Energy/Momentum Diagram

[I Love Pi]

Hello! The problem and my solutions are attached below.

I am most uncertain about the velocity values that I solved for.

I know if my velocity values are wrong/unrealistic, then the rest of my calculations are incorrect.

I would really appreciate critiques to my attempt at solving this problem. Thank you SO much!

 

[blamocur]

A question: if the second segment is frictionless and horizontal then why would Vf2 be different from Vf1?

 

[I Love Pi]

Given your question, I made the following alterations
1.) I used a different equation to find V1 and Vi3 (shown on page 1 at the top of the page)
2.) I determined V1f = V2i = V2f
3.) I attempted to solve for V3i since the velocity changes after the collision
4.) I attempted to use conservation of momentum to solve for V3i, however this velocity was greater than V1f, V2i, and V2f even though the car slows down due to friction after the collision. I am unsure how to correctly solve for Vi3 or use the conservation of momentum setup correctly (m1v2i+m2v2f=m1vi3+m2vf3).
5.) I resolved for Pi and Pf after the collision with my new velocity for Vi3 (the vi3 value may be incorrect)

Could you help me determine the correct value of vi3 and how to use the “Collison - Conservation of Momentum Equation” properly?

Also, any other feedback is helpful.

Thank you!!!

 

[blamocur]

I am unsure how to correctly solve for Vi3 or use the conservation of momentum setup correctly (m1v2i+m2v2f=m1vi3+m2vf3).

Two questions now:

1. What is the speed of the cup before the collision?
2. What is its speed after the collision?

 

[I Love Pi]

Okay. Given your question, I made the following alterations
1. I determined when the car and the cup collide, they create an inelastic collision since the two stick together.
2.) I found the speed of the cup before the collision
3.) I found the speed of the cup and car after the collisions since the two stick and move together
4.) I found V3i I am also unsure if my value for vi3 is correct (it seems reasonable because it is less than the velocity before the collision.)
5.) I resolved for delta P with my new value for velocity

I am most sure whether the conservation of momentum equation m1v2i+m2v2f=(m1+m2)vi3 is correct.

Please let me know if my values for velocity seem correct and if you notice any other incorrect calculations.

Thank you SO much for your direction!

 

[blamocur]

I don't understand most of the lines in your attachments, but my computations for speeds produce the same results as yours.
I am assuming that W and F stand for work in joules and force in newtons respectively. If that's correct then my computations for the first segment yield the same numbers.
But: for the third segment (with friction) you are computing W and F before computing the initial speed there -- how can one do that? My numbers for the third segment are different from yours.

 

[I Love Pi]

Could you please clarify what the conservation of momentum equation would be? Would it be m1v2f+m2v2i=(m1+m2)vi3?

This would help me correctly find Vi3 and solve the third section correctly. Thank you!!!

 

[I Love Pi]

Or would it be m2v2f+m1v2i=(m1+m2)vi3?

 

[topsquark]

Or would it be m2v2f+m1v2i=(m1+m2)vi3?

Conservation of momentum: [imath]p_i = p_f[/imath].

[imath]m_{car} v_{car} + m_{cup}(0) = (m_{car} + m_{cup})v_f[/imath]

Keep the velocity of the car with the mass of the car! You will never have a term like [imath]m_1 v_2[/imath].

-Dan