A mass weighing 10 pounds stretches a spring 3 inches. This mass is removed and replaces with a mass weighing 20 pounds, which is initially released from a point 4 inches above the equilibrium position with an upward velocity of 54 ft/s. Find the equation of motion, x(t) .

In a bubble chamber experiment, the decay of a Σ+ particle into a π+ particle and a neutron is observed when a 1.03 T magnetic field is applied perpendicular to the paths of the particles. The Σ+ and π+ particles leave curved tracks of radii 2.01 m and 0.588 m respectively. The rest masses are mΣ+ = 1189.4 MeV/c2 and mπ+ = 139.6 MeV/c2. If at the moment of decay, the angle between the momentum of the Σ+ and π+ particles is 71.6°, what is the magnitude of the momentum of the neutron? (Express your answer in units of MeV/c.)

I have an exame question about huygens ocular lenses, and it is asked to determine the equivalent focal distance . And then asks me to determine and draw the position of the focal planes relativity to the vertices? Whats the difference between calculating the equivalent focal distance and the position of the focal planes? They provide f1 = 6,35 cm and f2= 2,5 cm, whcih I though it was the position of the focal planes so I dont get really the question. Also they provide the distance between the lenses which is d=4,5 cm?

Huygens ocular lenses is a combination of two thin lenses, and not thick lenses, right? I am asking these because in the same question, it is asked to draw (with rays)the position of the principal plane, prior to the object, which I dont understand either.

The RBE (relative biological effectiveness factor) for several different types of radiation is shown in the chart below. Type of Radiation RBE X-rays and gamma rays 1.0 Beta particles 1.0 – 1.7 Alpha particles 10 – 20 Thermal neutrons 2 – 5 Fast neutrons and protons to the eye 32 Fast neutrons and protons 10 Heavy ions 20 Using the above chart, determine the dose in Gy for the maximum biological effectiveness from each of the following. (a) A 2.13 rad exposure to x-ray Gy (b) A 48.7 mSv exposure to α particles Gy (c) A 21.2 mrem exposure to β− particles

1) Find the uncertainty in kinetic energy. Kinetic energy depends on mass and velocity according to this function E(m,v) = 1/2 m v². Your measured mass and velocity have the following uncertainties     2.58 kg and   0.36 m/s. What is is the uncertainty in energy,  , if the measured mass, m = 4.75 kg and the measured velocity, v = -3.76 m/s? Units are not needed in your answer

2)Find the uncertainty in kinetic energy. Kinetic energy depends on mass and velocity according to this function E(m,v) = 1/2 m v². Your measured mass and velocity have the following uncertainties     0.47 kg and   2.48 m/s. What is is the uncertainty in energy,  , if the measured mass, m = 3.95 kg and the measured velocity, v = -22.69 m/s? Units are not needed in your answer.

3) The propagation of uncertainty formula for the equation y = ax^2 is

where ,and  . and . The values  and  are the uncertainties on a and x respectively.

If a = -4.5 +/- 0.4 and x = -4.7+/-0.7 then what is the uncertainty on y

4) After a million measurements of thing x, we find a sample mean of 60.45 and standard deviation of 3.24. What chance, in percent (0-100) does the next measurement have of being outside 3 standard deviations from the mean? Do not include the percent sign.

5) Find the uncertainty in a calculated average speed from the measurements of distance and time. Average speed depends on distance and time according to this function v(t,x) = x/t. Your measured distance and time have the following values and uncertainties x = 5.1 meters,   2.8 meters and t = 9.1 seconds and  0.2 seconds. What is the uncertainty in the average speed,  ? Units are not needed in your answer.

explain the three dimensional, time-independent Schrödinger equation.

describe the atomic structure of hydrogen atom.

explain nuclear binding energy and structure.

explain nuclear reactions, nuclear fission and nuclear fusion.

PLEASE DO NOT WRITE IT BY HAND.

Thanks.

Predictive analytics in business is an important application of multiple regression analysis. Generally speaking, what is meant by predictive analytics? As a business owner, how could you use regression analysis and predictive analytics to increase your company's sales?

(a) Show that the quantity

has the dimension of speed, where ε₀ is vacuum permittivity and μ₀ is vacuum permeability.
(b) Explain how each constant is important for electricity or magnetism, and what does it mean in practical terms that one is small and the other one is large?
(c) Compare the numerical value of

with the speed of light.

