A lamb grows with its mass proportional

[Nerdlight]

A lamb grows with its mass proportional to the cube of its length. When the lambs length changes by 15.8% its mass increases by 17.3kg. Find the final mass.

Really stumped thanks for any help

m_f=kx_f³
length change by 15.8%
x_i+.158x_i=x_f
x_f=1.158x_i

m_f=k(1.158x)³
m_f=1.55kx³

I couldn't get the right answer because at this point, my book shows kx³ turning into m_i and continuing the problem from there. Why?

kx³=m_i
m_f=1.55m_i
m_i=m_f/1.55

 

[haruspex]

m_f=kx_f³

The information given is more general than that. It tells you m=kx³. In particular, m_i=kx_i³ and m_f=kx_f³.

x_f=1.158x_i

m_f=k(1.158x)³

You dropped the subscript on the x. Based on your equations to this point, it should be m_f=k(1.158x_i)³

 

[Nerdlight]

It was a little confusing ill try to make it more clear.
Need to find the value of m at the end of this process.

m = kx³

length change by 15.8%
x_i+.158x_i = x_f
x_f = 1.158x_i

mass increase of 17.3kg
m_f = m_i+17.3

m_f = kx_f³
m_f = k(1.158x_i)³
m_f = 1.55kx_i³

The solutions manual does something here I don't understand
m_f = 1.55(kx_i³)
m_f = 1.55m_i
m_i = m_f/1.55

Why does kx_i³ = m_i
k and x_i³ just disappear and m_i shows up
I got 109kg from 2 different methods which is incorrect and the manual isn't helping much on this one.

 

[D H]

m = kx³

…

Why does kx_i³ = m_i

The answer should be staring you in the face. It's because #m=kx^3##.

 

[Nerdlight]

Lol gotcha, subscripts were throwing me, got to remember that m=kx^3 can take any x value whether its initial/final/middle. Thanks

 

[Chestermiller]

You have it and you don't know it:

1.55m_i-m_i=17.3

 

[D H]

Except he's been asked to solve for m_f, not m_i. It's better to eliminate m_i rather than m_f so you can solve for m_f directly.

 

[Chestermiller]

Except he's been asked to solve for m_f, not m_i. It's better to eliminate m_i rather than m_f so you can solve for m_f directly.

Potatoes, Potahtoes. I thought it would be easier for him to see it that way. I would have done it your way.

Chet