(b) A car is stopped in a horizontal road. The car weighs 4500N and its center of gravity C is 40cm behind the front wheels axle and 80cm in front of the rear wheels axie. Find the normal force on each tyre. (C) Considering the centripetal force for a car moving on a banked track (or road). Show that for a given velocity, V and radius, r, the angle of inclination of the track (or banking angle) is = tan-). (Hint: R and R are the normal reactions of the wheels; 0= angle of the curved track or road). SECTION C 5 (a) Two circles in a plane, C and C, each rotate with frequency o (relative to the inertial frame) as shown below. The center of C, is fixed in an inertia frame. The center of C is fixed on C. A mass is fixed on C. The position of the mass relative to the center C, is R(t). Find the fictitious force felt by the mass. (b) 6. (a) (b) (c) N=4 C3 N circles in a plane, C, each rotate with frequency o (lative to an inertial func) u show!! below. the centre of mass C, is fixed in an inertial frame. The center of mass C is fixed on C-1, (for i = 2,..., N). A mass is fixed on CN. The position of the mass relative to the center of C, is R(t). Find the fictious force felt by the mass. 20 Derive the wave equation of a vibrating string. Deduce the normal mode equations of the vibrating string X (c) A mass rests motionless with respect to the lab frame, while a frictionless turntable rotates beneath it. The frequency of the turntable is oo, and the mass is located at radius, r. In the frame of the turntable, what are the forces on the mass? 1/2m2 651049 Show that the flow of power per cycle across any point of a vibrating string can be expressed as P = (@KTA)/2 wherek = 2n is the wave number and is the amplitude of the wave