You will measure the acceleration of gravity by dropping a picket fence through a photogate. The leading edges of the black stripes are 0.050m apart. As the fence accelerates, the gate will record shorter time periods between stripes. Fromh this information, it will compute the velocity of the picket fence. For your calculations you will get a table with the measured time and velocity data, as well as the graph velocity vs time. The procedure consists in the following steps a) Prepare software and hold the picket fence above the photogate as shown in Figure 1. (Be sure that the picket fence has a soft, foam pad to land on.) f Figure 1. Picket fence and photogate nllln b) Click “record” on the display, then release the picket fence. c) After the picket fence lands, click “stop”. Picket fence must not hit the gate d) Use the velocity vs time in Table 1 to calculate the acceleration of the picket fence due to gravity using the following equation where a(t0) is the acceleration evaluated at time = to ∆t is the increment of time. For example from 1 to 2. ∆t=(10.016-9.976)s v(t0+∆t) is the velocity evaluated at time = to+∆t v(t0) is the velocity evaluated at time = to To get an approximation of the acceleration use Table 1. Recorded time and speed data. Time [s] Speed [m/s] 1 0.000 1.45 2 0.032 1.75 3 0.058 2.00 4 0.082 2.23 5 0.103 2.44 6 0.123 2.62 Results Determine the acceleration due to gravity using consecutive data and then use the first and final data. Table 2. Determined values of the acceleration of the picket fence due to gravity. data ∆t [s] Acceleration [m/s2] 1-2 2-3 3-4 4-5 5-6 1-6 Conclusions Do you know what is the expected answer? (If results is very different something in your procedure is wrong) How does your result compares with the expected answer? What is the difference between the expected result and your result in %?
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
You will measure the acceleration of gravity by dropping a picket fence through a photogate. The leading edges of the black stripes are 0.050m apart. As the fence accelerates, the gate will record shorter time periods between stripes. Fromh this information, it will compute the velocity of the picket fence.
For your calculations you will get a table with the measured time and velocity data, as well as the graph velocity vs time.
The procedure consists in the following steps
- a) Prepare software and hold the picket fence above the photogate as shown in Figure 1. (Be sure that the picket fence has a soft, foam pad to land on.) f
Figure 1. Picket fence and photogate
nllln
- b) Click “record” on the display, then release the picket fence.
- c) After the picket fence lands, click “stop”. Picket fence must not hit the gate
- d) Use the velocity vs time in Table 1 to calculate the acceleration of the picket fence due to gravity using the following equation
where
a(t0) is the acceleration evaluated at time = to
∆t is the increment of time. For example from 1 to 2. ∆t=(10.016-9.976)s
v(t0+∆t) is the velocity evaluated at time = to+∆t
v(t0) is the velocity evaluated at time = to
To get an approximation of the acceleration use
Table 1. Recorded time and speed data.
|
|
Time [s] |
Speed [m/s] |
|
1 |
0.000 |
1.45 |
|
2 |
0.032 |
1.75 |
|
3 |
0.058 |
2.00 |
|
4 |
0.082 |
2.23 |
|
5 |
0.103 |
2.44 |
|
6 |
0.123 |
2.62 |
Results
Determine the acceleration due to gravity using consecutive data and then use the first and final data.
Table 2. Determined values of the acceleration of the picket fence due to gravity.
|
data |
∆t [s] |
Acceleration [m/s2] |
|
1-2 |
|
|
|
2-3 |
|
|
|
3-4 |
|
|
|
4-5 |
|
|
|
5-6 |
|
|
|
1-6 |
|
|
Conclusions
Do you know what is the expected answer? (If results is very different something in your procedure is wrong)
How does your result compares with the expected answer?
What is the difference between the expected result and your result in %?
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