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What Numbers Tell You For the centripetal force lab, You made three plots On all three of them your ~slope yielded a zero percent error. Based on those three numbe...

Question

What Numbers Tell You For the centripetal force lab, You made three plots On all three of them your ~slope yielded a zero percent error. Based on those three numbers alone; can you determine whether Fc 40? Why or why not?47 r M Tc= T2 T Yan 27. 4cm (7)

What Numbers Tell You For the centripetal force lab, You made three plots On all three of them your ~slope yielded a zero percent error. Based on those three numbers alone; can you determine whether Fc 40? Why or why not? 47 r M Tc= T2 T Yan 2 7. 4cm (7)



Answers

If the centripetal force is of the form $\mathrm{m}^{\mathrm{a}} \mathrm{v} \mathrm{b}_{\mathrm{r}}^{\mathrm{c}}$ find the values of $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ (a) $1,2,1$ (b) $1,2,-1$ $\begin{array}{ll}\text { (c) } 1,3,-2 & \text { (d) }-1,3,-1\end{array}$

F. Equals M V. Squared over our. Now we're given that m Is 2.8 plus or -0.1 kg. V is 14 plus or -2 meters per second. Okay. And our is eight Plus or -0.2 meters. Okay, So uh we can just put that in a calculator first of all. That's not the calculator that I wanted. That one. Um M is 2.8. v. is 14 2.8 times 14 squared Over our our is eight. Thank you. That gives us uh 69. Which is the easy part of the problem, Which is in Newton's. Now, we need to look at the uncertainties. Um the uncertainty and M is 0.1. The uncertainty in V is to and the uncertainty and our is 0.2. So if we add those together, go ahead and do that. Uh huh. Okay. Here we go. 0.1 Over 2.8. Um Plus Plus two times to over 14 plus zero point 2/8. And now I need to multiply all of that by the answer which is 69 two. And that gives me plus or -23. Just verify this over this Plus two times this over this. This over this 10 69 is 24 which actually is the answer that's in the back of the book. Even though the answer in the back of the book looks weird. Seven times 10 is 70 and then two times 10 is 20. Um Now there is only one significant digit here in the uncertainty. So um I think it does make sense that this Would be 20. Now there's two significant digits In force so that really should be 69. All right. Thank you for watching. Okay.

We're given the formula for the centripetal acceleration. A particle moving in a circle were asked to approximate the maximum error in this formula, given errors in velocity and diminishment of the radius, What to find? Approximate and that's 1% here. So formula for acceleration is a of r V equals B squared of art where V is velocity and R is the radius of the circle percentage error A is from the hint total differential they invited by a itself. So to calculate the percentage error will need to calculate. So differential of a A R R V is equal to negative b squared over r squared. Okay, and A or B is equal to to the overall. So we have the total differential d a. This is equal to they are, which is negative. B squared over r squared er plus baby which is to be over. Or so we have the percentage error is going to be equal to negative. He squared over our spirit er plus to be over our You mean all over a which is B squared over R. This is equal to flipping. We gets negatives. One of her are you are Waas two over the TV. So forgiven Nets. We have an air of 3% the so Delta V when you're three and error of 2% in or we have to, Then we have That's Senator A given that don't be equals 0.3. Don't our equals point to is approximately negatives one of her arm times Delta are So we get negative Oh, to over over plus two of the V times Delta V. It's a to 10.3 or 0.6 over the okay. And so to maximize this percentage error instead of making this approximation, this is different. We have a sequel to Negative. One of our even will keep the PR with that waas two times TV over the instead of having Delta V and dental are beauties, we have the devia ravine er so that gets make it is when you're too plus two times we know three to this is going to be six. This too is 0.4. So nothing to remember is this is actually just absolute value of DP that's the value of deer are in order to find the maximum very said this is going to be less than or equal to absolute value of D R plus two times the absolute value of TV over which is equal to I know too, plus two times 23 which is equal to 08 So we have that percentage error in a is approximately 8% maximum.

Yeah. For part A the centripetal exhibition. Easy. It's given his view square upon us. And the centripetal acceleration you can say the center of the exhibition is that you proposed to describe the three. And the center with an exhibition is inversely proportional with various. Uh huh. And in the example to the radius is almost infinite. So in that case the centripetal acceleration will we meet him? So A C. Is minimum in example two part B. The centripetal exhibition. Yes, he's maximum when the ratio of the v square upon the ratio of the orbital radius. Other radios of the circular path is greatest. So this ratio is greater. Testing example one. So the centripetal acceleration is maximum. An example no part C. The centripetal acceleration for example. one is The spiral. The speed that is 12 m for second square Upon the radius that is 0.5 m. Other significant acceleration for example, when you use 290 m/s squared Remember Dad does answer should be given in two significant things, and the centripetal acceleration in the second case is The square of the speed that is 35. We just pause it and square upon the radius and the radius is almost in finite. So in this case the centripetal acceleration is almost equal to 0m for seconds. In the third example, The centripetal exhibition is described, this food that is 2.3 we just for a second Square upon the radius, that is 1.8 m, and in the in this case the same typical accelerations 2.9 m four seconds.

And this you present. We here centripetal force uh depends on moss. So it depends on mars we consider our message. A. This is the case in the manifest centripetal force also depend on the speed of body. So this is followed. We powder and the The case # two Incentive. Their force depend on radius of parts who are and policy so strong. Easy question. When two and three. Uh huh. Director of national empower A. We power bi. And our power tends to see the four day Dimensions average was two force. Energy goes to mask. We equals to speed and our energy goes to radius. So we put the dimensions so we know that dimension of for someone volunteering to and dimension of masks. Um Wonderful. M. A. Dimension up we L. D -1. L. one d -1. B. And dimensional radius. L. Policy press simplify. We get empower A. Help our B plus E. And T tends to power bi. So comparing from bedding as the left hand side and right hand side. We get 81- one. This is eight and this is one. B. Policy music was too one and minus begic was to minus two. So B. J. Was too they were losing this So two plus C. Was to one. So sees it was two minus these are we lose of abc. So refugee was too and one we too. I don't mind this one strategy was to I am we squared divided by our this is formula for centripetal force and this really given in centripetal force. Diesel given in option B. Hands option. Be each correct? Okay, thanks.


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