A 0.75-kg ball is attached to a 1.0-m rope and whirled in a vertical circle. The rope will break when the tension exceeds 450 N. What is the maximum speed the ball can have at the bottom of the circle without breaking the rope?
A)24 m/s
B)12 m/s
C)32 m/s
D)16 m/s
E)38 m/s

Question

Quizplus · Accepted Answer

At the bottom of the circle, the tension is maximum and is the sum of the gravitational force and the centripetal force. Using the formula T = mg + mv^2/r, where T is the tension, m is the mass, g is the acceleration due to gravity (9.8 m/s²), v is the velocity, and r is the radius, we solve for v: 450 = 0.75*9.8 + 0.75*v^2/1. Solving gives v ≈ 24 m/s.

A 075-Kg Ball Is Attached to a 1