.You are required to design a roller coaster with the profile shown in Figure Q2(a). An electric motor will pull the coaster to the top of the first hill. After the coaster has been pulled to the top, no more external work will be added to it. Hint: the amount of energy the coaster has to complete its journey on the track depends on the potential energy on the first hll. This will give you the relationship berween the height of this hill and the speed of the coaster. The shape of the first hill will determine if the coaster will safely travel on the track and speed of the coaster. Hint: you can imagine the coaster as a particle that moves in space along the track in a projectile motion. The coaster exit through a second hill to maintain feeling of speed and thrill in the ride. The second hill is also to maintain the speed to the next stage of the ride. Hint: the safety of travel on the track depends on the speed you are travelling and is related to the hill you are coming from. Instead of adding a loop to your coaster, the coaster is allowed to gradually cruise to a stop. Assume is a flat path. (c) (d) Height of the fint hill Supe af the fint hill The it path The loep Figure Q2(a) Profile of roller coaster: (a) The height of first hill height 20m, (b) Shape of the first hill and radius at the bottomp = 60 m, (c) The exit path height 5m, and (d) The loop to end the ride is a level ground, ignore the small height. Assuming a total mass of 1000kg, explain with calculations how would you design the roller coaster from start till the end of coaster ride: O the power of the electric motor to pull the coaster up the first hill. the force at the bottom of the first hill to make sure it is strong enough to support (i) the coaster.

A rectangular tank 7m long by 2.4m deep and 2.65m wide, contains 1.2m of water.If the linear acceleration horizontal in the direction of the tank's length is 2.75m/s²a) Compute the total force due to the water acting on each end of the tankb) Show that the difference between these forces equals the unbalanced force necessary to accelerate the liquid massc) If the tank is filled with water and accelerate in the direction of its length at the rate 1.72m s³, how many litres of water are spilledd) What is the maximum acceleration should be to keep no water will spill out

5.5

Q2.characteristics of a small underwater craft are studied under dynamic similarity conditions in a varable density wind tunnel on a model scale of 1:12. What prototype speed and power are indicated by model values of 100m/sec of velocity and 30N of drag force? The model is operated at 8atm pressure [Take Pair at atmospheric pressure-0.95Kg/m³, Pwater-998Kg/m³. Hwater 1.0*103 pa.sec and Hair-2.17*105 pa.sec].