Asked Sep 20, 2019

Consider a 2270 lb automobile clocked by law‑enforcement radar at a speed of 85.5 mph (miles per hour). If the position of the car is known to within 5.0 ft at the time of the measurement, what is the uncertainty in the velocity of the car?


Expert Answer

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Step 1

Refer to the question and calculate the uncertainty in the velocity of the car from the given data.

Uncertainty in the velocity of the car can be calculated by the use of the Heisenberg’s uncertainty principle that is given below.:


Δx is the uncertainty in the position and Δpx is the uncertainty in the momentum.

h is the Planck’s constant.

Дх. Дрх

Image Transcriptionclose

h Дх. Дрх .-(1) 4л

Step 2

Uncertainty in the velocity can be calculated as follows:


p m.v
Ap m.Av
Av= Ap

Image Transcriptionclose

p m.v Ap m.Av Av= Ap ..2)

Step 3

1 feet = 0.3048 meters

Now uncertainty in the position can be calculated as follows:

Since the mass of the ca...

Ax = 5.0 ft x 0.3048 m
1 ft
= 1.524 m
m 2270 lb x 0.4536 kg
1 lb
= 1029.67 kg

Image Transcriptionclose

Ax = 5.0 ft x 0.3048 m 1 ft = 1.524 m m 2270 lb x 0.4536 kg 1 lb = 1029.67 kg


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