A 247 lb fullback runs the 40 yd dash at a speed of 17.09 ± 0.1 mi/h.
(a) What is his de Broglie wavelength (in meters)?
(b) What is the uncertainty in his position?
** I found part A but I am unsure how to use this information to get part B. Any help is appreciated :)
delta x (position) = h/4*pi*mdeltav.
delta x = h you know
4*pi you know
mass = 247 lb converted to kg.
delta v is 17.09 x 0.1 m/hr conerted to m/s.
Here is a site that does a pretty good job of explaining how to do this. I've also included another site that helps, too.
http://www.relativitycalculator.com/Heisenberg_Uncertainty_Principle.shtml
http://www.relativitycalculator.com/Heisenberg_Uncertainty_Principle.shtml
To calculate the uncertainty in the fullback's position, we need to use the concept of Heisenberg's uncertainty principle, which states that there is a fundamental limit to how precisely both the position and momentum of a particle can be known simultaneously.
The uncertainty Δx in the position of an object can be related to the uncertainty Δp in its momentum using the equation:
Δx * Δp ≥ h/4π
where h is Planck's constant (h = 6.626 x 10^-34 J · s).
In this case, we are given the uncertainty Δv in the fullback's speed, which we can use to calculate the uncertainty Δp in his momentum. Then, we can use the calculated uncertainty in momentum to find the uncertainty in his position.
Here's how you can calculate the uncertainty in the fullback's position:
Step 1: Convert the speed uncertainty from miles per hour (mi/h) to meters per second (m/s).
Given: Speed uncertainty (Δv) = 0.1 mi/h
Conversion factor: 1 mi/h ≈ 0.44704 m/s
Calculate: Δv (m/s) = 0.1 mi/h * 0.44704 m/s ≈ 0.044704 m/s
Step 2: Calculate the uncertainty in momentum (Δp) using the equation:
Δp = m * Δv
where m is the mass of the fullback and Δv is the speed uncertainty in m/s.
Given: Mass (m) = 247 lb
Conversion factor: 1 lb ≈ 0.453592 kg
Calculate: Δp = 247 lb * 0.453592 kg/lb * 0.044704 m/s ≈ 5.562 kg·m/s
Step 3: Calculate the uncertainty in position (Δx) using the uncertainty principle equation:
Δx ≥ h/(4πΔp)
Given: h = 6.626 x 10^-34 J·s, Δp = 5.562 kg·m/s
Calculate: Δx ≥ (6.626 x 10^-34 J·s) / (4π * 5.562 kg·m/s)
The resulting value of Δx will give you the lower limit of the uncertainty in the fullback's position.