10.5 m/s and directed at an angle of 52.4° above the horizontal.

What is the speed of the ball just before it strikes the ground? Use energy methods and ignore air resistance.

What is the answer if the initial velocity is at an angle of 52.4° below the horizontal?

If the effects of air resistance are included, will part (a) or (b) give the higher speed? Why?

Bohr theory of the atom:

In the hydrogenic Bohr orbit of quantum number n compute the ratio of the circumference of the orbit to the wavelength of the electron. Provide an interpretation of this result in terms of the concepts of de Broglie.

Treating the Bohr orbit as a circulating electrical current, compute the magnetic moment of the electron in a Bohr orbit of quantum number n (Hint: use Ampere’s law). What is the ratio between the magnetic moment and the angular momentum?

1-The Large Hadron Collider in Europe smashes together near-light speed protons to discover new fundamental particles of nature. As part of the detection process, the “debris” from the collision is made to pass through a magnetic field. What is the purpose of this magnetic field?

2-If you are outside on a dark night you might see an aurora (i.e. northern or southern lights). What produces this display and why is it most common at middle to high latitudes?

A horizontal disk with radius R and charge density σ is centered originally. A particle with charge Q and mass m is in equilibrium at a height h above the center of the plate, as shown. A gravitational field is present. R = 1.5 m σ = -5⋅10-7 C / m2 h = 2 m Q = -2 µC a) Calculate the mass m of the particle if it is at equilibrium (use g = 9.81 m / s2 ). b) Calculate the electric potentials created by the disc at the following two positions on the Y axis: at y = 2 m and at y = 4 m. c) If we remove the gravitational field, calculate how fast the particle will reach the position y = 4 m. d) In the absence of a gravitational field, calculate the external work required to bring the particle Q from infinity to the center of the disc (i.e. y = 0 m), without variation of speed. (Reminder: V∞ = 0)

Answer the following four sub-questions. Each sub-question is independent and has no no link with the other sub questions. a) Two neutral spheres are spaced 3 m apart. Calculate how many electrons must be transferred from one sphere to another so that they each experience a force of 14 N, and say whether the forces will be attractive or repulsive. b) Calculate the uniform electric field to be applied parallel to a moving proton at 2⋅106 m / s in order to immobilize it in 20 µs, and say if this field must be oriented in the direction of speed or in opposite direction. c) A long insulating cylinder has a charge density of -1 µC / m3 . The material component the cylinder suddenly becomes conductive; we see that the density load area is then -1 µC / m2 . Calculate the radius of the cylinder. d) Calculate the magnitude of the electric field at position r = 10 cm in question 4. Your gait must show, among other things, that the load (or surface density) of the shell thin has no effect on your response.

4 questions:

1). A 5 cm spring is suspended with a mass of 2.417 g attached to it which extends the spring by 2.409 cm. The same spring is placed on a frictionless flat surface and charged beads are attached to each end of the spring. With the charged beads attached to the spring, the spring's extension is 0.259 cm. What are the charges of the beads?

2). Two equally charged, 1.862 g spheres are placed with 3.188 cm between their centers. When released, each begins to accelerate at 261.446 m/s². What is the magnitude of the charge on each sphere? Express your answer in microCoulombs.

3).A +3 nC charge is located at (0,11.90) cm and a -8nC charge is located (3.38, 0) cm.Where would a -8 nC charge need to be located in order that the electric field at the origin be zero? Find the distance r from the origin of the third charge.

4). Two equally charged, 1.862 g spheres are placed with 3.188 cm between their centers. When released, each begins to accelerate at 261.446 m/s². What is the magnitude of the charge on each sphere? Express your answer in microCoulombs.

Assume if the shear stress in steel exceeds about 4.00x10⁸ N/m² the steel   ruptures.

(a) Determine the shearing force necessary to shear a steel bolt 1.25 cm in diameter.

(b) Determine the shearing force necessary to punch a 1.60-cm-diameter hole in a steel plate 0.530 cm thick

A 155 gg mass attached to a horizontal spring oscillates at a frequency of 3.70 Hz . At t =0s, the mass is at x= 6.40 cmcm and has v =− 45.0 cm/s . Determine:

a)The maximum speed

b)The maximum acceleration.

c)The total energy.

d)The position at t= 4.80 s

8. How do mirrors for most lasers achieve high (>95%) reflectivity not possible with simple metal coatings alone? Describe the structure of these mirrors (include a diagram showing the "stack" of multiple layers used) and describe, in a paragraph, how dielectric mirrors (also called "dichroic" mirrors) work. Be sure to detail the principles of operation, the thickness of the layers, and why that thickness is a critical parameter.

What is the purpose of the ballast resistance in a HeNe supply? Make specific reference to the electrical characteristics of a gas discharge as compared to an "ohmic" resistance. What might happen to a power supply if the ballast resistor was omitted?

"Summarize the pairing effect in terms of lowest angular momentum of nucleons.

At t=0t=0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by θ(t)=(θ(t)=( 260 rad/srad/s )t−()t−( 20.5 rad/s2rad/s2 )t2−()t2−( 1.49 rad/s3rad/s3 )t3)t3.

A- At what time is the angular velocity of the motor shaft zero?

B- Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity.

C- How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero?

D- How fast was the motor shaft rotating at t=0t=0, when the current was reversed?

E- Calculate the average angular velocity for the time period from t=0t=0 to the time calculated in part A.

An entrepreneur has proposed sending a probe to Alpha Centai 4 light years away. His idea is to use a "solar sail", which is a large area reflective sheet, and propelling the spacecraft to 10% of the speed of light using a high powered laser. If the laser sends 1200 nm light at the sail and the power reaching the reflective sheet is 1500 W:

(a) What is the force due to light pressure on the reflective sheet, assuming the light backscatters with 20% efficiency?
(b) If an engineer is testing the spacecraft far away from the solar system so that the gravity of the sun and planets can be ignored, and the spacecraft is 65 kg, what would be the power necessary to achieve 10% of the speed of light if the acceleration part of the journey was only 5.0 x 10^5 km? (ignore relativistic effects)

A small current loop can be used as a compass. (a) When it's placed in an external magnetic field, which plane will it be rotated into, and in which direction will its magnetic dipole moment p point? (b) Will the foop then be stretchedor compressedby B? (c) lf B varies with position, will the loop be forced toward positions where Bis greateror les!? (dl When a charged particle orbits in a magnetic field (see Ex 27-7, pg 7151, p is antiparallelto B. The force on the orbiting particle is inward (centripetal), but on the wire foop it must be outwardfor sl€bility-why?

Given: M1= 75kg; M2 = 50kg; V (M1) = 10 m/s North; V (M2) = 10 m/s West

Action: Collision, two masses stick together, move at unspecified angle in M2's initial direction

Question: Find magnitude of their speed together after collision.