Mechanical Energy Tutorial & Question

Lets start talking about energy. First of all what is energy? Energy is simply a quantity. Energy can be found in many forms for example, sound energy, kinetic energy, chemical energy, and potential energy. In this post I will be going to set ground rules for energy in general and will go into the specifics of mechanical energy, or the sum of the kinetic and potential energy.

You all probably know what kinetic energy (KE) is already. If you don't know kinetic energy is the energy of motion. All objects that are moving have kinetic energy. Potential energy (PE) comes in two forms. One is gravitational potential energy and one is elastic potential energy. Gravitational potential energy is found only when objects are above ground. The energy comes from the constant pull of gravity on an object, and the objects resistance to fall with it. Examples of gravitational potential energy (GPE) are when a roller coaster goes up a hill and when someone climbs a mountain. Gravitation potential energy often has to do with climbing up structures (this is important to remember during tests). Elastic potential energy (EPE) often correlates with things that are stretched out like springs and rubber bands.

In order to understand mechanical energy (ME), one must know the law of conservation of energy, which states in this situation, the sum of the total potential energy and the total kinetic energy of a system is always going to be constant.

Formulas to memorize
ME (always constant in a system)= KE + PE
GPE = mass * height * acceleration due to gravity (on Earth is equal to 9.81 m/s/s)
EPE = (1/2) * k(spring constant) * distance (the spring stretched)
KE = (1/2) * (mass) * (velocity of the object)^2
((1/2)(mass)(velocity1)^2) + (mass*height1*acceleration due to gravity)=((1/2)(mass)(velocity2)^2) + (mass*height2*acceleration due to gravity)

Study these equations very closely before continuing especially the last one, which is the hardest to remember. To familiarize with the technique I will be using go down to the first post.

Sample Cutnell and Johnson 1-Star(aka the second hardest questions in the book) question on Energy
The only reason I am doing a 1 Star question was because the 2 Star questions needed a diagram. However this 1 Star question is fantastic in teaching this concept.

1) Two pole-vaulters just clear the bar at the same height. The first lands at a speed of 8.90 m/s, while the second lands at a speed of 9 m/s. The first vaulter clears the bar at  a speed of 1 m/s. Ignore air resistance and friction and determine the speed at which the second vaulter clears the bar.

What we Know
Velocity1=8.90 m/s
Velocity2=9m/s
Top of the Jump Velocity1 = 1m/s

What we Need to Know
Top of the Jump Velocity2?

Formulas Needed to Solve
All of the Formulas needed to solve the problem can be found under "Formulas to memorize" above.

Steps to Solve this 1-Star Cutnell and Johnson Question
First you need to find the height of the bar in order to find the velocity of the second jumper.
The formula can be created from rearranging the final equation in the list.

((8.9 m/s/s)-(1 m/s/s))/(2*9.8 m/s/s) = 3.99 meters high
Knowing the height of the bar, the velocity of the person at the top can be solved.

sqrt (9 m/s/s - (2*9.8 m/s/s)*3.99m) = 1.7 m/s

Wow that was quite a difficult question. Please take sometime to rearrange the formulas and try to solve the question yourself. Be simply doing this question again, it would be much easier on a test to solve the same kind of question. Get ready to learn about something new next week! Good luck and subscribe for more posts! Get ready for a tutorial on heat by Saturday.