Pulley System with Rotational Inertia PHY 2048C Cumulative Final Examination Points: 10 Suggested Time: 20–25 minutes Instructions: Show all work. Begin each derivation with an appropriate physics principle. Clearly define any additional symbols you introduce. Block 1 of mass m1 rests on a frictionless incline of angle θ. It is connected by a light cord over a pulley to a hanging block of mass m2. The pulley has radius R and moment of inertia I. The cord does not slip on the pulley. Assume block 2 moves downward and block 1 moves up the incline. Tasks Part A. Write Newton’s second-law equation for each block and the rotational equation for the pulley.Part B. Derive the magnitude of the acceleration a of the system.Part C. Determine the two cord tensions T1 and T2.Part D. Starting from rest, determine the speed v of the blocks after block 2 descends a distance s. You may use either Newton’s laws or conservation of energy.

Composite Rolling Body and Projectile Motion PHY 2048C Cumulative Final Examination Points: 10 Suggested Time: 25–30 minutes Instructions: Show all work. Begin each derivation with an appropriate fundamental physics principle. Clearly define any additional symbols you introduce. Unsupported answers may not receive full credit. A rigid composite wheel consists of a uniform solid cylinder of mass 2m and radius R rigidly attached to a thin hoop of mass m and radius R. The wheel starts from rest at a vertical height H above the end of a track. It rolls without slipping down the track and leaves the track horizontally from the edge of a platform that is a height h above the floor. Neglect rolling resistance and air resistance. Reference Information Isolid cylinder = (1/2)MR2,    Ithin hoop = MR2 Tasks Part A. Determine the total moment of inertia of the composite wheel about its central axis. Part B. Using conservation of mechanical energy, derive the translational speed v of the wheel’s center of mass as it leaves the track. Part C. Determine the angular speed ω of the wheel at the edge of the platform. Part D. Determine the horizontal distance x from the edge of the platform to the point where the wheel first contacts the floor. Treat the wheel’s center of mass as the projectile point for this calculation. Part E. Determine the fraction of the wheel’s total kinetic energy that is rotational immediately before it leaves the track. Explain whether this fraction depends on H.

What is the rate of return for alternative B? [Express your answer using 2 significant decimal digits (X.xx%), and do not enter the percentage sign when entering your answer.] 

Should Guy pay the Once-A-Month Haircut Club annual membership if his personal annual minimum attractive rate of return is 18%? I recommend that Guy [recommendation] the upfront membership.

Problem X – Best alternative using IRR

Problem VIII – Effective annual interest rate paid by bond issuer

Problem I – Forever car maintenance

The last step of the accounting cycle is:

Sales minus Cost of Merchandise Sold is equal to

A recent graduate buys a car for $39,000, and his aunt pays the down payment of $5,500 to celebrate their academic milestone. The rest of the amount is financed through the car manufacturer at 5.5% annual nominal interest with 60 monthly payments, with the first of the 60 payments taking place at the end of the 13th month. How much will the monthly payment be for this loan? The college graduate will pay $_________ starting from month 13 (with the last payment at the end of month 72).