1. The Pendulum Lab

2. Example 1 The Pendulum Lab5 2 4 3
System = Pendulum Bob, String, Clamp, Earth
System = Pendulum Bob, String
System =
System = Pendulum Bob
System = Pendulum Bob, String, Clamp

3. Example 1 The Pendulum Lab 15
Is the system isolated?
Yes, there are no external forces! 2 4 3
Since the system is isolated, energy is conserved.
System = Pendulum Bob, String, Clamp, Earth
Since energy is conserved all five pies must be the same size.
Pie 1 is completely filled with gravitational potential energy as it is yet to move and it is able to fall.
Pie 2 has less gravitational potential since the pendulum is lower, but more kinetic energy as the pendulum is now moving. The rest of the pie is filled with dissipated energy due to air resistance or friction at the mounting point.
The zero of Eg is a choice. It is best to put it at position 3 because then there is no Eg. Position 3 is a logical choice for the zero of Eg as the pendulum will never go any lower.
Notice that the amount of dissipated energy in pie 3 continues to grow. Also, the amount of kinetic energy is larger as the pendulum is moving faster than before.
There is less kinetic energy in pie 4 as the pendulum is moving slower than in position 3. There is more Eg as the pendulum is above zero and Ediss continues to grow.
There is once again no Ek in pie 5 because at this point the pendulum bob is instantaneously at rest. Eg is greater as the pendulum is higher and Ediss continues to grow. 1 2 3 4 5

4. Example 1 The Pendulum Lab 15
How can we tell from the diagram that energy is dissipated? 2
Position 5 is lower than position 1! 4 3
System = Pendulum Bob, String, Clamp, Earth
Since energy is conserved all five pies must be the same size.
Pie 1 is completely filled with gravitational potential energy as it is yet to move and it is able to fall.
Pie 2 has less gravitational potential since the pendulum is lower, but more kinetic energy as the pendulum is now moving. The rest of the pie is filled with dissipated energy due to air resistance or friction at the mounting point.
The zero of Eg is a choice. It is best to put it at position 3 because then there is no Eg. Position 3 is a logical choice for the zero of Eg as the pendulum will never go any lower.
Notice that the amount of dissipated energy in pie 3 continues to grow. Also, the amount of kinetic energy is larger as the pendulum is moving faster than before.
There is less kinetic energy in pie 4 as the pendulum is moving slower than in position 3. There is more Eg as the pendulum is above zero and Ediss continues to grow.
There is once again no Ek in pie 5 because at this point the pendulum bob is instantaneously at rest. Eg is greater as the pendulum is higher and Ediss continues to grow. 1 2 3 4 5

5. The Toy Car Lab

6. Yes, there are no external forces!
Example 2 Toy Car Lab 1 2 3
Is the system isolated?
Yes, there are no external forces!
System = Toy Car, Earth
System =
System = Toy Car
Since the system is isolated, energy is conserved. 1 2 3
Since energy is conserved, all three pies must be the same size.
Students will think that pie 1 is all Ek. Since the car moves at a constant velocity, each pie must have the same amount of Ek, so where does the obvious Ediss fit? There is also energy stored in the battery and as it is part of the system it must be included in pie 1.
Pie 2 then has the same amount of Ek, but some of the battery energy is stored as Ediss.
Pie 3 then has the same amount of Ek, but even more of the battery energy is stored as Ediss.
Eventually, all of the battery energy will be stored as Ediss, at which point Ek will decrease meaning that the car will slow down. Eventually, the entire pie will be Ediss and the car will stop.

7. The Ball Rolling Down an Incline Lab

8. Example 3 Ball Rolling Down an Incline
System = Ball, Earth
System = Ball, Earth, Incline
System =
System = Ball 1
Friction = ?
Friction = yes 2 3
Is the system isolated? 4
Yes, there are no external forces!
Since energy is conserved, all three pies must be the same size.
Pie 1 is completely filled with Eg as the ball is not yet moving, but it is able to move lower.
Pie 2 has less Eg as the ball is lower, but some Ek as the ball is moving. Since the ball is about one quarter of the way down, there is only about three fourths as much Eg as before. It also has some Ediss due to the decision to include friction. If this was an ideal situation no energy would be dissipated.
In position 3 the ball is half of the way down so the Eg is only half of the pie. Ek increases as the ball is accelerating and Ediss also increases.
Pie 4 has no more Eg as the ball is on the ground, the obvious place to select as the zero of Eg. The Ek is a maximum and so is the Ediss.

9. Example 3 Ball Rolling Down an Incline
System = Ball
System = Ball, Earth
System =
System = Ball, Earth, Incline 1
Friction = ?
Friction = yes 2 3
Since the system is isolated, energy is conserved. 4
Since energy is conserved, all three pies must be the same size.
Pie 1 is completely filled with Eg as the ball is not yet moving, but it is able to move lower.
Pie 2 has less Eg as the ball is lower, but some Ek as the ball is moving. Since the ball is about one quarter of the way down, there is only about three fourths as much Eg as before. It also has some Ediss due to the decision to include friction. If this was an ideal situation no energy would be dissipated.
In position 3 the ball is half of the way down so the Eg is only half of the pie. Ek increases as the ball is accelerating and Ediss also increases.
Pie 4 has no more Eg as the ball is on the ground, the obvious place to select as the zero of Eg. The Ek is a maximum and so is the Ediss. 1 2 3 4