A high-speed lifting mechanism supports a 710 kg object with a steel cable 20.0 m long and 4.00 cm² in cross-sectional area.

(a) Determine the elongation of the cable.
_____ mm
(b) By what additional amount does the cable increase in length if the object is accelerated upward at a rate of 2.6 m/s²?
_____ mm
(c) What is the greatest mass that can be accelerated upward at 2.6 m/s² if the stress in the cable is not to exceed the elastic limit of the cable, 2.2 ✕ 10⁸ Pa?
______ kg

Plaque builds up on the walls of an artery decreasing its diameter from 1.16 cm to 0.66 cm. If the flow speed is 12.5 cm/s before reaching the region of plaque buildup, determine the following.

(a) speed at which blood is traveling through the plaque-constricted region
  cm/s

(b) pressure change within the plaque-constricted region. (Assume the density of blood is 1050 kg/m³. Be sure to include the appropriate sign with your answer.)

Using only the spring gun with the catcher removed, fire the steel ball, making sure the launch velocity is horizontal. Using carbon paper (and something to catch the ball after impact with the floor), determine the ball’s horizontal range and its total vertical displacement (i.e., height at point of firing). Repeat several times in order to obtain statistical data.

Derive a formula in symbolic form for the initial velocity of the projectile in terms of the following three quantities only: the horizontal range (x), the vertical height at launch (y) and the acceleration due to gravity (g). Finally, determine the initial velocity of the steel ball and refer to this velocity as v1 .

Need help deriving the equation (italics). Please show all intermediate derivations too (i.e. how to come to horizontal range (x) = v1*t). Thank you!

Problem 2 – The plates of a parallel-plate capacitor are separated by a distance d = 0.2 m. There is vacuum between the plates. The voltage difference between the plates is 150 V. The capacitance of the plates is 3 μF.

a) (6 pts) Find the magnitude of the electric field between the plates (ignoring edge effects).

b) (12 pts) An alpha particle, which is doubly ionized helium, He2+ (charge = 2e where e is the elementary charge, mass = 4.7 × 10-27 kg) is released from rest at the positively charged plate. Find the speed of the alpha particle as it hits the negatively charged plate.

c) (6 pts) Find the magnitude of the total charge on one of the plates of the capacitor.

d) (6 pts) Find the total energy stored in the capacitor.

Find the expression for the electric field due to a finite size of a line charge in a certain distance. Then derive an expression for the electric field due to an infinite size of a line charge from what you found for the finite charge. Show that you can come up with a same using the Gauss law.

For the some unknown Hamiltonian, we will use a trial wave function ?? = ??₁??₁ + ??₂??₂ . Where ??1 ?????? ??2 are known functions

a. What are the variational parameters of this trial wave function (2 points)?

b. Minimizing the average energy will lead to a secular Determinant.Write down an expression for the Secular Determinant for this system using the following symbols (4 points)

??_11, ??₁₂ = ??_21, ??₂₂, ??_11, ??₁₂ = ??_21, ??_22, E.

c. Write a mathematical expression using ??₁, ??₂, and any necessary operators to define (2 points)

??₂₂=

??₂₁=

Two resistors of exactly the same resistance are hooked in series to a power supply and the total current: I_tot(series) is measured. The same two resistors are then connected to the same power supply in parallel. The total parallel current is related to the total series current through the relationship:

Select one:

a. I_tot(parallel) = 1/4 × I_tot(series)

b. I_tot(parallel) = 1/2 × I_tot(series)

c. I_tot(parallel) = 2 × I_tot(series)

d. I_tot(parallel) = 8 × I_tot(series)

e. I_tot(parallel) = 1/8 × I_tot(series)

f. I_tot(parallel) = 4 × I_tot(series)

g. I_tot(parallel) = I_tot(series)

2. a)

A 0.20 kg hockey puck on a frictionless surface is hit with a stick. The force of the stick on the puck, during the 0.4 seconds while they are in contact, causes the puck to go from rest to 36 meters per second east. What was the magnitude of the average force of the stick on the puck while they were in contact?

b)

A 3-kg block is placed on a frictionless ramp-incline, where it slides from rest, 18 m down along the ramp- incline in 4 seconds.

What was the angle of the incline, with respect to the horizontal?

The position of a particle moving along an x axis is given by x = 12.0t2 - 4.00t3, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t = 5.00 s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at what time is it reached? (h) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)? (i) Determine the average velocity of the particle between t = 0 and t = 5.00 s.

From atomic mass and density, estimate the lattice constants of Si, Ge, GaAs, InAs, and InSb. (I'm having trouble with the GaAs, InAs and InSb).

-Discuss three real-life quantities that are naturally described by complex numbers. Show that by mathematical equations.
-In A.C. circuit what does real part of the circuit present? And, what does the imaginary part present?
_Through explaining different forms of complex numbers show which for present a position vector.
-How does Laplace Transform relate to the complex plane?
-Complex functions used to describe Potential Flow in two dimensions in fluid dynamics.

Suppose that 132 moles of a monatomic ideal gas is initially contained in a piston with a volume of 0.94 m³at a temperature of 348 K. The piston is connected to a hot reservoir with a temperature of 1064 K and a cold reservoir with a temperature of 348 K. The gas undergoes a quasi-static Stirling cycle with the following steps:

1. The temperature of the gas is increased to 1064 K while maintaining a constant volume.
2. The volume of the gas is increased to 3.38 m³ while maintaining a constant temperature.
3. The temperature of the gas is decreased to 348 K while maintaining a constant volume.
4. The volume of the gas is decreased to 0.94 m³ while maintaining a constant temperature.

It may help you to recall that CV = 12.47 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadros number (6.022

A) A 46.1 kg girl is standing on a 169 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.61 m/s relative to the plank. What is her velocity relative to the ice surface?

B) What is the velocity of the plank relative to the ice surface?