Question

a In mechanics, the energy of a moving body is called kinetic energy. If an object of mass (kilograms) is moving with a velocity v (meters per second), then the kinetic energy k( joules) is given by the equation ke we model the mass and inputs to a system (moving body) and the energy as output, then obnerve the system for while and deduce the following two rules of inference based on our observations Rule 1: IF x is small maxs and x2 is high velocity, THEN y is medium energy Rule 2: IF x1 is large mass or x2 İs medium velocity, THEN y is high energy. Let input (d) -0.35kg (mass) and input )-55 m/s (velocity), Find the output using Mamdani implication (use Centroid method for defuzzification) 114 marks Rule I Small High 0 20 40 60 00.1 0.3 0.3 Input) Inputta) High Rule 2 A Medium 0.8 0.4 100 300S x2 0 20 40 60 80 0 12 345 Inputco Input)

Answer 1

For Rule 1, both the conditions on mass and velocity must be satisfied.

So the output would include all the three figures in this case.

Here m =0.25, v=40 then y = 200, which is well satisfied by these three figures.

For rule 2,

m= 3.5, y= 200 then v = 10.7

Or

V = 50, y=200, then m= 0.16