A spherical mylar balloon filled with Hydrogen gas, with density 0.0899 kg/m³ and having radius 7 meters is immersed in a gas having density X1=1.205 for the first 10 km and X2=2.489 for the second 10 km (with the upper atmosphere density smaller than the lower atmosphere density). Determine how long it takes the balloon to reach the top of the second layer. To do this, you will have to: a) find the net force on the balloon (assume the mylar is massless) in the first layer, then assuming constant acceleration, determine the time to get to the bottom of the second layer, then b) repeat the exercise, but now calculating the buoyancy using the second layer of atmospheric gas.

Using Hamilton’s equations, show that for any solution ρ(t) of Liouville’s equation that asymptotically approaches the equilibrium solution ρ(eq), there is a time-reversed solution that diverges from it. What does this mean?

The parameters of the apparatus that are important to its function are: Solenoid winding: # turns N=1000; winding length Ls = 10 cm; radius R=2.5 cm; wire radius r=0.05 mm; wire resistivity rs= 2 x 10-8 Wm; length of the core extending above the solenoid Lc=10 cm.
a Calculate the resistance and the inductive reactance of the solenoid winding for its response when an applied e.m.f. of 110 V r.m.s, 60 Hz is applied to it.
b Calculate the impedance of the solenoid winding, and the r.m.s. current that is induced to flow in it.
c Calculate the r.m.s. magnetic flux produced inside the solenoid.
d Assume that the magnetic flux through the solenoid is channeled through the extended length of the steel rod core above the solenoid, fringes radially along the length of that extended region so that no flux leaves the top of the extended core. Calculate the radial field magnetic field in that region.
e Calculate the current that would be induced in the aluminum ring if it is located to surround the bottom of the extended region of the core. The parameters of the ring are: Length 4 cm, radial thickness 2 mm, resistivity rr= 3x10-8 Wm
f You close the switch long enough for the ring to be accelerated vertically above the top of the extended core. Estimate how high above the extended core it will travel before coming to a stop and falling.
g Identify the parameters of the entire apparatus that determine how high the ring will jump. Optimize the values for those parameters to make the ring jump to the maximum possible height. Assume the applied voltage and overall size of the apparatus cannot be changed.
h If the solenoid has 1000 turns, how many turns should the secondary have in order to apply 6 V across its terminals.
i The value of the capacitance C should be chosen so that it forms an LC circuit in series with the inductance of a 10-turn secondary winding that is resonant at the 60 Hz frequency of the AC voltage that is applied to the primary winding. What should be the value of C?

2. Answer the following questions about the motion of an object launched from the roof of a building with a height of 10 m at an initial velocity of 20 m/s and an angle of 60°. (1) Find the x and y components of the initial velocity. (2) Find the x and y components of the velocity after 2.0 seconds. (3) Find the time to reach the highest point. (4) Find the height of the highest point. (5) Find the time until it falls to the ground.

A satellite is launched into an orbit at an altitude 200 km above the surface. Onboard is an exquisitely sensitive atomic clock that is synchronized with an identical clock on Earth. After orbiting for one year, the satellite is captured, returned to Earth, and the clocks compared. What will be the shift in time between the two clocks?

Two solid spheres are running down from incline of height 3.7 m. Sphere A has mass 3.3 kg; radius 15.7 cm; sphere B has mass 7.4 kg and radius of 39.3 cm. Find the ratio of their angular velocities omegaA/omegaB at the bottom of the incline.

1. (Experiment)

Measure all the dimension of the four objects and fill out the table below. As the ‘proof’ that you did the experiments, take a screenshot of your PC screen for at least one dimension of each and insert (copy and paste) the screenshots to the end of this data sheet. (For Window’s users, ‘snipping tool’ is convenient to take a screenshot. You can search the tool by searching ‘snipping tool’ on Windows Search. For Mac users, press ‘Command’ + ‘Shift’ + ‘3’ to capture a screenshot). Also, calculate the volume of each object using the following formulas. The volume of the sphere of dimeter reads

Eq. 1

the volume of the block of length , breadth as and thickness

Eq. 2

the volume of the cylinder of dimeter and height

, Eq. 3

and the volume of the beaker of internal diameter and the internal height (depth)

Eq.4

Please Type Answer

A person who has their feet spread apart, when pushed against by another person is able to stay stable. A person who has their feet together, when pushed against by another person is not stable at all. What is the reason for this? Take into consideration the mechanical principles in relation to torque, levers, area of supporting base, and position of your center of gravity.

A sailboat runs before the wind with a constant speed of 3.5 m/s in a direction 28 ∘ north of west. You may want to review (Pages 89 - 92) .

How far west has the sailboat traveled in 22 min?

How far north has the sailboat traveled in 22 min?

The Bipolar Junction Transistor (BTJ) characteristic Curve experiment source of error

A child on a sled starts from rest at the top of a 20.0° slope.

1)

Assuming that there are no forces resisting the sled’s motion, how long will the child take to reach the bottom of the slope, 250 m from the top? (Express your answer to two significant figures.)

the nuclear shell model, orbitals are filled in the order 1s1/2,1p3/2,1p1/2,1d5/2,2s1/2,1d3/2, etc.
(a) What is responsible for the splitting between the p3/2 and p1/2 orbitals?
(b) In the model, 16O (Z = 8) is a good closed-shell nucleus and has spin and parity Jπ = 0+ . What are the predicted Jπ values for 15O and 17O?
(c) For odd-odd nuclei a range of Jπ values is allowed. What are the allowed values for 18F (Z = 9)?
(d) For even-even nuclei (e.g. for 18O) Jπ is always 0+ . How is this observation explained?

Using Faraday’s Law and Lenz’s Law, explain why a change of current in a conducting wire loop will induce an electrical potential difference which will oppose this change. Use relevant equations and/or diagram(s).