Final answer:
To find the magnitude of the speed and maximum tension in the string, the minimum tension is used to calculate the speed at the top of the circle. Then that speed is used to find the maximum tension at the bottom of the circle. The correct answers are Speed = 1.5 m/s, Maximum tension = 0.6N (choice c).
Step-by-step explanation:
The question is asking to calculate the magnitude of the speed and the maximum tension in the string that is rotating a mass in a vertical circle. We can use the concepts of circular motion and dynamics to solve this problem.
Step-by-step Solution:
- First, we note that the minimum tension will occur at the top of the circle where the forces acting on the mass are gravity and tension, both downwards.
- At the top, Tension (T) + Weight (mg) = Centripetal Force (mv²/r), where T is the minimum tension, m is the mass, g is the acceleration due to gravity (9.8 m/s²), v is the speed, and r is the radius.
- Plugging the values in, we get 3N + (0.2kg * 9.8 m/s²) = (0.2kg * v²/1m), solving for v gives us the speed.
- Maximum tension occurs at the bottom of the circle as here tension has to counteract both the centrifugal effect and gravity. We now have Tension (T) = Centripetal Force (mv²/r) + Weight (mg).
- Using the speed found, we calculate the maximum tension by plugging the values into the above formula.
From the calculations, we find that the speed is 1.5 m/s and the maximum tension in the string is not 3N, as that is given to be the minimum tension. The choice that matches our calculated speed and acknowledges a difference in maximum tension from the minimum tension is (c) Speed = 1.5 m/s, Maximum tension = 0.6N.