Compute the solution of each part of given problem:

Problem: A 400 kg roller coaster cart travels along the inside of a vertical circular track of radius 10 m. At its highest point it moves at 20 m/s. Friction between the cart and track is negligible.

Part A: Find the cart's speed one quarter of a loop later (when it's at the same height as the loop's center)

Part B: Find the magnitude of the normal force one quarter of a loop later (when it's at the same height as the loop's center).

Please show each step and detailed calculation.