Final answer:
The magnitude of the centripetal accelerations for both objects, one with mass m and the other with mass 2m moving in a circular path of radius 2.0 m at a constant speed of 3.5 m/s, is 6.125 m/s². Mass does not affect the acceleration as they are moving at the same speed and radius.
Step-by-step explanation:
We are provided with two objects moving at a constant speed on a circular path with a radius of 2.0 m. One object has a mass m and the other has a mass 2m. To find their individual centripetal accelerations, we use the formula for centripetal acceleration:
ac = v2/r
Where ac is the centripetal acceleration, v is the velocity, and r is the radius of the circular path. Plugging in the given values (v = 3.5 m/s, r = 2.0 m), we get:
ac = (3.5 m/s)2 / (2.0 m) = 6.125 m/s2
Therefore, the magnitude of the centripetal accelerations for both objects at a single point in time is 6.125 m/s2. Note that the mass of the objects does not influence the magnitude of the centripetal acceleration when they are moving at the same speed and radius.