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.

An unstable nucleus of mass 1.7 ✕ 10⁻²⁶ kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of

m₁ = 1.8 ✕ 10⁻²⁷ kg,

moves in the positive y-direction with speed

v₁ = 5.4 ✕ 10⁶ m/s.

Another particle, of mass

m₂ = 8.0 ✕ 10⁻²⁷ kg,

moves in the positive x-direction with speed

v₂ = 3.2 ✕ 10⁶ m/s.

Find the magnitude and direction of the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.)

Problem Statement

Charges -2nC and 2nC are located at x= -0.1cm and x=0.1cm respectively. Determine the electric field at the points (-1 cm, 0 cm), (1 cm, 0 cm), (0 cm, 1cm), (0 cm, -1 cm) and (1 cm, 1 cm).

Visual Representation

• Draw a sketch of the charge distribution.

• Establish a coordinate system and show the locations of the charges.

• Identify the point P at which you want to calculate the electric field.

• Draw the electric field of each charge at point P. ⃗

• Use symmetry to determine if any components of Enet are zero.

Mathematical Representation ⃗

• For each charge, determine its distance from P and the angle of E i

• Determine the field strength of each charge.

• Write each vector in component form. ⃗

• Sum the vector components to determine E net.

• Check result for correct units and that it is reasonable.

A guy was dumped by his girlfriend and wants to jump off from a building 200 ft high. What is the required velocity he must start in order to touch down on her new boyfriend who stands on the ground, 30ft from the building. a) if he jumped out horizontally b)the guy jumped down with a depression angle of 30 degrees. Find the impact velocity and speed. Does he have any chance?