A roller coaster at the Six Flags Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop. The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure that the cars remain on track. The biggest loop is 40.0m high. Suppose the speed at the top is 14.4m/s and the corresponding centripetal acceleration is 2g. (a) What is the radius of the arc of the teardrop at the top? (b)If the total mass of a car plus the riders is M, what force does the rail exert on the car at the top? (c) Suppose the roller coaster had a circular loop of radius 21.4 m. If the cars have the same speed, 14.4 m.s at the top, what is the centipetal acceleration at the top?
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
A roller coaster at the Six Flags Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop. The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure that the cars remain on track. The biggest loop is 40.0m high. Suppose the speed at the top is 14.4m/s and the corresponding centripetal acceleration is 2g.
(a) What is the radius of the arc of the teardrop at the top?
(b)If the total mass of a car plus the riders is M, what force does the rail exert on the car at the top?
(c) Suppose the roller coaster had a circular loop of radius 21.4 m. If the cars have the same speed, 14.4 m.s at the top, what is the centipetal acceleration at the top?
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