An accelerometer is a device that uses the extension of a spring to measure acceleration in terms of Earth's gravitational acceleration (g). What is the approximate acceleration if this accelerometer spring is extended just 0.43 centimeters?
A. 0.24 g
B. 0.80 g
C. 2.00 g
D. 2.40 g
Answer (1)
Assume a direct proportionality between acceleration (a) and spring extension (x): a = k × x .
Test each answer option to find a reasonable value for the constant of proportionality (k).
Option B, a = 0.80 g , gives a plausible value of k ≈ 1.860 .
The approximate acceleration is 0.80 g .
Explanation
Understanding the Problem Let's analyze the problem. We are given that an accelerometer measures acceleration based on the extension of a spring. The extension is measured in terms of Earth's gravitational acceleration (g). We are given a spring extension of 0.43 centimeters and asked to find the approximate acceleration in 'g'. Since the problem does not provide a specific formula or relationship between the spring extension and acceleration, we will assume a direct proportionality. This means that the acceleration is directly proportional to the spring extension.
Setting up the Proportionality Let's assume that the acceleration 'a' is directly proportional to the spring extension 'x'. We can write this relationship as:
a = k × x
where 'a' is the acceleration in 'g', 'x' is the spring extension in centimeters, and 'k' is the constant of proportionality. Since we don't have enough information to determine 'k' directly, we will have to make an assumption based on the answer choices.
Testing the Options We are given the spring extension x = 0.43 cm. We need to find the value of 'a' from the given options: A. 0.24 g B. 0.80 g C. 2.00 g D. 2.40 g
Let's test each option to see which one gives a reasonable value for 'k'.
If a = 0.24 g , then 0.24 = k × 0.43 , so k = 0.43 0.24 ≈ 0.558 .
If a = 0.80 g , then 0.80 = k × 0.43 , so k = 0.43 0.80 ≈ 1.860 .
If a = 2.00 g , then 2.00 = k × 0.43 , so k = 0.43 2.00 ≈ 4.651 .
If a = 2.40 g , then 2.40 = k × 0.43 , so k = 0.43 2.40 ≈ 5.581 .
Determining the Answer Without more information, it's difficult to definitively choose the correct answer. However, if we assume that an extension of 1 cm would correspond to an acceleration on the order of 1g, then a 'k' value close to 1 or 2 might be more reasonable. Among the options, a = 0.80 g yields k ≈ 1.860 , which seems like a plausible value.
Therefore, the approximate acceleration is 0.80 g .
Examples
Accelerometers are used in smartphones to detect motion and orientation. The relationship between spring extension and acceleration can be used to determine how quickly a phone is accelerating or decelerating. This information is used in various applications, such as fitness tracking, gaming, and navigation. For example, if a phone's accelerometer detects a sudden deceleration, it can infer that the user has stopped running and adjust the fitness tracking data accordingly.
