baseball pitcher executes a pitch in 0.32 sec. (assume that his motion of the pitching arm is a circular, also assume that v₁ = 0). If his pitching arm is 90 cm long, what are the magnitudes of the tangential and radial accelerations on the ball just before ball release, when tangential ball speed is 35 m/s (in m/s²)? What is the magnitude of the total acceleration on the ball at this point (in m/s²)?

A generator at a utility company produces 100 A of current at 4.0 x 103 V. The voltage is stepped up to 2.4 x 105 V by a transformer before being sent on a high voltage line across a rural area to a city. Assume the effective resistance of the line is 30.0 Ω and the transformers are ideal.

a. Determine the percentage of power lost in the transmission line.

b. What percentage would be lost if the voltage would not have been stepped up?

c. How many kW-hr of energy is lost each day if the voltage would not have been stepped up?

d. Calculate the cost of this energy loss if the price of electricity is $.11/kW-hr.

The Boeing 777 aircraft has a takeoff mass of 240000kg and a takeoff speed of 90m/s . Assume that's the speed of air across the wing's bottom. The total surface area of both wings is 428m(sqrd). What airflow speed across the top of the wing is necessary for the plane to fly?

I know I have to use bernoulli's equation, but I'm not sure how to get all the variables. Could someone help, and also explain the process please?

A football quarterback is traveling straight backward at a speed of 5.1 m/s when he throws a pass to a receiver 15.5 m straight downfield.

(a) If the ball is thrown at an angle of 25° relative to the ground and is caught at the same height as it is released, what is its initial speed relative to the ground in m/s?

(b) How long does it take to get to the receiver in s?

(c) What is its maximum height above its point of release in m?

Could you explain the answer and show detailed work? Thanks! :)

A disc and solid sphere are both rolling without slipping so that both have a kinetic energy of 294. What is the translational kinetic energy of the disc ? What is the translational kinetic energy of the solid sphere ?

A bowling ball of mass m and radius r has a coefficient of static friction µ when in contact with an oiled wood surface. Model the ball as a solid uniform sphere. The surface is inclined at an angle θ with respect to the horizontal. What is the maximum angle of inclination of the surface such that the ball rolls without slipping? How does the angle change if the ball is now a hollow shell with all its mass concentrated at the rim? Explain

How do LaserTweezers work? What can you do with LaserTweezers? Discuss three examples for bio-applications of LaserTweezers.

In a ballistics test, a 23.0g bullet traveling horizontally at 1300m/s goes through a 40.0cm -thick 450kg stationary target and emerges with a speed of 900m/s . The target is free to slide on a smooth horizontal surface. How long is the bullet in the target? What average force does the bullet exert on the target? What is the target's speed just after the bullet emerges?

The parity operator P is defined by

ˆ Pψ (x) =ψ (−x)

for any function ψ(x).

(a) Prove that this parity operator P is Hermitian.

(b) Find its eigenvalues, and also its eigenfunctions (in terms of ψ(x)).

(c) Prove that this parity operator commutes with the Hamiltonian when potential V(x) is an even function.

Provide a description of our home galaxy, the Milky Way. Include in your description the location and stellar populations (new stars/ old stars) of the central bulge, disk, and halo. Also provide details such as the Hubble classification, disk structure, location of star forming regions, and the best estimate of the number of spiral arms.

USING CONSERVATION OF ENERGY AND WORK ENERGY PRINCIPLE:

A block of mass m=1.8 kg on a table is pushed against a spring that has a force constant of k=250 N/m, compressing it 20 cm (the block is not attached to the spring). The block is then released, and the spring pushes the block to move to the right. The coefficient of kinetic friction between the block and the table is 0.45.

(a) Find the distance the block will travel before it stops. (b) Find the maximum speed of the block.

A pendulum has a length 1 m and a mass 1 kg. Assume Earth free fall acceleration equal to 10 m/s^2. When the pendulum oscillates, the maximal deflection angle is +/- 1 degree.

a) If the maximal deflection angle doubles, what would be the new period?

b) If the pendulum mass goes up 100 times, what would be the new period?

c) If the length goes up 100 times, what would be the period?

d) If the pendulum moves to Moon, what would be the period?

Two blocks are positioned on surfaces, each inclined at the same angle of 52.5 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 5.05 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.510. Assume static friction has been overcome and that everything can slide. What is must be the mass of the white block if both blocks are to slide to the LEFT at a constant velocity?

A pendulum has a length 1 m and a mass 1 kg. Assume Earth free fall acceleration equal to 10 m/s^2. When the pendulum oscillates, the maximal deflection angle is +/- 1 degree.

a) How long will it take before the energy drops to half of the initial value at t=0?

b) How long will it take before the max deflection angle drops to half of the initial value at t=0?

c)

If the damping was produced by a force given by F = -v*k, where v is the velocity and k is some friction coefficient, find k.

(Hint: derive the equation of motion for the pendulum including friction and compare to the textbook one describing the damped harmonic oscillations.)

d)

Suppose you are aiming to excite a resonance of this pendulum by kicking it with a periodically modulated force at a frequency f. What should be f in Hz and approximately how accurately should you be able to adjust f, i.e. f +/- how much?

(Hint: look up the expression for the amplitude of forced vibration of a harmonic oscillator and see how it depends on the frequency of the external force and the dambing constant.)

A photovoltaic solar collector with an area of 2 m2 is tracking the sun for 8 hours on a sunny day. Assume that, the solar flux on the collector is constant through the day as 1000W/m2. PV Solar collector properties are:

FF: %75, Efficiency: %18.2

V (MPP, nominal) = 28 V

V (Open Circuit) = 32 V

a) What is the total amount of energy converted to electricity?

b) Assume a reasonable price for the cost of electricity and then calculate the value of electricity ($) produced for whole day.

c) Calculate the generated current and Short Circuit Current.