Potential energy - work that is independent of the path - or only depends on position.
G = 6.67*10^-11 Nm^2/kg^2
V = Fdh = mgh
h →r
g = GM/R^2
W = mg = m (GM/R^2)
Recall from 13.2
Then, the potential energy of a spring is...
0.5*m*Vo^2 + (mg)L = 0.5*m*vf^2
vo = 0
vf^2 = 2*g*L
V = Fdh = mgh
h →r
g = GM/R^2
W = mg = m (GM/R^2)
See D2L for HW and examples:
Problems 13.55-13.117
Examples: 13.61, 13.70, 13.86HW: 13.64, 13.71, 13.89
Simulation: Energy Skate Park:
Open up:
http://phet.colorado.edu/en/simulation/energy-skate-park
Have a look around.
1. Watch the energy graphs, make sure you understand what the kinetic and potential energies are doing. Sketch out the energy graphs, and label what is happening on it.
2. Go to tracks (upper left hand corner), and choose "double well roller coaster".
Turn off your graphs, and predict what your energy graphs will look like. This sort of thing would make a great exam question - so no cheating! Sketch out what you think the energy should be before turning your graphs on, then check your answer.
3. Another prediction problem. Switch to the loop graph, and predict, then check, what the energy graphs look like.
4. Influence of mass:
How does increasing the mass of your skater change the energy profiles?
If the mass of the skater is doubled, what does this do to the:
maximum velocity -
Kinetic energy -
Potential energy -
Does the answer to the above change depending on what track you are using?
5. Influence of gravity
If the gravity of the planet is cut in half, what does this do to the:
maximum velocity -
Kinetic energy -
Potential energy -
Does the answer to the above change depending on what track you are using?
6. Solve for velocity as a function of position using energy conservation principles.
The equation for a parabola is:
Create a graph in excel,
Solve for values of a, h, and k to create a parabola that spans 0→14 meters, and is 8 m tall:
Write down your equation for y =
Drag your track in the simulation to positions that match your equation.
Graph the kinetic and potential energies of the skater in excel, then check your graphs with the simulation. Turn in your excel sheets - use equations in excel!
Graph the skater's velocity as a function of position. Think about where velocity is a maximum, and where it is a minimum.
Use the velocity to graph the skater's potential and kinetic energy as a function of time:
hint: Just add another column "time" and think about how you can get time from the other columns that you have!
Hint: To get a couple of cycles, vary the position from 0→14→0.
Email/ submit in D2L the excel spreadsheets so I can see the equations you entered!
7. Influence of Friction
Switch back to the friction parabola track,
Set the friction a quarter of the way to "Lots", and drag your track to positions that match your equation.
Run the simulation, and notice what happens to the kinetic and potential energy when friction is added.
c.) How would you calculate the friction coefficient from the position and energy graphs?
Open up:
http://phet.colorado.edu/en/simulation/energy-skate-park
Have a look around.
- Use the right hand menu to show the grid, and create graphs for energy vs. position and energy vs. time.
- The tracks can be expanded by grabbing them out of the yellow tracks in the upper left hand corner
- Drag and reposition the tracks using the purple dots
- slow down or speed up simulations speed at the bottom by the play button.
- Choose different skaters, change gravity, etc.
- Track friction → change friction
- Edit Skater → change mass
- Careful! If you hit reset, you will lose your track setup etc. You can start a new graph by hitting "clear" etc. instead of resetting the entire simulation.
1. Watch the energy graphs, make sure you understand what the kinetic and potential energies are doing. Sketch out the energy graphs, and label what is happening on it.
2. Go to tracks (upper left hand corner), and choose "double well roller coaster".
3. Another prediction problem. Switch to the loop graph, and predict, then check, what the energy graphs look like.
4. Influence of mass:
How does increasing the mass of your skater change the energy profiles?
If the mass of the skater is doubled, what does this do to the:
maximum velocity -
Kinetic energy -
Potential energy -
Does the answer to the above change depending on what track you are using?
5. Influence of gravity
If the gravity of the planet is cut in half, what does this do to the:
maximum velocity -
Kinetic energy -
Potential energy -
Does the answer to the above change depending on what track you are using?
6. Solve for velocity as a function of position using energy conservation principles.
The equation for a parabola is:
Create a graph in excel,
Solve for values of a, h, and k to create a parabola that spans 0→14 meters, and is 8 m tall:
Write down your equation for y =
Drag your track in the simulation to positions that match your equation.
Graph the kinetic and potential energies of the skater in excel, then check your graphs with the simulation. Turn in your excel sheets - use equations in excel!
Graph the skater's velocity as a function of position. Think about where velocity is a maximum, and where it is a minimum.
Use the velocity to graph the skater's potential and kinetic energy as a function of time:
hint: Just add another column "time" and think about how you can get time from the other columns that you have!
Hint: To get a couple of cycles, vary the position from 0→14→0.
Email/ submit in D2L the excel spreadsheets so I can see the equations you entered!
7. Influence of Friction
Switch back to the friction parabola track,
Set the friction a quarter of the way to "Lots", and drag your track to positions that match your equation.
Run the simulation, and notice what happens to the kinetic and potential energy when friction is added.
Use the playback feature to collect information.
b.) What happens to energy conservation when friction is added to the system?
c.) How would you calculate the friction coefficient from the position and energy graphs?
