Final answer:
To find the tension in the string when the object is at the bottom of its path, we need to consider the forces acting on the object. At the bottom of the path, the tension will be equal to the weight plus the centripetal force. At the top of the path, the tension will be equal to the weight minus the centripetal force.
Step-by-step explanation:
To find the tension in the string when the object is at the bottom of its path, we need to consider the forces acting on the object. At the bottom of the path, the tension in the string will be equal to the sum of the weight of the object and the centripetal force required to keep it moving in a circle. The tension will be equal to the weight plus the centripetal force, which can be calculated using the formula:
Tension = weight + centripetal force = mg + (mv^2)/r
where m is the mass of the object, g is the acceleration due to gravity, v is the speed of the object, and r is the radius of the circular path. Plugging in the values given (m = 2.0 kg, v = 12 m/s, r = 1.5 m), we can calculate the tension at the bottom of the path.
For the object at the top of its path, the tension in the string will be equal to the difference between the weight of the object and the centripetal force required to keep it moving in a circle. The tension will be equal to the weight minus the centripetal force, which can be calculated using the same formula as before. Plugging in the values given, we can calculate the tension at the top of the path.