A pendulum is swinging in an elevator that is accelerating upward at a constant acceleration a. (a) Using the Lagrangian method, what is the equation of motion? Note be careful here, the velocity needs to be measured from an inertial reference frame. (b) What is the frequency of small oscillations?

When someone falls from a tall building, the most effective way to save him is to provide a net at the bottom so that the person slows down himself conveniently without hurting himself, the impulse here is same that would have been without the net but the net provides extra time for the change in momentum. Another example is, in the game of cricket when the ball is hit by the bat the time to change the momentum is expected to be the least by the batsman to get an excellent shot.

Support your claim using equations and provide two scenarios with numbers and calculations.

A sample of an unknown material appears to weigh 300 N in air and 222 N when totally immersed in alcohol. What are (a) the volume and (b) the density of the material? (c) What material is it?

Show what the expression E • J represents in field theory, what would its analogous expression be in circuit theory?

(d) Given a condition with three different wind velocities, u1, u2 and u3 fluctuating towards a base station, which have different heights, let say z1 , z2 and z3. Apply the correlation function between of the condition of the velocities and wind loads at the various heights.

What's the difference between direct and indirect measurements? and which is better

Driving down a quiet street on a summer day with the car windows down, you see a convertible
approaching from the opposite direction, with the driver playing her car stereo loudly. Having a
well-trained musician’s ear, you notice that the song you hear is in a key one semitone (the
interval between two adjacent keys on a piano) above the key in which the song is typically
heard. You also know that to shift any note by one semitone, the frequencies must be related by
a factor of 1.06. Assume both drivers are traveling at the same speed, what is their speed?

A point particle slides frictionlessly down a sphere, starting from rest a the top(θ=0). Show that the particle leaves the sphere when cos θ= 2/3. Use lagrange multiplier instead of newtonian mechanics

A very long coaxial cable consists of a solid cylindrical inner conductor of radius 3.8mm , surrounded by an outer cylindrical conductor with inner radius 7mm , and outer radius 9.3mm . The region between the two conductors is filled with a waxlike insulating material to keep the conductors from touching each other. The inner conductor carries a current 4.65A , into the page, while the outer conductor carries a current 4.6A , out of the page.

Part A

Use Amp�re's law to derive an expression for the magnetic field as a function of r(the distance from the central axis) at points between the two conductors (R1<r<R2i). Use this expression to find the magnetic field at 4.8mm .

Use Amp�re's law to derive an expression for the magnetic field as a function of r(the distance from the central axis) at points inside the outer conductor (R2i<r<R2o). Use this expression to find the magnetic field at 7.1mm .

Use into page as negative and out of page as positive current.

Comment

Hint 1. Ampere's Law

Ampere's Law states:  ?B??s=?0?Ienclosed Therefore you need to figure out what the enclosed current is for this case.

Hint 2. Enclosed current

The enclosed current is the current in the inner conductor + that portion of the current enclosed in the outer conductor. Use Itotal/Atotal=Ienclosed/Aenclosed Don't forget Atotal=pi?(R22o?R22i) and there is a corresponding expression for Aenclosed.

A uniform thin rod of length 0.4 m and mass 0.5 kg can rotate in a horizontal plane about a vertical axis on the left end of the rod. The rod is at rest when a 10.0-g bullet traveling in the horizontal plane of the rod is fired into the right end of the rod at an angle 90o with the rod. The bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after the collision. The rotational inertia of a rod about axis through center perpendicular to length L is (1/12)*ML2.

Find the rotational inertia of the rod-bullet system when the bullet lodges in the rod. Keep 5 decimal places.

What is the angular momentum after the collision? Keep 4 decimal places.

Find the bullet’s initial velocity.

What mass of steam at 100∘C must be added to 1.90 kg of ice at 0∘C to yield liquid water at 15 ∘C? The heat of fusion for water is 333 kJ/kg , the specific heat is 4186 J/kg⋅C∘ , the heat of vaporization is 2260 kJ/kg .

When a potential difference is applied to the piece of metal wire, a current of 4.1 mA flows through it. if this wire is replaced with a silver wire having twice the diameter of the original wire, how much current will flow through the silver wire?

Assume that the lengths of the potential difference across both wires are the same. ( the resistivity of the original metal is 1.68x10^-2 ohm . m, and the resistivity of silver is 1.6x10^-8 ohm . m )

Suppose that a particle with charge q and mass m is initially at the origin with zero velocity in the presence of external electric and magnetic fields given by

E = (Ex, 0, Ez),

B = (0, 0, Bz).

(1) Find x(t) and draw the trajectory the particle follows in space.

A pair of radio transmitters separated by 118m along a north-south line each transmit an in-phase 5.55MHz wave. Using small angle approximations, the smallest angle (with respect to the easterly direction from the pair of transmitters) of destructive interference is closest to

A.16°

B.19°

C.6.4°

D.9.7°

E.13°