Your vertical spring accelerometer has a 200 g mass hanging from it. You climb aboard the roller coaster and watch the accelerometer read 0.4 g for 3 seconds while descending and read 1.5 for 2 seconds while climbing the next peak. The car weighs 2000 kg. What is your acceleration going down, and what is your acceleration going up?
To determine the acceleration going down and the acceleration going up, we need to understand the readings on the accelerometer and the concepts involved.
The accelerometer measures the acceleration experienced by the mass hanging from the spring. It measures an acceleration value in terms of "g," where 1 g is equal to the acceleration due to gravity.
Given that the accelerometer reading was 0.4 g for 3 seconds while descending, we can determine the acceleration experienced during this period.
To find this acceleration, we can use the formula:
acceleration = (accelerometer reading - 1) * g
where g = 9.8 m/s² (acceleration due to gravity).
For the descending acceleration:
acceleration_down = (0.4 - 1) * 9.8 m/s²
acceleration_down = -0.6 * 9.8 m/s²
acceleration_down = -5.88 m/s²
The negative sign indicates that the acceleration is in the opposite direction of the gravity vector, suggesting a downward acceleration.
Now, let's calculate the acceleration going up. The accelerometer reading was 1.5 g for 2 seconds while climbing the next peak.
For the ascending acceleration:
acceleration_up = (1.5 - 1) * 9.8 m/s²
acceleration_up = 0.5 * 9.8 m/s²
acceleration_up = 4.9 m/s²
The positive sign indicates that the acceleration is in the same direction as the gravity vector, suggesting an upward acceleration.
Therefore, the result is:
Acceleration going down: -5.88 m/s²
Acceleration going up: 4.9 m/s²