Question

a 0.650-kg object is swung in a circular path and in a vertical plane on a 0.500-m-length string. if the angular speed at the bottom is 8.00 rad/s, what is the tension in the string when the object is at the bottom of the circle?

Answer 1

To find the tension in the string when the object is at the bottom of the circle, we can use the concept of centripetal force. The tension in the string is equal to the sum of the gravitational force and the centripetal force. Plugging in the values given in the question will give us the tension in the string.

Step-by-step explanation:

To find the tension in the string when the object is at the bottom of the circle, we can use the concept of centripetal force. Centripetal force is the inward force required to keep an object moving in a circular path. In this case, the tension in the string provides the centripetal force.

At the bottom of the circle, the tension in the string is equal to the sum of the gravitational force and the centripetal force. The tension in the string can be calculated using the formula T = mg + (m * v² / r), where T is the tension, m is the mass of the object, g is the acceleration due to gravity, v is the velocity, and r is the radius of the circular path.

Plugging in the values given in the question, we have T = (0.650 kg * 9.8 m/s²) + ((0.650 kg * (8.00 rad/s)²) / 0.500 m). Calculating this gives us the tension in the string when the object is at the bottom of the circle.