Question

A 16 g ball at the end of a 1.4 m string is swung in a horizontal circle. It revolves once every 1.09 s. What is the magnitude of the string's tension?

Answer 1

The magnitude of the string's tension is 8.96 N.

Step-by-step explanation:

To find the magnitude of the string's tension, we can use the equation for centripetal force. The centripetal force is equal to the product of the mass of the ball, its tangential velocity squared, and the radius of the circle. In this case, the centripetal force is provided by the tension in the string.

Using the given values, the centripetal force can be calculated as:

Centripetal force = (mass of the ball) x (tangential velocity^2) / (radius)

Substituting the given values, we find:

Tension = (16g) x (1.4m/s)^2 / (1.4m) = 8.96 N

Therefore, the magnitude of the string's tension is 8.96 N.

If there are no bends in the string, as occur with vibrations or pulleys, then tension is a constant along the string, equal to the magnitude of the forces applied by the ends of the string.

The magnitude can also be thought of as the strength of the force. When forces are represented as vectors, the magnitude of the force is usually explicitly labeled.