A roller coaster is a machine that travels through clothoid loops with steep slopes, sharp turns, and sometimes inversions by using gravity and inertia forces. A clothoid loop is a loop that has a larger radius of curvature at the bottom of the loop and a smaller radius of curvature at the top of the loop. Since, centripetal acceleration needed to complete a circle is velocity squared over the radius, a large centripetal acceleration at the top where the radius is small causes an incoming lower speed car to maintain its circular motion track still successfully. As the roller coaster travels through the loop, due to a change in speed and direction, a person at the top of the loop feels weightless but is not weightless.
A roller caster experiences two forces; the normal force perpendicular to the track (contact force between the rider and the chair) and the gravitational force pulling the earth downwards. At the bottom of the loop, the track applies normal force upward upon the car, and the rider experiences the same force due to her weight exerted on the car. This is explained by Newton's third law of motion, which states that all forces between two objects exist in equal magnitude and opposite direction. When the roller coaster moves along the loop at a constant speed, the car keeps changing direction, and as a result, a force towards the center of the circle acts upon the rider. This force is known as the centripetal force requirement.
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At the bottom of the loop, the gravitational force upon the rider is directed downwards (outwards) and thus a need for a large upwards normal force to meet the centripetal force requirement. At the top of the loop, both the normal and gravitational forces are acting downwards, and there is no need for a large normal force to sustain the circular motion. Therefore, at the top of the loop, the rider experiences a weightless sensation because there is no contact force. The normal force is now less than the body weight, and the only force acting upon the rider now is the gravitational force. During this free fall at the top, the gravitational force supplies the centripetal force required to sustain the circular motion.
Mass of an object can often refer to its weight, although there are distinct differences between them. An object's weight is the force acting on its mass due to gravitational acceleration, mathematically expressed as ( ). In contrast, the mass of an object is the quantity of matter present in an object, mathematically expressed as ( . For example, an object weighs less on the moon's surface than on the earth's surface while its mass remains the same because the gravitational field strength is weaker on the outer space, but the object's volume and density remain intact.
References
Amusement Park Physics. (n.d.). The Physics Classroom. Retrieved October 29, 2020, from https://www.physicsclassroom.com/class/circles/Lesson-2/Amusement-Park-Physics
Etkina, E., Planinsic, G., & Heuvelen, A. V. (2018). College Physics: Explore and apply. Pearson.
