Determine the maximum speed at which the car with mass m can pass over the top point A of the vertical curved road and still maintain contact with the road.(Figure 1) Express your answer in terms of some or all of the variables m, r, and appropriate constants. If the car maintains this speed, what is the normal reaction the road exerts on the car when it passes the lowest point B on the road? Express your answer in terms of some or all of the variables m, r, and appropriate constants.

An engine, weighing 3000 n, is supported on a pedestal mount. it has been observed that the engine induces vibration into the surrounding area through its pedestal at the maximum operating speed. determine the stiffness of the dynamic vibration absorber spring in (n/m) that will reduce the vibration when mounted on the pedestal. the magnitude of the exciting force is 250 n, and the amplitude of motion of the auxiliary mass is to be limited to 2 mm note: in this question type-in right numbers, no decimals, no fractions, no unit. approximate to right number if needed