1-D Inelastic Block Collision and Spring Compression w/photo

[Yamahonda450]

Homework Statement

Homework Equations

The Attempt at a Solution

Here is the work that I've done. This is an even problem in my book so the answer is not given. The professor did gave the answer to this problem as .33m. The most recent answer I got is .4m which means block b is moving too fast in my solution. The mass is constant and I thought that I used the correct equations to calculate the V_f for both blocks (Eq. 5&6). Where have I gone wrong?

 

[tiny-tim]

welcome to pf!

hi Yamahonda450! welcome to pf!

what was your value for the initial speed of the combined blocks (i don't see it in your work)?

 

[Yamahonda450]

Thank you. Please clarify what you mean by "combined blocks"?

 

[tiny-tim]

the question says "the two blocks stick together" …

that's the combined blocks …

what was your value for their initial speed (just before the spring starts compressing)?

 

[Yamahonda450]

I realize my mistake. I completely missed that part about the blocks sticking together after the collision. That would make this a "completely Inelastic Collision" meaning that I should have used this formula below (not sure if it will show) as the initial velocity. In equation 7, I changed the formula on the right to -1/2MV^2 and used the mass of both blocks for M and plugged in my new V-value, then solved for d. I got 0.33m.

Thank you for the help!

\mathbf v_f=\frac{m_1 \mathbf v_{1,i} + m_2 \mathbf v_{2,i}}{m_1 + m_2}

 

[Yamahonda450]

Here is the equation that I should have used for the final velocity of a "Completely Inelastic Collision"

 

[tiny-tim]

Hi Yamahonda450!

(just got up :zzz: …)

In equation 7, I changed the formula on the right to -1/2MV^2 and used the mass of both blocks for M and plugged in my new V-value, then solved for d. I got 0.33m.

Woohoo!

btw, I think the reason your LaTeX didn't work in your first post was that you didn't use enough {}s …

though you may find it easier to use the X² and X₂ icons just above the Reply box … eg (m₁v_1,i + m₂v_2,i)/(m₁ + m₂) )​