Unit 7 - Energy

Unit 7 – Energy:

Intro Brainstorming - “What do you know about Energy”

Learning objectives:

Allows student opportunity to think about what they already know and connect to previous classes.

Kinetic/ Gravitational Intro Discussion:

Kinetic: tossing a ball horizontally – “what will hurt more, if I throw faster or slower?”  & “ What will hurt more a racquet ball or bowling ball”

Gravitational:  Dropping ball - “what will hurt more, if I drop higher or lower?”  & “ What will hurt more a racquet ball or bowling ball”

Elastic:  “what will hurt more, small displacement vs large displacement?”  & “What will hurt more …. (different types of springs) ”

Learning Objective:

Allow students to discover that kinetic energy depends on mass and speed

Allow students to discover that gravitational energy depends on mass and change in height.

Allow students to discover that elastic energy depends on “resistance to stretch” and displacement

Lab -  “What is relationship between force and how far it stretches”  :

Students with various springs measure force versus how far it stretches.    Graph force on y axis and displacement on x axis.

Graph is a linear graph with different slopes.  Students discuss the slopes and what it means.  The conclusion is that the slope is the spring constant (resistance to stretch).  The equation is  F=kx. 

Fyi: Brian cut these springs all from same spring (same gage wire, etc).  Laura mentioned that sometimes the springs have a y-intercept.    Make sure you are ready to discuss this or pick springs carefully.

Learning Objective:

Develop hooke’s law equation( F=kx).

Develop understanding for spring constant (k)

Elastic Energy Demo- Take two different springs with different spring constants (based on above) .  In our case, one had a spring constant of 25 N/m and the other one had a spring constant of 12 N/m.

Put two cart on a track.  A different sprint is attached to each and the car is pulled back and released.

 “Will they travel at same speed? “

1)      Same force –  Applied 3N to both car (note : 12N/m stretched further

a.       No,  car with 12N/m spring was faster.

2)      Same distance -  Stretched both spring 30cm.

a.       No, car with  25 N/m spring was faster.

3)      “What else can we look at?”  “ What else have we analyzed on graphs?”   - Area under curve. 

Look at area under each curve and make sure they are equal.  We randomly picked 13cm for 25N/m spring.  Solved for area under curve and then set that equal for 12N/m spring and solved for delta x.   

A= ½ bh = ½ x (F) = ½ x (kx) = ½ kx²  (Note Energy equation:   E = 1/2kx²).  In order to get equal areas the 12 N/m spring was stretched 1.8

a.        Same speed !  13cm for 25N/m spring and 18cm for 12N/m Spring.

Post Demo Discussion:

In order to get same speed, they must have same energy.  Area under the curve was Energy!  Elastic Energy equation was developed. A=E= ½ bh = ½ x (F) = ½ x (kx) = ½ kx² 

Area was looked at graphically.  If we double delta x, we will not have 4 equal triangles, so Energy is quadrupled.  If we triple delta x, 9 equal triangles under curve, so Energy is 9x greater.

Learning Objective:

Develop elastic energy equation

Understand that area under F vs. delta x curve for a spring is Elastic Energy

Begin understand for what happens to energy as you change delta x.

Kinetic and Gravitational Energy Labs:

Prior to labs, repeat intro lab to determine spring constant.

Kinetic energy lab:  Use spring to pull back car and release.   Using spring constant and amount spring pulled back, calculate initial elastic energy.  Then, record time to travel a set distance and calculate velocity.  Repeat by pulling spring back further.  We plotted energy on y and velocity on x.   The best fit curve was a quadratic.  All group determined that E = ____ v².    Through questioning and unit analysis, students developed kinetic energy equation E = 1/2 m v².  It was also helpful that the results from our initial discussion were still on board that kinetic energy depends on mass and speed.

Gravitational energy lab: Use spring to pull back car and release.   Using spring constant and amount spring pulled back, calculate initial elastic energy.  Then distance (height) the car travels up the ramp.  Repeat by pulling spring back further.  We plotted energy on y and height on x.   The best fit curve was linear.  All group determined that E = ____ delta y.  Through questioning and unit analysis, students  discovered that the slope had to be a force in Newtons.  Using prior discussion that mass may be a factor, the class concluded the slope represents the weight.   The equation E=mgy  was developed.  

Learning Objectives:

Develop kinetic energy equation

Develop gravitation energy equation

What is Energy Discussion & replacement worksheet Unit 7 3A was completed:

Laura used an analogy between building blocks and energy.   Laura gave away energy, she took energy from someone else, and she put energy (stored) it in her pocket.   There was discussion on perspective (system).    Energy may be gained/  lost from one object’s perspective, but the overall energy is constant.   L O L Energy diagrams were introduced.  Worksheet was completed , followed by a whiteboard discussion.

Learning Objectives:

Help students have a better of energy and conservation of energy

Introduce energy diagrams.

Introduce Work  - Energy Equation

Previously, I have always taught work prior to energy.  After being in the workshop, it makes a lot more sense to introduce it at the end of the unit.  I will definitely make this change next year.

Bryan did a demo with a book asking about if the energy changed.   Students also drew FBD diagrams.  This led nicely into the understanding that force must be in direction of motion for work to be done.  If the force applied does not cause an energy change, then no work was done.

We plotted force vs. delta y for a book that was lifted.  The area under curve was a rectangle.  The equation:   Energy change = F delta y   or Energy change = F delta x    (depending on horizontal or vertical motion)

Complete: Unit 7 Worksheet 3b and Worksheet 4.

Learning Objectives:

Develop work energy equation.

Understand that force must be parallel to motion for work to be done.

Use work energy equation (along with LOL) diagrams to solve problem.

Unit 7 Practicum – Kiss the Egg.

Student groups were each given a spring and and egg  in a cup.  They had to determine the correct amount of mass to apply to the spring to “kiss the egg” without breaking it.