Physics Unit | Grades 7-9 | Student Study Guide 5: Energy Use of significant figures and scientific notation is left to the discretion of the instructor.

Concepts

Gravitational Potential Energy Conservation of Energy Kinetic Energy Potential Energy

Energy (Kinetic & Potential) Description

Potential energy (PE) is a stored form of energy that can produce motion (the potential for motion). The Earth’s gravitational attraction can be used as a source of PE. When the roller coaster car is at the top of the highest hill, it has the greatest amount of gravitational PE for the ride. PE(grav) = mgy, where mg represents the weight of the car and its riders, and y represents the height in meters. The downward displacement of an object results in a decrease in PE.

Kinetic energy (KE) is a form of energy related to an object’s motion. KE = (1/2) mv2, where m is the mass (in kg) of the car and its occupants and v is the velocity (m/s) of the car. If the mass of two objects are equal, then the object having the higher speed or velocity will have more KE than the other. The roller coaster car’s kinetic and potential energies change as the car moves along the track. The sum of the two is called the total mechanical energy of the car. If gravity is the only force acting on the car, then the total mechanical energy is constant. This is referred to as the law of conservation of mechanical energy. In most real-life situations, however, friction and air resistance are present also. As the roller coaster falls, only part of its potential energy is converted to KE. Due to air resistance and friction, the part of the PE that is not converted to KE is converted to heat energy and possibly sound energy too. In these cases, the law of conservation of mechanical energy is not true because the sum of the PE and KE is not constant throughout the ride. Sometimes there are situations where the friction and air resistance are almost nothing, like when the moving object is very dense and rolling on a smooth surface. For purposes of simplicity in this guide, air resistance will be ignored, and it will be assumed that the law of conservation of mechanical energy is true for the amusement park rides.

Kinetic Energy Examples

Kinetic Energy KE = ½ mv2 The energy of an object due to its motion. The unit for kinetic energy is joule J. KE depends on an object speed and mass.

Question 1a. Which has more KE a bowling ball or a volleyball if velocity is same? b. Why?

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Permission is granted to reprint or photocopy this lesson in its entirety for educational purposes, provided the user credits the authors, Herschend Family Entertainment Corporation and Silver Dollar City, www.silverdollarcity.com. Grade level expectations were taken from the Missouri Department of Elementary and Secondary Education.

Physics Unit | Grades 7-9 | Student Study Guide 5: Energy Use of significant figures and scientific notation is left to the discretion of the instructor.

Question 1b. Find the KE of a 40 kg student running to get in line for Thunderation at 7.0 m/s.

2. Find the velocity of rollercoaster with a mass of 12,000 kg and KE of 3,750,000 J.

3. How much work is required to accelerate an 8000 kg car from 15 m/s to 30 m/s?

Potential Energy Examples

Potential energy PE (stored energy) Energy associated with an object due to the its position (h). Examples include gravitational (mgh) and elastic potential energy (1/2kx2).

Gravitational Potential Energy PEg = mgh the potential energy associated with an object due to position (h) relative to the Earth or some other gravitational source.

Example: Walking to Thunderation a 45 kg student climbs stairs consisting of 10 steps, each step is .20 m high. Calculate the student’s gravitational potential energy on the 10th step.

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Permission is granted to reprint or photocopy this lesson in its entirety for educational purposes, provided the user credits the authors, Herschend Family Entertainment Corporation and Silver Dollar City, www.silverdollarcity.com. Grade level expectations were taken from the Missouri Department of Elementary and Secondary Education.

Physics Unit | Grades 7-9 | Student Study Guide 5: Energy Use of significant figures and scientific notation is left to the discretion of the instructor.

Potential and Kinetic Energy Classroom Example

Using the information provided, label where potential and kinetic energy occur as well as the amount of energy (i.e. High, Low, No, Increasing, Decreasing) for each of Silver Dollar City’s roller coasters. Then ride them yourself to feel energy in action!

1. PowderKeg

A C

B

A)

B)

C)

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Permission is granted to reprint or photocopy this lesson in its entirety for educational purposes, provided the user credits the authors, Herschend Family Entertainment Corporation and Silver Dollar City, www.silverdollarcity.com. Grade level expectations were taken from the Missouri Department of Elementary and Secondary Education.

2. WildFire

A

B

C

A) B) C)

A) A

E B)

C)

D D)

B E)

C

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