Question

Imagine a universe in which h = 2π J · s. A block with mass m = 4.50 kg is sliding on a frozen pond which is L = 3.00 m wide.

(a) What is the minimum uncertainty (in m/s) in the component of the block's velocity parallel to the pond's width?

Δu ≥ ___ m/s

(b) Assuming this uncertainty in speed prevails for t = 6.25 s, determine the uncertainty in the block's position (in m) after this time interval.

___ m

Answer 1

The momentum is defined as
  
So, the uncertainty in the momentum is
   
And at time t = 0, the uncertainty is
   
And according to the uncertainty relation, at t=0
  
  
   
In an universe in which
  
And so, for given m = 4.50 kg, we have



  

b)

The uncertainty in the velocity remains constant in time whereas the uncertainty in the position increases, with time according to the the following formula
   
where,
  
And so, if we assume
  
then for time t = 6.25 s, we have
   
  
And so, the uncertainty in the position after time t is