Isaac Physics Submerged Spheres on Scales

Hi all,

I've been working on this question: https://isaacphysics.org/questions/submerged_spheres_scales?board=3ffc04fa-6080-4c4d-8225-d5f5d84f4577 : Two solid spheres of densities ρ
A, ρ B and radii rA rB hang from the two ends of a beam on a symmetrical lever arm balance. The scales become perfectly balanced after being submerged in a fluid of density ϕ. Find an expression for ϕ in terms of ,ρA ρB rA and rB?
I think I'm missing something as I think it reduces to something like rho_A-rho_B but it says incorrect so I must be making a foolish error somewhere. If someone could post a worked solution I'd be very grateful!
.

Reply 1

happyapple5

11

The answer is something you can't just guess
1) Have a look at the weights
2) how much dose the weight change in the new fluid ( due to up thrust)
3) write an equation linking the two (they are equal as the scale is balanced)
4) cancel any common factors
5) rearrange for phi
Good luck!

(edited 3 years ago)

Reply 2

username4492254

13

Original post by happyapple5

The answer is something you can't just guess
1) Have a look at the weights
2) how much dose the weight change in the new fluid ( due to up thrust)
3) write an equation linking the two (they are equal as the scale is balanced)
4) cancel any common factors
5) rearrange for phi
Good luck!

I'd like to chip in and say that you should consider the resultant force (zero) on each sphere separately, and then equate them. This little guide thingy helped me work it out as well! Think carefully about the relative magnitudes of the densities.

Reply 3

TheScholar!

OP

5

Thanks a lot guys- I was getting it right all along just forgetting to cancel out 4*pi! So foolish. I feel like a lot of the algebraic Isaac Physics questions can trip you up like this!

Reply 4

LaraDiamonds18

7

Hey, how did you get the answer? I've been trying this question for a while now and I genuinely don't know how to do it anymore - feel like I've tried everything!

Reply 5

happyapple5

11

Original post by LaraDiamonds18

Hey, how did you get the answer? I've been trying this question for a while now and I genuinely don't know how to do it anymore - feel like I've tried everything!