For the system of four capacitors shown in the figure below, find the following. (Use C1 = 1.0

A block attached to a spring is displaced from equilibrium to the position x=+1.3m and released. The period is 2.6s. At what positions and times during the first complete cycle do the following conditions occur.

a) |v|=0.5vmax|, Where vmax is the maximum speed?

First position:  m . . . First time:  s.
Second position:  m . . . Second time:  s.
Third position:  m . . . Third time:  s.
Fourth position:  m . . . Fourth time:  s.

b) |a|=0.5amax. Where amax is the maximum magnitude of the acceleration?

First position:  m . . . First time:  s.
Second position:  m . . . Second time:  s.
Third position:  m . . . Third time:  s.
Fourth position:  m . . . Fourth time:  s.

An RLC series circuit has a 2.50 Ω resistor, a 100 µH inductor, and an 87.5 µFcapacitor.

(a)

If the voltage source is Vrms = 5.60 V , what is the Irms at 120 Hz?

A ( ± 0.001 A)

(b)

What is the phase angle of the current vs voltage at this frequency? Enter a positive number between 0 and 90

degrees ( ± 0.1 degrees)

(c)

What is the Irms at 5.0 kHz?

A ( ± 0.01 A)

(d)

What is the phase angle of the current vs voltage at this frequency? Enter a positive number between 0 and 90

degrees ( ± 0.1 degrees)

(e)

What is the resonant frequency of the circuit?

kHz ( ± 0.01 kHz)

(f)

What is Irms at resonance?

A ( ± 0.01 A)

(g)

What is the phase angle of the current vs voltage at resonance? Enter a positive number between 0 and 90

degrees ( ± 0.1 degrees)

Use the exact values you enter to make later calculations.

A ray of light strikes a flat, 2.00-cm-thick block of glass (n = 1.57) at an angle of ? = 31.2

) A 1.53-kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm.   This pulley is frictionless in its axle, and has the shape of a solid uniform disk. After the bucket has been released, what is the angular acceleration of the pulley?

Carnot Engine questions: What was the full name of the man who imagine the first Carnot Engine? What thermodynamic theory did he use to calculate its efficiency? Describe a Carnot engine, in terms of thermodynamic processes. What does Carnot's Theorem say about the efficiency of a Carnot engine operating between two absolute temperatures? What does Carnot's Theorem say about the efficiency of a reversible engine which is not a Carnot engine operating between two absolute temperatures? What does Carnot's Theorem say about the efficiency of an irreversible engine operating between two absolute temperatures?

In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.10 m. The mug slides off the counter and strikes the floor 0.20 m from the base of the counter.
(a) With what velocity did the mug leave the counter?
____________m/s ????

(b) What was the direction of the mug's velocity just before it hit the floor?
_____________

What is the maximum weight that can be suspended on a 25kg poll, 3/5 from the end? The maximum tension of the 30 degree guy-wire is 1500N. Find the horizontal and vertical forces exerted on the poll by the hinge.

An alpha particle is a nucleus of helium. It has twice the charge and four times the mass of the proton. When they were very far away from each other, but headed toward directly each other, a proton and an alpha particle each had an initial speed of 4.1×10^-3 c, where c is the speed of light. What is their distance of closest approach? There are two conserved quantities. Make use of both of them. (c = 3.00 × 10^8 m/s, k = 1/4πε 0 = 8.99 × 10^9 N · m2/C2, e = 1.60 × 10^-19 C, m proton = 1.67 x 10^-27 kg)

A.) 1.1 x 10^-13 m

B.) 1.6 x 10^-13 m

C.) 1.8 x 10^-13 m

D.) 1.4 x 10^-13 m

ESSAY TYPE QUESTION:    Define Newton’s three laws of motion, and explain what they represent collectively. Also provide at least one real life example of one of Newton’s laws. Some questions could further be explained by a diagram if possible.

2) A steel rod with a cross-sectional area of 0.25 sq. in. is stretched between two fixed points. The tensile load at 70 degrees F is 1200 lb. What will be the stress at 0 degrees F? At what temperature will the stress be zero?

Assume ? = 6.5 x 10^-6 °F^-1 and E = 30 x 10⁶ psi.

1. Write a couple (2) of paragraphs describing the origin of both the continuous background spectrum and the dark lines in the solar spectrum.

The Sun rotates around the center of the Milky Way Galaxy (the figure below (Figure 1)) at a distance of about 30,000 light-years from the center (1ly=9.5×1015m). 1.If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. Express your answer using one significant figure. 2.If all the stars had about the mass of our Sun (2×1030kg), how many stars would there be in our Galaxy? Express your answer using one significant figure.

1.

If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere.

Express your answer using one significant figure.

2.

If all the stars had about the mass of our Sun (2×1030kg), how many stars would there be in our Galaxy?

Express your answer using one significant figure.