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Chapter 8: Problem 46

Show that the uncertainty principle is not significant when applied to large objects such as automobiles. Assume that \(m\) is precisely known; assign a reasonable value to either the uncertainty in position or the uncertainty in velocity, and estimate a value of the other.

Short Answer

Expert verified
The calculated value for the uncertainty in velocity \(\Delta v\) is extremely small, around the order of \(10^{-34}\) m/s. This value is far too small to have any impact on the measurement or behavior of an automobile. Hence, it can be concluded that the uncertainty principle is not significant when applied to large objects like automobiles.

Step by step solution

01

Assign a value for uncertainty

Let's choose an uncertainty in position \(\Delta x\). A suitable value for an automobile might be \(\Delta x = 1\) mm, which represents a very small deviation in the position of a car, considering its size.
02

Identify Known Variables

The mass of an automobile \(m\) can be assumed to be about 1500 kg, a typical mass of a car. Planck's constant \(h = 6.62607015 × 10^{-34}\) m^2 kg / s
03

Calculate uncertainty in velocity

Substitute all the known values into the uncertainty principle formula to solve for \(\Delta v\). We get: \(\Delta v \geq \frac{h}{4\pi m \Delta x}\). After calculation, we will find that \(\Delta v\) is significantly small, implying that for such a large object like a car, the uncertainty principle has negligible impact.

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