# Acceleration of an Elevator, Hydraulic

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## Introduction

Acceleration is defined as the rate of change of velocity with respect to time. It is measured in SI units by meter/second^{2}. One common unit of acceleration is known as g, the acceleration due to gravity of the Earth. An accelerometer is an instrument used to measure acceleration and the effects due to gravity.

Materials Used:

- low-g accelerometer
- LabPro
- laptop
- masking tape

## Experiment 1

In this experiment we rode the elevator at Midwood High School and using an accelerometer that was connected to the laptop through the LabPro.We zeroed the accelerometer and let the Logger Pro software collect the acceleration of the elevator. It collected the elevator's acceleration at 0.1 second intervals for a total of 20 seconds. In this experiment we started collecting the data on the 3rd floor as the elevator travelled down to a stop in the basement. The results are compiled in this table.

- The acceleration vs. time graph shows that the peak acceleration of 0.64 m/s
^{2}was reached at 1.9 s, dropped to 0 m/s2 while the elevator was traveling at a constant speed, and decelerated to 0.71 m/s^{2}at 18.9 s until the elevator came to a rest. - We applied the integral function to the acceleration graph to graph the velocity vs. time graph.
- The velocity vs. time graph shows that the elevator started from rest and accelerated in the downward position reaching a peak speed of 0.820 m/s at 6.1 s, until it reached a constant velocity. When we reached the basement the graph shows that the elevator decelerated and came to a stop.
- We again applied the integral function to the velocity graph to graph the displcement vs. time graph.
- The displacement vs. time graph shows that the elevator started from rest and accelerated in the downward position a distance of 14.309 m, the distance from the 3rd floor to the basement of Midwood High School.

## Experiment 2

In this experiment we rode the elevator at Midwood High School, but instead of going down, we decided to go up.We zeroed the accelerometer and let the Logger Pro software collect the acceleration of the elevator. It collected the elevator's acceleration at 0.1 second intervals for a total of 20 seconds. In this experiment we started collecting the data on the 2nd floor as the elevator travelled up to a stop at the 4th floor. The results are compiled in this table.

- The acceleration vs. time graph shows that the elevator decelerated from
rest to 0.66 m/s
^{2}, then did not accelerate until it reached a peak acceleration of 0.74 m/s^{2}. - When we graphed the velocity, the graph showed that speed increased, reached a constant value for a few seconds, then increased and kept increasing even when the elevator stopped. Therefore, we adjusted our speed values by utilizing the function

"velocity"-0.06886-0.01138*"Time"

- Using our adjusted velocity values, we produced a new graph which showed that the speed increased, remained constant and then dropped to zero when the elevator came to a rest.
- The distance vs. time graph derived from utilizing the integral function for our adjusted velocity graph showed that the total displacement the elevator travelled was 8.176 m, about two floors of our school building.

Olga Strachna, Diana Kuruvilla, Dorothy Soo -- 2005