Energy is the ability of a system or object to perform work. It exists in various forms. Potential energy is the energy an object has inside a force field due to its position. In the roller coaster’s case, the potential energy comes from its height because the Earth’s force of gravity is acting on it. Roller coasters are able to move their passengers very rapidly up and down the hills because the cars gain a large amount of potential energy from the very first hill. The potential energy of an object is: PE=mghPE=mgh where m is the mass, g is 9.8 m/s2, and h is the height measured from reference. Kinetic energy is mechanical energy that is due to motion of an object. The kinetic energy of an object is KE=12mv2KE=12mv2 where m is the mass of the object, v is the velocity of the object. “Conservation of Energy” is a fundamental principle that energy cannot be created or destroyed. Rather, it is transferred between different forms, such as those described above. In other word, the total energy (sum of potential energy and kinetic energy) of an object at given time will be a constant if there is no frictional force considered). Total Energy=KE+PE we are going to employ an apparatus whose shape is similar to a Roller Coaster. We will use one round ball to run from the top of the roller coaster. We will calculate the potential energy, the kinetic energy, and the total energy of the ball at predetermined equal distance along the roller coaster track. The mass of the ball will be measured. To do that, we need know the height of the ball to calculate the potential energy. We need know the instantaneous velocity to calculate the kinetic energy, You can then simply add PE and KE to get the total energy of the ball at each location. The height of the ball at each location is given. The next thing is that we need know the velocity of the ball at each location. we have one method to calculate the instantaneous velocity of an object. We just need to record the time for the whole diameter of the ball to go through the photogate for this setup. Then the instantaneous speed will be the diameter of the ball divided by the time recorded. Once you are clear, all the necessary data will be provided to you and you need calculate the KE, PE, and TE. Mass of the ball (m) is 1 kg. g=9.8 m/s2. Diameter of the ball (d) is 5 cm= 0.05 meter. Position of the ball on the Roller Coaster Height (h) of the ball at the position, meter Time (t) for the ball go through the photogate, second Velocity (v) of the ball, m/s v=dtv=dt PE=m*g*h KE=12mv212mv2 TE=PE+KE 10 0.35 0.086 20 0.3 0.044 30 0.25 0.033 40 0.2 0.028 50 0.15 0.024 60 0.23 0.031 70 0.3 0.043 80 0.22 0.030 90 0.15 0.024 100 0.07 0.021 Note 1. The t you need in column 4 is the time provided in column 3. Note 2. The h you need in column 5 is the height provided in column 2. m=1 kg and g=9.8m/s2. Note 3. The v you need in column 6 is the v you calculated in column 4. Note 4. Column 7 is the sum of column 6 and column 5. Question: 1. Where you find the ball move the fastest? 2. Where you find the ball move the slowest? 3. Where did the ball have the highest kinetic energy? 4. Where did the ball have the smallest kinetic energy? 5. Is the total energy conserved at each position for the ball?
Energy is the ability of a system or object to perform work. It exists in various forms.
Potential energy is the energy an object has inside a force field due to its position. In the
roller coaster’s case, the potential energy comes from its height because the Earth’s force
of gravity is acting on it. Roller coasters are able to move their passengers very rapidly up
and down the hills because the cars gain a large amount of potential energy from the very
first hill. The potential energy of an object is: PE=mghPE=mgh
where m is the mass, g is 9.8 m/s2, and h is the height measured from reference.
Kinetic energy is mechanical energy that is due to motion of an object. The kinetic energy of an object is KE=12mv2KE=12mv2
where m is the mass of the object, v is the velocity of the object.
“Conservation of Energy” is a fundamental principle that energy cannot be created or
destroyed. Rather, it is transferred between different forms, such as those described
above. In other word, the total energy (sum of potential energy and kinetic energy) of an object at given time will be a constant if there is no frictional force considered).
Total Energy=KE+PE
we are going to employ an apparatus whose shape is similar to a Roller Coaster. We will use one round ball to run from the top of the roller coaster. We will calculate the potential energy, the kinetic energy, and the total energy of the ball at predetermined equal distance along the roller coaster track. The mass of the ball will be measured. To do that, we need know the height of the ball to calculate the potential energy. We need know the instantaneous velocity to calculate the kinetic energy, You can then simply add PE and KE to get the total energy of the ball at each location.
The height of the ball at each location is given. The next thing is that we need know the velocity of the ball at each location. we have one method to calculate the instantaneous velocity of an object. We just need to record the time for the whole diameter of the ball to go through the photogate for this setup. Then the instantaneous speed will be the diameter of the ball divided by the time recorded.
Once you are clear, all the necessary data will be provided to you and you need calculate the KE, PE, and TE. Mass of the ball (m) is 1 kg. g=9.8 m/s2. Diameter of the ball (d) is 5 cm= 0.05 meter.
| Position of the ball on the Roller Coaster | Height (h) of the ball at the position, meter | Time (t) for the ball go through the photogate, second |
Velocity (v) of the ball, m/s v=dtv=dt |
PE=m*g*h | KE=12mv212mv2 | TE=PE+KE |
| 10 | 0.35 | 0.086 | ||||
| 20 | 0.3 | 0.044 | ||||
| 30 | 0.25 | 0.033 | ||||
| 40 | 0.2 | 0.028 | ||||
| 50 | 0.15 | 0.024 | ||||
| 60 | 0.23 | 0.031 | ||||
| 70 | 0.3 | 0.043 | ||||
| 80 | 0.22 | 0.030 | ||||
| 90 | 0.15 | 0.024 | ||||
| 100 | 0.07 | 0.021 |
Note 1. The t you need in column 4 is the time provided in column 3.
Note 2. The h you need in column 5 is the height provided in column 2. m=1 kg and g=9.8m/s2.
Note 3. The v you need in column 6 is the v you calculated in column 4.
Note 4. Column 7 is the sum of column 6 and column 5.
Question:
1. Where you find the ball move the fastest?
2. Where you find the ball move the slowest?
3. Where did the ball have the highest kinetic energy?
4. Where did the ball have the smallest kinetic energy?
5. Is the total energy conserved at each position for the ball?
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