Phys 21 Energy 1 - Santa Monica College



Experiment 8

Conservation of Energy

The Inclined Plane

A glider coasts down an inclined air track. The potential energy and the kinetic energy of the glider are found at four different positions, and the total mechanical energy at those positions are compared.

Theory

The energy relationship for an object moving from some initial position 1 to a final position 2 is

[pic]1 (1)

where [pic] represents the kinetic energy of the body, [pic], [pic] the gravitational potential energy, [pic], and [pic] the work done by forces other than conservative forces that act on the body as it moves from position 1 to position 2.

When only conservative forces are present, or when the net work done by the forces that are not conservative is zero, then mechanical energy is conserved and (1) can be written as

[pic]2 (2)

In other words, the total mechanical energy, [pic], is conserved.

When a glider coasts down an inclined air track, the frictional forces acting on it are negligible and we can say that mechanical energy is conserved for this motion. This means that the sum of the kinetic energy and potential energy for the glider at all positions on the air track must have the same values.

In this experiment, the kinetic energy and the potential energy of the glider at four positions on the air track are found, and the total mechanical energy at the four positions are compared. The inclination of the air track is produced by placing metal "spacers" under the single foot of the air track. The spacers are of known thickness and produce different angles of inclination, [pic]. From Figure 1, it can be seen that [pic], where [pic] is the height of the spacers and [pic] is the distance between the supports for the air track. In this case [pic] is a distance of one meter. This makes [pic] equal to the value of [pic] in meters.

[pic]

1

Figure 1. The air track inclined at the angle [pic] by spacers.

The glider is released from rest at the top of the track and accelerates down the incline. Simultaneously, a spark timer produces sparks at regular intervals of time, [pic], and the location of the sparks is recorded on a strip of thermal spark paper. These data are then used to find the kinetic energy and the potential energy at four positions on the air track.

Figure 2 shows an example of the data recorded on the thermal spark paper. The spacing indicates that the glider accelerated to the right. The four positions are also marked indicating where the kinetic energy and the potential energy are to be calculated. Position 1 represents the position from which the glider was released. Because the glider was released from rest, the kinetic energy is zero. The gravitational potential energy at 1 relative to 4 is [pic], where [pic] is the difference in heights between positions 1 and 4. This height equals [pic]. The quantity [pic]is the distance from position 1 to position 4 on the spark tape.

[pic]

2

Figure 2. The spark tape with the four positions shown at which kinetic and

potential energies are to be found.

Because the glider is moving at position 2, the glider possesses kinetic energy. The velocity then needs to be found. In order to accomplish this, the distance from a data point preceding position 2 to a point following position 2 is measured ([pic]). By dividing this distance by twice the time interval of the sparker, the average velocity is found. However, for constant acceleration, the average velocity between points equals the instantaneous velocity halfway in time between the two points In this case, the instantaneous velocity at position 2 is [pic]. The gravitational potential energy at 2 is found in same manner as at position 1. The kinetic and potential energies at positions 3 and 4 are calculated in the same manner as at position 2.

Apparatus

o air track with air supply and sparker

o glider o spark tape

o 2 m meter stick o masking tape

o metal spacers o double pan balance

Procedure

1) Use the double pan balance to measure the mass of the glider. Record its value in kilograms.

2) Use masking tape to attach a one meter length of spark tape to the center portion of the yellow-colored mounting strip on the air track.

3) Place the appropriate thickness of metal spacer under the single foot of the air track, and adjust the spark timer timing interval to the value indicated for your group. (Refer to Figure 3.) Record the spacer height and the timing interval.

| Group | Spacer | Timing | Group | Spacer | Timing |

|Number |Height |Interval |Number |Height |Interval |

| |(cm) |(sec) | |(cm) |(sec) |

| 1 | 1.00 | 1/10 | 7 | 2.50 | 1/15 |

| 2 | 1.25 | 1/10 | 8 | 2.75 | 1/15 |

| 3 | 1.50 | 1/12 | 9 | 3.00 | 1/15 |

| 4 | 1.75 | 1/12 | 10 | 3.25 | 1/15 |

| 5 | 2.00 | 1/12 | 11 | 3.50 | 1/20 |

| 6 | 2.25 | 1/12 | 12 | 3.75 | 1/20 |

Figure 3. Values of spacer heights, [pic], and timing intervals, [pic], for each group.

4) Carefully place the glider on the air track. Place your finger in front of the glider to prevent the glider from moving. Turn on the air supply.

5) Start the timer, then release the glider. Keep the spark timer engaged until the glider passes the end of the spark tape.

6) Carefully remove the spark tape. Lay the tape on a flat surface and circle the first dot, a second dot approximately 1/3 the distance down the tape, and third dot another 1/3 distance, and a fourth dot near the end of the tape. These dots represent the positions at which the kinetic and potential energies are to be calculated.

7) Be sure that the mass of the glider, the spacer height, and the timing interval are recorded. In a table similar to the one shown in Figure 4, record the distance to dot 4 from dots 1, 2, and 3. These distances are [pic], [pic], and [pic]. Also record the distances [pic], [pic], and [pic].

| data | distance, d | height, y | distance, x | velocity, v |

|point |(m) |(m) |(m) |(m/s) |

| 1 | | | 0 | 0 |

| 2 | | | | |

| 3 | | | | |

| 4 | 0 | 0 | | |

Figure 4. A suggested form for the data table.

Analysis

Complete the table in Figure 4 by calculating the heights, [pic], of points 1, 2, and 3 relative to 4. Also calculate the velocities at 2, 3, and 4.

Calculate the gravitational potential energies at the four positions from the height information, and the kinetic energies from the velocity information at the same four positions. Report these values together with the total mechanical energy at the four positions in a results table so that the values can be easily compared.

Conclusions

Describe the major sources of error in the experiment and how they affect the values of the total mechanical energy. Explain whether or not the values of total mechanical energy reflect the presence of the sources of error.

-----------------------

4

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download