A 464-kg fully-loaded roller coaster car is traveling at 23.0 m/s at point A where the radius of curvature is 18.2 m.

In the World Peace Lab, Mia empties a bag of peas into a bucket and whirls the peas in a vertical circle using a 1.57-m long rope. What minimum speed can the bucket have so that the peas still remain in the bucket while moving through the top of the circle?

A 666-kg roller coaster car starts from the top of a hill and rolls down. It enters a loop for which the radius at the top is 23.1 meters. Determine the minimum speed in meters/second (at the loop's top) at which the 666 kg roller coaster car will complete the loop without falling out of the loop. (HINT: This is the speed at which the roller coaster car wheels are just barely in contact with the track; any slower speed would turn the car into a projectile.)

Avery is watching cartoons on the Nostalgia Network and a scene from the Tarzan toon reminds him of Physics. He created this problem and wants you to solve it:

The 75.5-kg Tarzan tries to cross a river using a 6.82-m long vine that has a breaking strength of 2670 N. What is the maximum speed that Tarzan can have at the bottom of the circular arc in order to avoid breaking the vine?

In 2002, professional skateboarder Bob Burnquist became the first to successfully navigate a 360° full pipe turn. Determine the minimum speed which would be required at the top of the circular loop to make it through the 1.82-m radius pipe.

Sheila (m=60.8 kg) is riding the Demon roller coaster ride at Six Flags. The turning radius of the top of the loop is 15.9 m. Sheila is upside down at the top of the loop and experiencing a normal force which is one-half of her weight. Draw a free body diagram and determine Sheila's speed.