Avolkswagen passat has a six-cylinder otto-cycle engine with compression ratio r = 10.6. the diameter of each cylinder, called the bore of the engine, is 82.5 mm. the distance that the piston moves during the compression, called the stroke, is 86.4 mm. the initial pressure of the air-fuel mixture is 8.50 x 104 pa, and the initial temperature is 300 k (the same as the outside air). assume that 200 j of heat is added to each cylinder in each cycle by the burning gasoline, and that the gas has cv = 20.5 j/mol k and y=1.40.a. calculate the total work done in one cycle in each cylinder of the engine, and the heat released when the gas is cooled to the temperature of the outside air. b. calculate the volume of the air-fuel mixture at point a in the cycle. c. calculate the pressure, volume and temperature of the gases at points b, c and d in the cycle. d. compare the efficiency of this engine with the efficiency of a carnot-cycle engine operating between the same maximum and minimum temperatures.

Amass m = 74 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius r = 18.4 m and finally a flat straight section at the same height as the center of the loop (18.4 m off the ground). since the mass would not make it around the loop if released from the height of the top of the loop (do you know why? ) it must be released above the top of the loop-the-loop height. (assume the mass never leaves the smooth track at any point on its path.) 1. what is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? 2. what height above the ground must the mass begin to make it around the loop-the-loop? 3. if the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4. if the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.4 m off the ground)? 5. now a spring with spring constant k = 15600 n/m is used on the final flat surface to stop the mass. how far does the spring compress?