Roller Coaster

one of the main forms of energy (kinetic is the other one), stored hidden energy, gravitational potential energy described as u=mgh, measured in joules , the reference point for h should be the lowest point in the situation, It is located at the tallest point on the coaster which is the orange starting track. Its the starting point for the coaster and in turn provides the coaster the maximum potential of energy which will propel the marble down.

potential energy that is stored and increases due to a force or change in the system .this occurs when the marble is climbing uphill, The formula for potential energy due to gravity is PE = mgh.. units are in joules. As the object gets closer to the ground, its potential energy decreases while its kinetic energy increases. This is located in two places of the coaster where the marble proceeds up in a vertical direction. This makes the marble slow down , but gains energy for the next part of the roller coaster.

A force that changes momentum in a certain amount of time, the equation for the impulse is J=Ft.F is the average force,J is the integral of Fdt, J is delta(mv), measured in Ns, found when the marble bounces off of a wall it has pos impulse going in since the velocity is positive, This is found in places where the marble hits the rail and continues ride. It makes the marble change momentum and energy for the next section of the ride.

should happen in a freefall , the acceleration due to gravity ,but without the factor of air resistance. Equation is written as F=mg .Also described as the rate at which velocity is changing and is a vector. Can be found at the end of the coaster after the jump. Makes the marble move downward and in turn speeds up the ride by 9.8m/s/s.

The increasing energy possessed by a system or object as a result of its motion. The kinetic energy of objects with mass is dependent upon the velocity and mass of the object. The equation can be written as k=1/2mv^2, when velocity is increased from acceleration due to forces such as g, Fn, Ff, etc. Can be found when the marble goes down a hill since gravity is acting on it and the velocity is increasing. This helps the marble gain energy and as a result increase the speed.

Wnet=delta(K). This occurs when the marble is going up hills since the marble is slowing down thus the loss of kinetic energy and the change in energy due to a force applied over a certain distance. Units are in joules. It makes the marble and ride slow down due to the negative work done by the gravity from going up the hills.

The max potential energy is wherever the potential energy is zero which would be at the bottom of a hill or incline. The equation can be written as K=1/2mv², and expressed in joules. Makes the rider feel the max force of energy at the bottom of the hill, or that sick feeling when you change direction really fast.

This force is involved in circular or curved paths. The force is directed to the center of the circle and can be found in loops or a curved turn. The equation is expressed in F=(mv²)/r with the units being Newtons. Makes the rider sort of shift their body toward the side due to the force from the center of the turn or loop.

Impulse is a force that changes momentum in a certain amount of time. Negative impulse occurs whenever force acts on the marble opposing motion and expressed by the equation J=Ft. Whenever change in momentum is negative then the equation is J=∆p(change in linear momentum).Found when the ball changes direction or slows down. Makes the ride slow down and loses energy .

Projectile motion is the curved path a trajectory. Found at the end of the ride when the marble is launched into the black cup. This would not be in a real coaster because the coaster would not be able to jump off the rails and tracks. Equations include Vf^2=V0^2 + 2aDx. and v0t +1/2(at)^2 and does not have a specific unit.

Velocity is the speed of an object in a current direction. Velocity is decreasing whenever there is an incline because it is going against the y-component of gravity . Can be found using the equation ∆V=at. Is found whenever the marble goes up the inclined track. Makes the coaster go slower.

Can be found wherever the velocity increases (gain in kinetic energy) or when positive gravity>friction which would be down a ramp or incline. Described using the equation Wnet=∆K and units are expressed in joules. Makes the coaster go faster and the ride more fun.

Maximum velocity is when velocity reaches it max speed during the duration of the ride. Which would be after the final down hill section of our coaster. Described with the equation Vf^2=Vo^2 +2adx. Units expressed in m/s. Make the coaster go the fastest speed possible in the ride.

Centripetal acceleration is acceleration towards the center of a circle. Found in the section of the funnel and uses the equation a(sub r) = v^2 / r. Where units are expressed in m/s/s.

Momentum of a system remains constant when there are no net external forces acting on it. Can be described with the equation Pi = Pf where the units are expressed in Ns. Found when the coaster or ride is over. Makes the fun stop..The roller-coaster train acquires momentum on each drop and sheds it on the following climb. Were it not conserved, the train would not be able to ascend the next climb

Mechanical Equilibrium is the state of an object or system of objects for which there are no changes in motion. Makes the roller coaster stop and in turn is found at the straight portion of the track. Fnet=0

Kinetic Friction is friction between moving surfaces,is the force resisting the relative motion of solid surfaces , which can slow down the ride and in turn make it less fun. The equation is written as Ff = Mu*Fn with units written in Newtons.

Newtons 3rd law states that for every action there is an equal and opposite reaction. This can found when the marble is rubbed or pushed against by a piece of track or rail. The equation can be written as F1 = -F2.

The work due to gravity can be written is the equation Work = mgh where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object. Work due to gravity occurs at all points on the rollercoaster except when the marble is at our reference point which is the bottom of the rollercoaster in this instance. The potential work due to gravity is greater when the height is higher. Makes the rider feel that sick feeling.

Can be written as delta v=at where a is the acceleration of the object and t is the time elapsed. Velocity increases whenever an object is accelerating, units are expressed in m/s/s. This occurs on the rollercoaster whenever the marble travels downhill or whenever it goes through a curve. It speeds up the roller coaster and makes the ride more enjoyable.

The equation of the conservation of energy can be written as K(initial) + U(initial) + Work(due to nonconservative forces) = K(final) + U(final). Energy is always conserved and cannot be created or destroyed. Non-conservative forces include outside forces and friction. Conservation of Energy occurs at all points on the rollercoaster. Work due to non-conservative forces on the rollercoaster only comes in the form of friction, which is everywhere except when the marble is in free-fall. Expressed in joules

Equation follows as sigma F = 0, or dv/dt=0. Newton's First Law states that if the net force is 0 then the velocity is constant. This means that whenever an object is not accelerating or decelerating, Newton's First Law is in effect. On the rollercoaster, Newton's First Law is never really present in our coaster. It would make the riders feel like if they were moving at a constant speed... so no fun.

Can be expressed as sigma F= ma where m is the mass of the object and a is the acceleration of the object. The sum of the forces = the mass times the acceleration. This occurs at all points on the rollercoaster. When the marble is in free-fall then it has an acceleration of about 9.8 m/s/s which but is slowed a little bit by air resistance. When the marble is in contact with the track, it acts upon the track perpendicularly to the track and the normal force = the force due to gravity perpendicular to the track. The earth is always taken into account and the marble acts on the earth as well as the track. Happens towards the end of the coaster when the ball flies off. Makes the rider feel the force and acceleration due to gravity

Equation is expressed as U=(1/2)k(x^2) where k is the force of the spring and x is the compression of the spring. Hooke's law states that the force needed to extend or compress a spring by some distance is proportional to that distance.Although our roller coaster does not include a spring it compresses the paper when it lands on certain parts of the track and when it lands into the cup. Units are expressed as N/m.