Uncertainty principle

[zoner7]

Homework Statement

A mosquito of mass .15mg is found to be flying at a speed of 50 cm/s within an uncertainly of .5 mm/s.

a) How precisely can it's position be known?

Homework Equations

Delta p * Delta x = h bar / 2
p = mv

The Attempt at a Solution

I look at problem originally and simply solved for momentum using the given velocity 50 cm/s. Then i plugged that into the delta x * delta p = h bar / 2.
I got the answer 7.033 X 10^-31

Then I realized that I never used the variable describing the uncertainly of the fly's velocity. Clearly this is relevant to the solution of the problem. I think that I calculated the acutal momentum, as opposed to the uncertaintly of momentum, which the above equation calls for. How am I supposed to differentiate between the actual velocity and the uncertaintly of velocity?

Does the problem want me to give a range of positions? I could solve for the uncertainly of momentum using 50 cm/s + or - .5 mm/s. Could I then could find a max and a min position using the uncertainly equation? What exactly should I be solving for?

Thank you in advance!

 

[Jasso]

I look at problem originally and simply solved for momentum using the given velocity 50 cm/s. Then i plugged that into the delta x * delta p = h bar / 2.

You found momentum p, which is not what the equation uses. It uses delta p.

Given that $p=mv$ , then $\Delta p=m\Delta v$.

The problem just wants to know delta x.

 

[kerimek]

I understand the concept of uncertainty principle, which states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously. In this particular problem, we are given the mass and velocity of a mosquito, but also an uncertainty in its velocity.

To answer the question of how precisely the mosquito's position can be known, we need to use the uncertainty principle equation: Δp * Δx = h bar / 2. Here, Δp represents the uncertainty in the momentum and Δx represents the uncertainty in the position. We also know that momentum is given by p = mv, where m is the mass and v is the velocity.

To incorporate the uncertainty in velocity, we can use the given range of 50 cm/s ± 0.5 mm/s. This means that the mosquito's velocity can be anywhere from 49.5 cm/s to 50.5 cm/s. We can use these values to calculate the uncertainty in momentum (Δp) and then use the uncertainty principle equation to solve for the uncertainty in position (Δx).

In summary, to accurately answer the question, we need to solve for the uncertainty in position (Δx) using the uncertainty in momentum (Δp) calculated from the given range of velocities. This will give us a range of positions within which the mosquito is likely to be found.