How Does Energy Affect Energy In Roller Coasters

Roller coasters are fun rides found in amusement parks all over the world. Globally, people indulge in the thrilling experience provided by the steep hills, loops, and sharp twists. This feeling is made possible by the various changes in forces and energy, concepts not uncommon to us.

energy

Initially, the cart of roller coasters are brought to the top of a hill mechanically. At the top, it possesses a large amount of gravitational potential energy (Ep). This is the largest amount of energy the cart will have throughout the ride, due to the conservation of energy. Dissipative forces such as air resistance and friction can be assumed to be negligible due to their small quantities. This means that throughout the ride, Ep and Ek will always

This relationship is shown using the formula Ep=mgh, where Ep ∝ m, g, h. As the ride continues, there will be multiple changes in energy, where Ep converts to Ek, and vice versa. Kinetic energy is dependent upon the mass of an object and the velocity it is travelling at. This is shown using the formula Ek=12 mv2, where Ek ∝ m and v. This transformation occurs when there is a loss in height (Ep∝ h, so as h decreases, Ep decreases). During a loss in height, e.g going down a steep hill, gravity acts downwards on the passenger cart, causing it to accelerate. This means that the velocity also increases ( a=vt, a ∝ v). This subsequently results in an increase in Ek (Ek ∝ v). Because energy is conserved, we can assume that the amount of Ep lost is the same as the amount of Ek

Because the cart is travelling in a circular motion, there must also be centripetal force (Fc).

Gravitational force acts downwards on the cart at all points, and is dependant on the mass of the cart and the gravitational constant (F= mg). The normal force is provided by the track, and acts perpendicularly to the track itself. The size of Fn is dependant on the Fg and radius of the point of the loop. These forces must combine to provide the Fc necessary. Centripetal force acts towards the centre of the circle, and is found using the formula Fc = mv2/r, where m= mass, v= velocity, and r= radius. Because the radius of a clothoid loop and velocity of the cart is ever changing, the centripetal force will not be constant.

When at the the bottom of a clothoid loop, Fg acts downwards. Fn acts upwards, perpendicular to the track, in the same direction as centripetal force. Because Fg acts opposing the normal force, and is always constant, the magnitude of Fn must be large to compensate, providing the necessary Fc. Adversely, at the top of the loop, both Fn and Fg act downwards. This allows for Fn to be smaller at the top, as it works in conjunction to Fg to provide the Fc.