Apparent weightlessness and Vertical Circular Motion Chapter 5 Lesson 3

Directions in centripetal force problems: Again... Directions in centripetal force problems: Positive direction is inwards toward center of circle. Negative direction is outward away from center of circle.

Vertical Circles The forces acting on a person sitting in a roller coaster car are shown. The person’s weight FW is present and so is the normal force FN that the seat exerts on him (this is your apparent weight).

Vertical Circles The normal force FN, the force you feel on the seat of your pants, can be positive, negative, or zero. A negative value for FN means the passenger has to be strapped in, with the straps exerting an upward force. Such a situation would be dangerous, and roller coaster designers avoid this. If FN = 0 N, the person seems to be weightless as well as upside down.

Vertical Circles The forces on Maverick and Goose at the bottom of a dive can be quite large. Gravity pulls downward and the seat exerts its usual normal force FN, this time upward.

Vertical Circles Experiencing a significant number of g’s makes the work of the heart more difficult. Accelerations of eight to ten g’s make it difficult for the circulatory system to get enough blood to the brain and may result in blackouts. Pressure suits that squeeze on the legs push blood back into the rest of the body, including the brain, and help prevent blackouts.

Vertical Circles For the Ferris wheel, the only difference occurs at the top where the seat is facing upward. Top: This equation is also for a car passing over the top of a curve. Bottom:

Tension For an object attached to a string and moving in a vertical circle, the centripetal force is at a minimum at the top of its vertical path and at a maximum at the bottom of its vertical path.

Tension Top: the centripetal force on the object equals the tension of the string plus the weight of the ball, both acting toward the center of the vertical circle. Mathematically: Bottom: the centripetal force on the object is equal to the difference between the tension of the string and the weight of the object. The tension is exerted inward toward the center of the vertical circle, while the weight is directed away from the center of the vertical circle. Mathematically:

Speed of a Satellite: Mem mv2 Fc= G = _______ ____ r² r

Speed of a Satellite: √ GMe v = r

v = velocity (m/s) G = gravitational constant Me = mass of Earth (kg) r = distance to center of the Earth (m)