A (cube, with a calculable volume of dimensions Xm=7 x Ym=7 x Zm=7), having density rho=80 kg/m³, is 80% (less than 100%) submerged in a fluid having density rho_fluid=1500 kg/m³. Find a) the tension in a string holding the object to the bottom of container holding the fluid (aside; this only makes sense if the buoyancy force exceeds the object's weight force), and b) the numerical value of the pressure at the top and the bottom of the object, including atmospheric pressure. Remember that: a) the buoyancy force depends only on the submerged volume, rather than the total volume of the object, and b) atmospheric pressure is 101325 pascal (Pa).

A bar magnet falls freely, with its north pole pointing straight down. It approaches and passes through a fixed, horizontally orientated, metal ring.

a) How, if in any way, is the magnet's motion affected as it approaches the ring?

b) How, if in any way, is the magnet's motion affected as it leaves the ring?

Explain briefly with appropriate diagrams showing induced currents and their magnetic effects.

Given the Ising model or a canonical ensemble how is the critcal temperature calculated?

Also, would you happen to know the relationship between how many neighbor interactions there are and how this affects temperature?

thanks!

10.A 12.3 kg child jumps up and grabs a (round) horizontal tree branch that has a diameter of 6 cm. The child grabs the branch 28 cm from the trunk, and the weight of the child causes the branch to sag. If the shear modulus for the tree is 1.016 x 10^6N/_m2, how how much does the branch sag when weighted?

11.Ropes for rock climbing have a diameter of 10.5 mm and a Young's modulus of 8.72x10⁷ N/m². If a rock climber of mass 82.4 kg falls when there is 45.8 m of rope out, how far will the rope stretch?

A 3kg object is attached to spring and will stretch the spring 392mm by itself. There is no damping in the system and a forcing function of F(t)=10 coswt, w=(k/w)^-2 is attached to the object. The spring is deflected y distance father than equilibrium position due to the F(t). k is the spring modulus and M is the mass of the object.

a) Derive the governing equation for the spring-object mass system decribed in the problem.Assume Mg=hk

b) if the object is initially displaced 20cm downward from its equilibrium position and given a velocity of 10cm/s upward find the displacement of the object at any time t.

c) suppose a damper is added to the mass-spring system that will exert a force of 45N when the velocity is 50cm/s, damping factor of 90kg/s is added to the system. And find the displacement of the object at any time t for this new system

d)Determine the amplitude , nature frequency and phase shift of the object for this new system.

(a) A particle is dropped (from radius a with zero velocity) into the gravitational potential corresponding to a static homogeneous sphere of radius a and density ρ. Calculate how long the particle takes to reach the other side of the sphere. [Hint: the equation of motion is d²r/dt² = −GM(r)/r² .]

(b) Calculate the time required for a homogeneous sphere of radius a and density ρ with no internal pressure support to collapse to zero radius under its own gravity. [Apply the previous equation of motion to a particle on the surface.]

1a Describe how thermal energy is obtained by fission, specifically when a U=235 atom is hit by a slow-motion neutron (less than 0.9 MeV). When one states that 200 MeV of energy are released by a fission event, what is the form of this energy?

1b. The energy released by fission is by the change in mass and Einstein’s equation (E=Δmc²). If the mass of one uranium 235 atom is 235.042924 amu and the mass of fission products is 234.92754 amu, determine the energy in Joules and MeV released by one fission. (Note: 1 amu = 1.66 x 10^-27kg and 1 ev = 1.6 \x 10^-19J).

1c. For an atom, the atomic number is the number of protons, while the atomic weight (i.e. molecular weight) can be 235 or 238 depending on the isotope. Determine the number of atomic particles (electrons, neutrons, and protons) for U-235, U-238, Kr-90. Note: The atomic number of Krypton is 36.

• If we recreated the scene from Fast & Furious 7 and dropped a Challenger SRT® Hellcat Redeye Widebody from a C-130 aircraft at 5,280 ft, how much horsepower would it take to drive past it before it hits the ground if you’re 1 mile away?
• Rephrase the question: How much horsepower is needed to travel the distance of one mile, before the dropped vehicle hits the ground, from a mile up in the air, out of the back of a C-130 aircraft. The falling vehicle is falling STRAIGHT down, no forward travel The vehicle on the ground that has to pass the point of impact BEFORE impact, has to start from a dead stop.
• Use the following data to compute the required hp to caver the distance of 1 mile, from a dead stop, and pass the point of impact. Will have to calculate the time of fall, to find the time needed to start from a standing start to cover a mile just past the point of impact.

