Question

A string requires 186 N of force to break. A 1.50 kg mass is tied to the string and whirled in a vertical circle with a radius of 1.90 m. What is the maximum speed that this mass can be whirled at the top of the vertical loop without breaking the string?

Answer 1

The maximum speed at which a 1.50 kg mass can be whirled at the top of a vertical loop without breaking a string that can withstand 186 N of force is calculated using the centripetal force formula, considering the tension the string can withstand and the weight of the mass.

Step-by-step explanation:

The question pertains to the maximum speed at which a 1.50 kg mass tied to a string can be whirled in a vertical circle without breaking the string, given that the string can withstand a force of 186 N. At the top of the vertical loop, the tension in the string plus the weight of the mass should be equal to the required centripetal force for circular motion. The tension the string can withstand is 186 N and the gravitational force on the mass is 1.50 kg × 9.81 m/s2, which equates to 14.715 N. Therefore, the maximum centripetal force that can be applied without breaking the string is 186 N - 14.715 N. Using the centripetal force formula Fc = m × v2/r, we can solve for v, the maximum speed. Substituting the given values, we have 171.285 N = 1.50 kg × v2/1.90 m, which leads to v2 = (171.285 N × 1.90 m) / 1.50 kg. Solving for v gives us the maximum speed at which the mass can be whirled without breaking the string.