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slasakai
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Help with error analysis! urgently needed
Using the theoretical prediction of t, find the errors of both t and x, . The problem is based on an experiment I did in Labs, In which a small metal ball was fired at 40° (uncertainty 0.5°) to the horizontal, at a height,y= 1.095m (with uncertainty of 0.005m) and fired at another measured quantity of initial speed V=5.23 m/s(uncertainty of 0.01m/s). and t is the time taken to hit the ground and x is the range of the ball.
y=y0 - (Vsinθ)t - (0.5g)t^2
using quadratic equation to solve for t
t=((Vsinθ+ sqrt((Vsinθ)^2 + (2gy))/g
and later plug in value of t
into equation x=(Vcos40)t for x
also we are instructed to ignore the uncertainty on the constant g
putting in values t=0.926 s(3sf) and although I cannot type all of my working here, I used a series of steps calculating the errors on individual functions of the equation for t and slowly combining them, however it keeps resulting in an error of 1.17616421... which obviously cannot be correct as this is larger than the predicted value! I'm clearly making a mistake somewhere, a solution will be greatly appreciated.
Thanks gneill, I see how not including any working would make it difficult to find my mistake. I will try my best to describe the method I used here.
I used the functional approach to calculate all the errors, as I couldn't really understand the calculus method.
here goes:
1. I first calculated the error on sinθ, using α=abs(cosθ) * error on sinθ = 0.3830222216
2. Then the error on Vsinθ, using α=sqrt((errorV/V)^2 + (errorsinθ/sinθ)^2) * Vsinθ = 2.003216532
3. Then the error on (Vsinθ)^2 , α=abs(2*Vsinθ) * (error on Vsinθ) = 13.4687433 [this value is the one where I start to doubt myself]
4. Then I calculate the error on 2gy using α= abs(2g) * (error on value of y) = 0.0981
[wasnt completely sure about taking g to be a constant despite being told to ignore the uncertainty]
5. combining errors of the (Vsinθ)^2 + (2gy) using α= sqrt( errora^2 + errorb^2) = 13.46910059 [an obviously massive value]
6. propogating this error through a power of 0.5, using same functional approach = 1.176164221
7. finally adding the errors of everything under the sqrt sign and the Vsinθ outside it using
α= sqrt( errora^2 + errorb^2) gives such a ridiculous answer = appx 2.3, which is so wrong...
I know this was a bad way to write it out, but if anyone can follow it I would greatly appreciate it
Homework Statement
Using the theoretical prediction of t, find the errors of both t and x, . The problem is based on an experiment I did in Labs, In which a small metal ball was fired at 40° (uncertainty 0.5°) to the horizontal, at a height,y= 1.095m (with uncertainty of 0.005m) and fired at another measured quantity of initial speed V=5.23 m/s(uncertainty of 0.01m/s). and t is the time taken to hit the ground and x is the range of the ball.
Homework Equations
y=y0 - (Vsinθ)t - (0.5g)t^2
using quadratic equation to solve for t
t=((Vsinθ+ sqrt((Vsinθ)^2 + (2gy))/g
and later plug in value of t
into equation x=(Vcos40)t for x
also we are instructed to ignore the uncertainty on the constant g
The Attempt at a Solution
putting in values t=0.926 s(3sf) and although I cannot type all of my working here, I used a series of steps calculating the errors on individual functions of the equation for t and slowly combining them, however it keeps resulting in an error of 1.17616421... which obviously cannot be correct as this is larger than the predicted value! I'm clearly making a mistake somewhere, a solution will be greatly appreciated.
Thanks gneill, I see how not including any working would make it difficult to find my mistake. I will try my best to describe the method I used here.
I used the functional approach to calculate all the errors, as I couldn't really understand the calculus method.
here goes:
1. I first calculated the error on sinθ, using α=abs(cosθ) * error on sinθ = 0.3830222216
2. Then the error on Vsinθ, using α=sqrt((errorV/V)^2 + (errorsinθ/sinθ)^2) * Vsinθ = 2.003216532
3. Then the error on (Vsinθ)^2 , α=abs(2*Vsinθ) * (error on Vsinθ) = 13.4687433 [this value is the one where I start to doubt myself]
4. Then I calculate the error on 2gy using α= abs(2g) * (error on value of y) = 0.0981
[wasnt completely sure about taking g to be a constant despite being told to ignore the uncertainty]
5. combining errors of the (Vsinθ)^2 + (2gy) using α= sqrt( errora^2 + errorb^2) = 13.46910059 [an obviously massive value]
6. propogating this error through a power of 0.5, using same functional approach = 1.176164221
7. finally adding the errors of everything under the sqrt sign and the Vsinθ outside it using
α= sqrt( errora^2 + errorb^2) gives such a ridiculous answer = appx 2.3, which is so wrong...
I know this was a bad way to write it out, but if anyone can follow it I would greatly appreciate it
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