Final answer:
The tension in the string when the stone is moving vertically upward is the sum of the centripetal force necessary for circular motion and the gravitational force acting on the stone, adjusted for the stone's position in the vertical circle.
Step-by-step explanation:
When a 4 kg stone tied to a string is rotating in a vertical circle, it experiences centripetal force towards the center of the circle as well as the force due to gravity. The tension in the string when the stone is moving vertically upward can be calculated by considering the forces acting on the stone at that point. The forces are the gravitational force (mg, with g as the acceleration due to gravity) acting downwards and the centripetal force needed to keep the stone moving in a circle, which depends on the mass (m), the speed (v) of the stone, and the radius (r) of the circle (mv2/r).
At the highest point in its vertical circular path, the tension (T) in the string plus the component of gravitational force must equal the centripetal force necessary for circular motion. Therefore, we have T + mg = mv2/r. We can rearrange this to find the tension: T = mv2/r - mg. Given the mass (m = 4 kg), the speed (v = 6 m/s), the radius of the circle (r = 3 m), and the acceleration due to gravity (g = 9.8 m/s2), we can calculate T.