Question

What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r=2.64±0.07m?
Express your answer using one significant figure.

Answer 1

ΔV / V specified ..it also has this in the question I am not sure how to incorporate it either

Answer 2

Mmm lemme see if I've got the right idea here.

Answer 3

\[\Large V=\frac{4}{3}\pi r^3 \qquad\to\qquad \Delta V=\frac{4}{3}\pi (\Delta r)^3\]

Answer 4

\[\Large \Delta r=\pm 0.07\]

Answer 5

So plugging that value in, what do we get for DeltaV ?

Answer 6

is it 0.29 ?

Answer 7

this is what I did before
v= 4/3 (pi) (2.64 + 0.07) = 11.35162
&
v= 4/3 (pi) ( 2.64 - 0.07) = 10.76519

now do I subtract these two answers from each other
like this

11.352-10.765 = 0.587

then do this
0.0587 / 2.64 x 100 = 22%... something seems wrong

Answer 8

Mmmm maybe that's the right approach.
But shouldn't there be a 3 exponent when you do that first step?\[\Huge V= 4/3 (\pi) (2.64 + 0.07)^{\color{red}{3}}\]

Answer 9

so I get 83.36

Answer 10

`ΔV / V specified`

What does that mean?

Answer 11

I really am not sure either it says
ΔV / V specified = ____%

Answer 12

the teacher said that delta doesnt always mean change but I dont get what he was trying to say

Answer 13

Ok ok ok ok ok I think this is what we do.
Lemme see if this makes sense.

Answer 14

Ahhh crap i gotta go :( SOrry sorry

Answer 15

@.Sam. @thomaster

Answer 16

You need to calculate three volumes:
when R=2.64-0.7=2.57----->V1=71.10--->(V1-Vo)/Vo=-7.7%
when R=2.64------>Vo=77.07
when R=2.64+0.07=2.71-------->V2=83.37--->(V2-Vo)/Vo=+8.2% Then
V=77.07 (+8.2%/-7.7%)

Answer 17

Another way to calculate it\[V=\frac{ 4 }{ 3 }\pi r^3\rightarrow \Delta V=\frac{ \delta V }{ \delta r }\Delta r=4 \pi r^2 \Delta r \rightarrow \frac{ \Delta V }{ V } =3\frac{ \Delta r }{ r }\]for r=2.64 and ∆=0.07 you get:\[\frac{ \Delta V }{ V }=\frac{ 3·0.07 }{ 2.64 }=0.080\] and that correspoonds to an 8.0%(+/-)

Answer 18

so 8% is % uncertainty

Answer 19

thank you very much, thank you thank you!

Answer 20

If you use the second approach, it is 8%.

Answer 21

oh do you know what you got for Vo in the 1st approach ?

Answer 22

I do not understand your question

Answer 23

never mind but thank you!

Answer 24

ok

Answer 25

do you mind helping me on this other question I have

Answer 26

shoot

Answer 27

Compare the acceleration of a motorcycle that accelerates from 80 km/h to 90 km/h with the acceleration of a bicycle that accelerates from rest to 10 km/h in the same time.
Part A
Compare the distance traveled between the motorcycle and the bicycle

-- The motorcycle and bicycle travels the same distance.
-- The motorcycle travels a greater distance than the bicycle.
-- The motorcycle travels a smaller distance than the bicycle.

Answer 28

For the motorcycle:\[ V_m=v_{0m}+a_m·t \rightarrow t=\frac{ V_m-v_{0m} }{ a_m }=\frac{ 90-80 }{ a_m }\] For the bike\[V_b=v_{0b}+a_b·t \rightarrow t=\frac{ V_b-v_{0b} }{ a_b }=\frac{ 10-0 }{ a_b }=\frac{ 10 }{ a_b }\]

Answer 29

As all that happens in the same time:\[\frac{ 10 }{ a_m}=\frac{ 10 }{ a_b }\]and that means accelerations are the same

Answer 30

this is Part B
Compare the acceleration between the motorcycle and the bicycle.
Compare the acceleration between the motorcycle and the bicycle.
The motorcycle has a greater acceleration than the bicycle.
The motorcycle has a smaller acceleration than the bicycle.
The motorcycle and bicycle have the same acceleration.

Answer 31

would it also be same?

Answer 32

yes, both increase the velocity by the same amount (10 Km/h) in the same period of time, then accelerations are the same

Answer 33

the other one is asking for distance though?

Answer 34

That is easy, distance is given by the following formula:\[D=v_0t+\frac{ 1 }{ 2 }a t^2\]And accelerations are the same and time is the same, then the only thing that will make both distances (the motorcycle and the bike) is their initial velocity. Since the only one that has initial velocity is the motorcycle, then its distance is longer than the bike's
Does it make sense to you?

Answer 35

Let me rephrase it:

And accelerations are the same and time is the same, then the only thing that will make both distances (the motorcycle and the bike) DIFFERENT is their initial velocity. Since the only one that has initial velocity is the motorcycle, then its distance is longer than the bike's Does it make sense to you

Answer 36

ok so the motorcycle has the greater distance than the bike but in acceleration there both the same?

Answer 37

Exactly!

Answer 38

It is just a problem, I guess it is not like this in real life (the acceleration thing, I mean)

Answer 39

can you also think of as the motorcycle is faster so it goes a longer way than the bike

Answer 40

Is faster because it had an initial velocity. If they had both started from rest they would have run the same distance because they had the same acceleration. Then what makes the difference is the initial velocity of the motorbike =80 Km/h

Answer 41

ohh okay thank you! are sticking around for a little bit I had a few more questions if you dont mind

Answer 42

Well, can we leave them for tomorrow? I am writing from Spain and it is 05:00. I would love to hit the hay!

Answer 43

oki thank you very much

Answer 44

talk to you tomorrow!

Answer 45

thanks bye GN!

Answer 46

GN!