Example 1.7a in the Textbook [ENDORSED]

[Danielle Sumilang - 1F]

Hello!

Can someone please explain how the uncertainty in the position of a marble of mass 1.0 g given that its speed is known to within 1.0 mm s^-1 was calculated? I understand that the equation for the uncertainty principle is delta p x delta >= 1/2 h bar, but where did the equation delta p = m times delta v come from? Thank you!

[AshleyLamba1H]

The equation to find momentum is p = mv (momentum = mass * velocity). To find the change in momentum, you would put a delta in front of every variable except mass, because in the case of the marble, its mass is not changing.

[Phil Timoteo 1K]

P=mv

[Andre-1H]

Yep just to add on it makes sense that the second equation is like that because for an object like a marble its speed can change, meaning that its momentum can change, leading to the delta symbol. However, its mass is constant, and cannot change.

[QuincyH1G]

Like this example, when calculating the uncertainty in position, is the uncertainty in velocity always positive.