An object is moving along a straight line and the uncertainty inits position is

Question

An object is moving along a straight line and the uncertainty inits position is 0.7 m. (a) Find the minimum uncertainty in themomentum of the object.
1 kg · m/s

(b) Find the minimum uncertainty in the object's velocity, assumingthat the object is a golf ball (mass = 0.045 kg).
2 m/s

(c) Find the minimum uncertainty in the object's velocity, assumingthat the object is an electron.
3 m/s (a) Find the minimum uncertainty in themomentum of the object.
1 kg · m/s

(b) Find the minimum uncertainty in the object's velocity, assumingthat the object is a golf ball (mass = 0.045 kg).
2 m/s

(c) Find the minimum uncertainty in the object's velocity, assumingthat the object is an electron.
3 m/s

Explanation / Answer

The uncertainty equation states x*p>= h/4 where x is uncertainty in position and p isuncertainty in momentum and h is plancks constant ---------------------------------------------------------------------------------------------------------- 1) 0.7 * p >= 6.626*10-34 /(4)     Solving for p p >= 7.53 * 10-35 kg m/s ------------------------------------------------------------------------------------------------------ 2) momentum eqquals mass times velocity so p=m*v x*p>= h/4 x*m*v>= h/4 v >= h/(4*x*m) Now plugging in values we will get v >=  6.626*10-34 /(4*0.7*0.045) v>= 1.67 * 10-33 m/s ----------------------------------------------------------------------------- 3) v >= h/(4*x*m) v >=  6.626*10-34 /(4*0.7*9.109*10-31) v >=  6.626*10-34 /(4*0.7*9.109*10-31) v>= 0.0000579 m/s

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