What is the maximum strength of magnet approved for medical imaging of patients?

7T

5T

3T

1.5T

What does precession mean?

The spinning of hydrogen protons around their own axis.

The change in orientation of hydrogen molecules when exposed to radiowaves at the Larmor frequency.

The wobble of hydrogen protons exposed to a large magnetic field.

Water molecules gain an extra molecule of hydrogen when exposed to a magnetic field.

Which of these is a disadvantage of MRI?

High dose of ionizing radiation.

Shows vasculature without contrast

Unsuitable for pacemaker wearers

Two-dimensional images

In MRI the resonant frequency of a specific tissue is NOT determined or affected by the:

Specific isotope being imaged

Characteristics of the molecule

Orientation of magnetic field

Strength of the magnetic field

Writing Prompt(s)

We have seen that making a ``good guess'' can turn the problem of solving a second order linear differential equation into finding the roots of a quadratic equation; specifically, for constant coefficient equations we make the guess y = e m xand for Cauchy-Euler equations we make the guess y = x m. Naturally, we'd like to know if there are other types of second order linear DEs that can be solved in this fashion. Are these the only ones or can you find others? For example, is there a type of second order linear DE that can be solved by guessing y = sin ⁡ ( m x ) and finding the roots of an associated polynomial?

A transmitter of power P sits atop a radio tower broadcasting in all directions. A man standing on the ground a radial distance r away from the transmitter measures the intensity of the radio waves to be
A) P/(4πr2)
B) P/(πr2)

C) P/(2πr)

D) P/(r2)

What happens when you put a small ice cube in a thermally isolated container (like a Thermos) containing considerably greater volume of hot coffee?
A) Heat flows from the ice into the hot coffee. Both ice and coffee evaporate into a warm, brown fog at an equilibrium temperature that is the average of the original ice and coffee temperatures.
B) Heat flows from the hot coffee into the ice. The equilibrium temperature drops to 0 ̊C and you end up with iced coffee.
C) Heat flows from the ice into the hot coffee. The ice gets colder and the coffee begins to boil.
D) Heat flows from the hot coffee into the ice, melting the ice and warming the resulting water up to the equilibrium temperature, which is close to the hot coffee’s original temperature.

An isolated sample of an ideal gas has an initial volume V0. Its container slowly changes shape until only half the volume V0/2 remains with no change in temperature. What happens to pressure of the gas in the sample?
A) It becomes only half as great.

B) It does not change.
C) It becomes 2 times as great.

D) It becomes 4 as great.

Question 1

If the theoretical value of a quantity is 3.142, and the calculated value is 3.146, what is the percent error? (closest value)

Group of answer choices

0.1 %

0.2%

0.3%

Question 2

In an experiment to measure the value of pi, the following results are obtained for pi:

3.14                    3.13                 3.24                 3.06                 3.02                                        

If the correct value is 3.14159, calculate the Percent Error (closest value)

Group of answer choices

0.3%

0.7%

1 %

2%

Question 3

What determines the number of significant figures used in reporting measured values?

Group of answer choices

The accuracy of the calculations

The accuracy of the equipment

Question 4

Calculate, to the correct number of significant figures:

21.414 + 15.231 + 17.24 + 5.01

Group of answer choices

58.90

58.9

58.895

58.89

Question 5

If the time period for a certain pendulum while standing in the Lab. on Earth is T second, will the time period be longer or shorter if It is taken to the Moon:

Group of answer choices

Longer

Shorter

Question 6

If the time period for a certain pendulum while standing in the Lab. on Earth is T second, will the time period be longer or shorter if it is taken to the planet Jupiter

Group of answer choices

Longer

Shorter

Question 7

If the time period for a certain pendulum while standing in the Lab. on Earth is T second, will the time period be longer or shorter if it is in an elevator that is accelerating upwards

Group of answer choices

Longer

Shorter

Question 8

For a vertically oscillating spring-mass system, should the time period depend on the amplitude of oscillation?

Group of answer choices

Yes

No

Question 9

What error can you expect if you use the stopwatch to measure the time for only 10 oscillations instead of 50 as mentioned in the manual?

Group of answer choices

The time period becomes smaller

Time period remains same, but the error in its measurement increases.

The time period remains same, and the error in its measurement decreases.

The time period becomes longer

A vector has components (4,2). When the vector is multiplied by the scalar 9, how does its magnitude and direction change?