Data available:

• Air density @ sea level, 59 degrees, no wind = p = .002377 slugs/ft^3
• Coefficient of drag (flat plate, NASA) = C(d) = 1.28
• Weight = W = 4451 lbs
• Gravitation constant = g = 32.2 ft/sec^2
• Area = A = 197.5" long x 78.2" wide x (1 ft^2/ 144 in^2)
• Vehicle falls flat, wheels 1st, straight down, at constant acceleration with no aerodynamic drag until terminal velocity
• Horsepower needed to accelerate is AVERAGE - not peak
• 100% driveline efficiency

A man walks 1.55 km south and then 2.25 km east, all in 2.80 hours.

(a)

What is the magnitude (in km) and direction (in degrees south of east) of his displacement during the given time?

magnitude km direction ° south of east

(b)

What is the magnitude (in km/h) and direction (in degrees south of east) of his average velocity during the given time?

magnitude km/h direction ° south of east

(c)

What was his average speed (in km/h) during the same time interval?

km/h

A sledge loaded with bricks has a total mass of 18.2 kg and is pulled at constant speed by a rope. The rope is inclined at 20.1° above the horizontal, and the sledge moves a distance of 19.2 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500.

(a) What is the tension of the rope?
N
(b) How much work is done by the rope on the sledge?
kJ
(c) What is the mechanical energy lost due to friction?
kJ

Consider an experiment in which we bombard an unknown, quantum system with a broad beam of monochromatic light. By varying the frequency of the light, we detect which frequencies are absorbed by the system and which pass through. What characteristics do those frequencies exhibit if our system is a simple harmonic oscillator?

Students are sitting in a classroom and listening to a lecture. If the lecture has a sound level of 65 dB to the student sitting in the front row, what is the sound level according to another student sitting 3 times further away?

Show all the steps.

1. Two long solenoids are placed in the coaxial position, one inside the other, they have 30 cm and 20 cm diameters, respectively. The outer solenoid is 2 m long with 5000 turns, and carrying a current of 4 A. The inner one is 1 m long with 2000 turns, and carrying a current of 2 A in the opposite sense. Find the magnitude of the magnetic field (in mT) at any point on the solenoid axis inside.

A. 10.52
B. 3.68
C. 15.08
D. 7.54

2.

A straight conductor is split into identical semicircular turns, as shown in the figure. What is the magnetic field at the center of the circular loop?

  
A. μoi/2R
B. μoiR/4
C. 0
D. μoi/4R

3.

Which of the followings are correct for Ampere’s Law? (Choose three correct answers)

A. The magnetic field decreases non-linearly outside of a current carrying wire  
B. The net magnetic field is zero at the both end of the current carrying wire  
C. The magnetic field has its maximum value on the surface of a current carrying wire  
D. The magnetic field increases linearly within a current carrying wire from its center to its surface

Dodge is known for appearing in the most badass action movie stunts. Well, now we’re challenging you to think about what it takes to pull it off...

If we recreated the scene from Fast & Furious 7 and dropped a Challenger SRT® Hellcat Redeye Widebody from a C-130 aircraft at 5,280 ft, how much horsepower would it take to drive past it before it hits the ground if you’re 1 mile away?

Pro Tips

• Air density @ sea level, 59 degrees, no wind = p = .002377 slugs/ft^3
• Coefficient of drag (flat plate, NASA) = C(d) = 1.28
• Weight = W = 4451 lbs
• Gravitation constant = g = 32.2 ft/sec^2
• Area = A = 197.5"" long x 78.2"" wide x (1 ft^2/ 14 in^2)
• Vehicle falls flat, wheels 1st, straight down, at constant acceleration with no aerodynamic drag until terminal velocity
• Horsepower needed to accelerate is AVERAGE - not peak
• 100% driveline efficiency