Go to http://www.glenbrook.k12.il.us/gbssci/Phys/mmedia/energy/ce.html

Read the information on roller coasters, filling in the appropriate blanks:

A roller coaster ride is a thrilling experience that involves a wealth of physics. Part of the physics of roller coaster is the physics of ________and __________. The ride often begins as a chain and motor (or other mechanical device) exerts a ___________ on the train of cars to lift the train to the top of a very tall hill. Once the cars are lifted to the top of the hill, _____________takes over and the remainder of the ride is an experience of the physics of ____________ transformation.

At the top of the hill, the cars possess a large quantity of ____________energy. Potential energy – the energy of __________ _____________ - is dependent upon the _________ of the object and the _____________ of the object. The car's large quantity of potential energy is due to the fact that they are elevated to a ___________ height above the ground. As the cars descend the first drop they lose much of this ___________ energy in accord with their loss of height. The cars subsequently gain _____________energy.

Kinetic energy - the energy of ____________ - is dependent upon the __________of the object and the __________of the object. The train of coaster cars speeds up as they lose height. Thus, their original potential energy (due to their large ___________) is transformed into kinetic energy (revealed by their high __________). As the ride continues, the train of cars is continuously losing and gaining height. Each gain in ___________ corresponds to the loss of speed as ___________ energy (due to speed) is

transformed into _____________ energy (due to height). Each loss in height corresponds to a gain of speed as potential energy (due to height) is transformed into kinetic energy (due to speed). This transformation of ______________ _________from the form of potential to the form of kinetic and vice versa is illustrated in the animation.

Watch the animation of the roller coaster and notice what happens to KE and PE to answer the following:

• When the coaster is at the top of the incline the KE is _____ and the _____is at a

  maximum.

• When the coaster is at the bottom of a loop the _____ is at a maximum and the PE is

  _______.

• The total mechanical energy (TME) for both columns _________the same throughout

  the ride.

  The work-energy theorem states that the work done by _____________ __________ is capable of changing the total amount of ____________energy from an initial value to some final value. The amount of work done by the external forces upon the object is equal to the amount of __________in the total mechanical energy of the object. The theorem is often stated in the form of the following mathematical equation.

  KE_initial + PE_initial + W_external = KE_final + PE_final

  The left side of the equation includes the total mechanical energy (KE_initial + PE_initial) for the __________ state of the object plus the work done on the object by external forces (W_external) while the right side of the equation includes the total _____________ energy (KE_final + PE_final) for the ___________ state of the object.

  Once a roller coaster has reached its initial summit and begins its descent through loops, turns and smaller hills, the only forces acting upon the coaster cars are the force of ____________, the _________ force and dissipative forces such as ______ __________. The force of gravity is an ____________force and thus any work done by it does not change the total mechanical energy of the train of cars. The normal force of the track pushing up on the cars is an ____________force; however it is at all times directed ________________ to the motion of the cars and thus is unable of doing any work

  upon the train of cars. Finally, the air resistance force is capable of doing ________ upon the cars and thus draining a small amount of energy from the total mechanical energy that the cars possess. However, due to the complexity of this force and its small contribution to the large quantity of energy possessed by the cars, it is often __________. By neglecting the influence of air resistance, it can be said that the total mechanical energy of the train of cars is ________________during the ride. That is to say, the total amount of mechanical energy (kinetic plus potential) possessed by the cars is the _________throughout the ride. _____________ is neither gained nor lost, only ___________________ from kinetic energy to potential energy and vice versa.

  The conservation of mechanical energy by the coaster car in the above animation can be studied using a calculator. At each point in the ride, the kinetic and potential energies can be calculated using the following equations.

  KE = 0.5 * mass * (speed)² = ½ mv² PE = mass * g * height = mgh

  If the acceleration of gravity value of 9.8 m/s² is used along with an estimated mass of the coaster car (say 500 kg), the kinetic energy and potential energy and total mechanical energy can be determined. What value do you find for the total mechanical energy of the car at any point along the track?

  The work-energy bar charts for the coaster car illustrate that the car's energy is transformed from _____________ to _____________ and vice versa; yet the total amount of mechanical energy remains the __________during the course of the motion.

  Now scroll down and click on Work-Energy Bar Charts. You should be at the Physics Classroom, Lesson 2: The Work-Energy Theorem. Scroll down to the animation and click on the animation button. Read the information and complete the following:

  Stopping Distance of a Hot Wheels Car

  A GIF Animation

  Consider the motion of a Hot Wheels car beginning from rest at an elevated position. The Hot Wheels car rolls down a hill and begins its motion across a level surface. Along the level surface, the Hot Wheels car collides with a box and skids to a stop over a given distance. How could work and energy be utilized to analyze the motion of the Hot Wheels car? Would the total mechanical energy of the Hot Wheels car be altered in the process of rolling down the incline or in the process of skidding to a stop? Or would the total mechanical energy of the Hot Wheels car merely be conserved during the entire motion?

  Of course the answers to these questions begin by determining whether or not _________ forces are doing work upon the car. According to the work-energy theorem, if external __________ do work upon the car, the total ____________ ___________of the car is ______conserved; the initial amount of mechanical energy is _______ the same as the final amount of mechanical energy. On the other hand, if external forces _____ ______ _____ work upon the car, then the total mechanical energy is _____________; that is, mechanical energy is merely _______________ from the form of potential energy to the form of kinetic energy while the total amount of the two forms remains unchanged.

  While the Hot Wheels car moves along the incline, external forces do not do work upon it. This assumes that ___________ forces such as air resistance have a negligible effect on the car's motion (a reasonable assumption for the low speeds of the car and its streamline characteristics). Since ____________ forces do not do work on the car, the total mechanical energy of the car is ______________while moving along the incline. As the work-energy bar charts in the animation below depict, _________ is transformed from potential energy (the stored energy of position) to kinetic energy (the energy of motion). The car gains __________as it loses height. The bar chart also depicts the fact that the total amount of mechanical energy is always the _________; when the two forms are added together, the sum is unchanging.

  When the Hot Wheels car collides with the box and skids to a stop, external forces do a significant amount of __________upon the car. The force of friction acts in the direction ____________ the car's motion and thus does negative work upon the car. This negative works contributes to a _________in mechanical energy of the car. In fact, if 0.40 Joules of mechanical energy are lost, then -0.40 Joules of work are done upon the car. As this work is done, the mechanical energy of the car (in the form of kinetic energy) is transformed into ________________ forms of energy such as _____________and heat.

  Analyze the animation and use the principles of work and energy to answer the following questions.

  Questions to Ponder: (Show formulas and work on a separate page then check with chart.)

  1.Use energy conservation principles to determine the speed of a 0.050-kg Hot Wheels car that descends from a height of 0.60-meters to a height of 0.00 meters. Assume negligible air resistance.

  2.Use energy conservation principles to determine the speed of a 0.050-kg Hot Wheels car that descends halfway down a 0.60-meter high hill (i.e., to a height of 0.30 meters). Assume negligible air resistance.

  3.If the mass of the Hot Wheels car were twice as great (0.100 kg), then what would be the speed at the bottom of the 0.60-meter high hill?

  Now go to http://www.learner.org/exhibits/parkphysics/coaster.html

  Make your own roller coaster and read up on the history!