A .4 kg ball attached to the end of a horizontal cord is rotated in a circle of radius 1 m on a frictionless horizontal surface. If the cord will break when the tension exceeds 90 N, what is the maximum speed the cord can have?

A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion. (Figure 1)Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. At the top and bottom of the vertical circle, the ball's speeds are vt and vb, and the corresponding tensions in the string are T⃗ t and T⃗ b. T⃗ t and T⃗ b have magnitudes Tt and Tb. Find Tb−Tt, the difference between the magnitude of the tension in the string at the bottom relative to that at the top of the circle. Express the difference in tension in terms of m and g. The quantities vt and vb should not appear in your final answer.

A hockey puck that has a mass of 0.150 kg is tied to a light string and spun in a circle of radius 1.15 m on frictionless ice. If the string breaks under a tension that exceeds 4.00 N, what is the maximum speed vmax of the puck without breaking the Umax = m/s string?

A roller coaster has a circular loop with a diameter (height) of 39 meters. When the coaster is upside down at the top of the loop, what is the minimum speed it must be traveling so that the passengers do not fall out?