a) Roller coaster moves down a slope of 10 m with an initial velocity of 1.5 m/s when it strikes a buffer as shown inFigure Q5. The buffer has a spring of stiffness, k = 15 kN/m. The roller coaster has a mass of 20 kg, a radius of 0.5 m and aninertia of 2.5 kgm?. Ignore the contact friction. Using the conservation of energy, calculate the following: i)The velocity of the disc just before striking the buffer. ii)The maximum compression in the spring.

b) A theoretical cycle consists of the following thermodynamic processes: 1An isobaric expansion process from a pressure of P1 and a volume of 1 m³ to a volume of 3 m3 An adiabatic expansion process to a volume of V3 and a pressure of 2MPa a according to Pv3=C. 3An isothermal expansion process back to the initial state in (1). i) Sketch pressure-volume diagram of the thermodynamic cycle ii) Calculate pressure P1and volume V3 Calculate the net work done in the cycle. Specify whether this work is done on or by the system.