Question

Physics Rolling Help Needed

Answer 1

I tired to use a conservation of energy and I kept get wrong answer. Why doesn't it work?

Answer 2

\[\large E_{tot_o} = E_{tot_f}\]\[\large U_o = K_t+K_r\]\[\large mgh = \dfrac{1}{2}mv^2 + \dfrac{1}{2}I\omega^2\]

Answer 3

did you get the h right? what did you calculate h as?

Answer 4

Well, I calculated h as R - Rcosθ (R represents radius of bowl)

Answer 5

Isn't that right?

Answer 6

yea yea thats right.. :)!!.. still getting it wrong? :-/.. show your work here!

Answer 7

\[mgh = \dfrac{1}{2}mv^2 + \dfrac{1}{2}\left(\dfrac{2}{5}mr^2\right)\dfrac{v^2}{r^2}\]
\[= \dfrac{7}{10}mv^2\]
\[\dfrac{10}{7}gh = v^2 = \omega^2 r^2\]\[\omega = \sqrt{\dfrac{10gh}{7r^2}}\]\[\boxed{\omega = \sqrt{\dfrac{10gR(1 - \cos \theta)}{7r^2}}}\]

Answer 8

@Mashy @Vincent-Lyon.Fr

Answer 9

isn't that right?

Answer 10

yea.. i don't see any flaw in it.. sorry computer got stuck :P

Answer 11

That's weird...

Apparently I cannot use conservation of energy for some reasons....

Answer 12

Do you know another way I can solve?

Answer 13

wait.. the general equation is \[( 2gh /(1 + Icm/Mr^{2}))^{1/2}\]

how do you put that division line?? mine comes slanted line :(

Answer 14

thats linear velocity :D

Answer 15

yea there is nothing wrong in it!!.. its correct.. but do tell me how do you put that division in equation editor

Answer 16

\[1 \div 2\]

Answer 17

What's that?

Just type \dfrac{}{}

Answer 18

HOW TO DO THAT?!?!? :XXXXX

Answer 19

ok ok wait

Answer 20

general equation, what's that?

Answer 21

ok got.. anwyays.. no no thats the equation for linear velocity of cm.. in a general case..

it turns out to be the same.. its correct.. i don't see any mistake.. probably the given answer is wrong!

Answer 22

Maybe using conservation of energy won't work for some reasons...

Answer 23

Thank you, though.

Answer 24

no it has to work.. conservation of energy has no exception.. except when you are dealing with mass energy equivalence..

but here certainly it should hold good!! gravity is conservative.. so it really doesn't depend upon the path taken!.. so regardless of whether its a bowl or whether its just a slope.. it should hold good and give same answer!

Answer 25

That's strange. I will ask physics teacher tomorrow. Thanks.

Answer 26

your welcome :)

Answer 27

and please do tell here what happens ok?

Answer 28

I will.

Answer 29

you gotta take the centre of mass of the ball here. so h=(R-r) - (R-r)costheta