The position of a 55 g oscillating mass is given by x(t)=(2.3cm)cos13t, where t is in seconds.

Determine the amplitude.

Determine the period.

Determine the spring constant.

Determine the maximum speed.

Determine the total energy.

Determine the velocity at t = 0.41 s .

A thin, uniform bar of length L and mass M is suspended horizontally at rest. It is suddenly released

and, at the same instant, it is struck a sharp blow vertically upwards at one end – the duration of

the impulse is negligibly short.

(a) Explain the meaning of the equation Fnet = Macom (com stands for center of mass). If we call z the vertical direction, write an equation for zCOM(t), draw a sketch of zCOM(t) vs t, and annotate it to show the initial

slope, the maximum value of zCOM(t), and the time(s) at which zCOM(t) = 0.

(b) Explain the meaning of the equation Tnet = Iα (net torque). Describe the rotational motion of the bar, by

giving an equation for the angular displacement θ(t). (The moment of inertia of a bar about

a perpendicular axis through its centre is 1/12ML^2.)

(c) By combining your answers to (a) and (b), describe in words how the bar moves after being

struck. (Note: you can try the experiment yourself, using a pen as the bar, and your finger

or another pen to impart the impulse.)

Problem 4. Suppose that 70% of a radioactive substance is gone after 6.43 years. What is the half life of this substance?

Question 1. What is N(t)/N0 in this problem? (2 points)

a. unknown

b. there isn’t such a thing in this problem

c. .70

d. 6.43 years

e. the half life

Question 2. What is the decay constant in this problem? (3 points)

a. 1.76 years

b. 5.34 years

c. 9.76 years

d. 12.5 years

Question 3. Using the radioactive decay equation to find the half life, what should N(t)/N0 equal? (2 points)

a. the half life

b. the decay constant

c. .50

d. none of the above

Question 4. What is the half life of this substance? (3 points)

a. 3.70 years

b. 2.62 months

c. 5.66 years

d. 11.4 years

Some particles are created via collisions. For instance, pions are created via collisions
with high energy protons and carbon, which releases neutrons and pions (which they
themself, decay into muons).
Suppose two particles with momenta of p1 = (3,-1, 0, 0) kg and p2 = (2, 1, 1, 0) kg collide.
Three particles are created as a result from this collision, two of which have momenta of
p3 = (1, 1, 0, 0) kg and p4 = (1,-0.5, 0, 0) kg, determine the four momentum, energy, rest
mass and three velocity of the third daughter particle.

A block of mass m=2kg can slide down a frictionless 53 degree incline but is connected to a pully of mass M=4kg and radius R=0.5m. The pulley may be treated as a uniform disk. Find:

a) The angular acceleration of the pulley

b) The speed of the block after it has slid 1m starting from rest

You are being asked to determine if there is any oxygen present in an unknown mixture of gas. You know that when oxygen is made to glow by placing a large potential difference across it, it will produce light most brightly at the following wavelengths (in nanometers): 408, 419, 441, and 465. You use a strong power supply to make a sample of this gas mixture glow then use a spectroscope to split the light into its components. The spectroscope contains an interference grating with 500 ± 10 ?????⁄??.

a. Assuming the mixture does contain oxygen, draw a labeled diagram showing what the interference pattern produced by that oxygen would look like.

b. Choose three features of the pattern. Determine the angle (with respect to the center of the pattern) that each of these features would appear at. For example, you could choose to find the angle for m = 0 for all wavelengths, and m = +1 for the 408 nm and 465 nm wavelengths. Or you could determine the angle at 3 different features – the choice is yours.

Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (⁴He) from gold-197 (¹⁹⁷Au). See the figure below. The energy of the incoming helium nucleus was 8.80  10^-13 J, and the masses of the helium and gold nuclei were 6.68  10^-27 and 3.29  10^-25 kg, respectively (note that their mass ratio is 4 to 197). If a helium nucleus scatters to an angle of 120° during an elastic collision with a gold nucleus, calculate the helium nucleus's final speed.

Put the origin of the coordinate system at the site of the stationary gold nucleus and the +x direction in the direction in which the incoming helium nucleus travels. Write a statement of conservation of energy, momentum in the x direction, and momentum in the y direction to obtain three equations and three unknowns. See if you can solve the three equations simultaneously for the three unknowns. m/s

Calculate the final velocity (magnitude and direction) of the gold nucleus. (Assume the positive x direction is the direction in which the helium nucleus is initially traveling, and that it scatters 120° clockwise from the +x-axis.)

The position vector F(t) of a moving particle at time t[s] is given by F(t)= e^t sin(t)i-j+e^t cos(t)k a) Calculate the acceleration a(t). b) Find the distance traveled by the particle at time t = 3π/2, if the particle starts its motion at time t = π/2. c) Find the unit tangent vector of this particle at time t = 3π/2. d) Find the curvature of the path of this particle at time t = 3π/2.

What are some ways to store energy from variable clean sources

There was a demonstration I did our Zoom class with a falling magnet in a simple copper tube. Explain, in detail, the physics behind why the magnet slows its descent through the tube (it does not touch the sides). In your discussion be sure to explain why the magnet doesn't come to a stop in the tube and why it does not speed up. Your response should include at least 3 paragraphs to show your mastery of the material.

Assume a square well as a shape of the scattering potential of a nucleus ? with ?−wave neutrons of a potential depth of ?_0=50 MeV and a potential radius of ?=6.5 fm.

a) Show that the internal wave function is given by ?_0(?)=?sin(??) with ?= √2?(?−?_0)/ℏ

b) Show with calculations, whether there are bound states of the compound system ?+? and what are their positions on the energy axis.

For polymer structure analysis with purposes given below; how microscopy (light and/or electron) can be used? How can you get information? Which method/tool you choose to determine the given properties? Please explain in detail.
1. Chemical Industry and Manufacturing
2. Crystallization
3. Failure Analysis Surface Topography

I need full report for "uncertainties & Error Analysis" included the summarized background, theory, procedure 5 steps, and conclusion"

1. The neutral Helium atom is made of a nucleus (containing two protons and two neutrons) and two electrons. The electrons have an average separation from the nucleus of r =31pm. Note: 1pm = 10^-12m (pico-meter)
   
   
   
   Consider the average configuration of the Helium atom shown above, treating the nucleus as a single charge of the appropriate size. What is the magnitude of the total electric force acting on one of the electrons?