What is the Minimum Uncertainty in Block's Speed on a Frictionless Surface?

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The discussion focuses on calculating the minimum uncertainty in the speed of a 1.70 kg block on a frictionless surface, given a position measurement precision of 0.30 cm. Participants explore the application of the Heisenberg uncertainty principle, noting that the correct conversion of position uncertainty to speed uncertainty is crucial. Errors in calculations arise from misinterpreting the relationship between speed and velocity, as well as incorrect unit conversions. One participant asserts they consistently arrive at a speed uncertainty of 1.62E-32, but others challenge the accuracy of this result. The conversation highlights the complexities of applying quantum mechanics principles to classical mechanics problems.
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Homework Statement


A 1.70 kg block rests on the icy surface of a frozen pond, which you can assume to be frictionless. If the location of the block is measured to a precision of 0.30 cm, what is the minimum uncertainty in the block's speed, assuming the mass is known exactly?


Homework Equations


xp=h/4(3.14)


The Attempt at a Solution


xp=h/4(3.14)
x(mv)=h/4(3.14)
I plugged in all the values and got v. The answer was wrong. I then multiplies by .0003 and that was also wrong.
 
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potential sources of error # 1:
0.3 cm = 0.003 meters, not 0.0003 meters


potential source of error # 2
they ask you for uncertainty in speed, while the equation for momentum p = mu considers VELOCITY
an uncertainty in speed of 10m/s , for example, is equal to an uncertainty in velocity of 20 m/s, since a speed up to 10 m/s implies a range of velocities from -10m/s to +10m/s
so try multiplying the speed by 2 :) (edit: or rather, try dividing the uncertainty in velocity you get by 2 to get the uncertainty in speed, since the block moves in both directions)
 
1.03E-32 the velocity by 2 and got 5.16E-33 which is wrong by 10% to 100%.

I used .003 meters.
 
are you sure your math is right? using the version of the Heisenberg uncertainty principle that you've provided (there are many variations of it) and the values for m and deltax youve given,
i get an uncertainty in velocity of 3.24807255 × 10-32
which is an uncertainty in speed of 1.62403627 × 10-32
 
The math is right i did a million times. 1.62E-32 is wrong and it was last my chance. thanks, anways...
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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