Spring and collision

[/0]

I don't know if this can be posted here, but there isn't a physics section in the University forums...

The diagram shows block 1 of mass 0.200kg sliding to the right over a frictionless elevated surface at a speed of 8.00m/s. The block undergoes an elastic collision with stationary block 2, which is attached to a spring of spring constant 1208.5N/m. (Assume that the spring does not affect the collision.) After the collision, block 2 oscillates in simple harmonic motion with a period of 0.140s, and block 1 slides off the opposite end of the elevated surface, landing a distance d from the base of that surface after falling height h = 4.90m. What is the value of d?

Thanks!

[Mao]

woah~ no idea...
wherever u got this from, it cannot be part of the VCE course!

try wikipedia
if i dont have an English SAC 2morrow, i'll actually read their section on that harmonic oscillation (under spring).

[/0]

Well good luck on that Mao! You can move this topic I guess

[enwiabe]

Lol I can write up a solution to that, but that's first year engineering dynamics. You most DEFINITELY don't need to know how to do it.

Simple harmonic motion is governed by

x = Asin(Wnt) + Bcos(Wnt)

And the differential equation you need to model it is:

md^2x/dt + kx = 0

Rofl seriously that is like... so far off the course it isn't funny.

[enwiabe]

I just started trying to work that out and... I'm stuck. Rofl. I'll keep trying to nut it out but omg this is hard.

[cara.mel]

Don't have time to help but quickly:
Angular frequency = sqrt(k/m) = 2*pi/f, from this get m of block 2.
Then you can get total energy of block 2 from either a^2*k/2 (a = w^2*x) or finding potential energy at the end or kinetic energy at the middle by using the normal KE formula but subbing in the equation for velocity in SHM, I haven't thought about this too much yet.
Then use conservation of energy to get final v of block 1, then youre on home stretch

Note: I cant think atm and I don't guarantee I've rememered all the SHM stuff right, it's at least half-right.

[enwiabe]

Is the mass of block 2 .6 kg?

[enwiabe]

wouldn't you use conservation of momentum, not conservation of energy?

[/0]

Is the mass of block 2 .6 kg?

Yeah sorry I didn't read your question correctly, using angular momentum I get block 2 = 0.6kg.

Now I just need to know if the collision is elastic or inelastic

[dcc]

note i did this with my ruler, measuring the relative lengths of h & d

[/0]

This is what I've got to so far:







Now I've go the acceleration but I'm missing the Amplitude, but somehow I hope to get the force from this.

(sorry for taking so long to get the latex working)

[cara.mel]

Is the mass of block 2 .6 kg?

Yeah sorry I didn't read your question correctly, using angular momentum I get block 2 = 0.6kg.

Now I just need to know if the collision is elastic or inelastic

Question said elastic.

Sorry I dont have time to help

[Neobeo]

Step 1: Mass of block 2
Using formula for simple harmonic motion for mass on a spring:




Step 2: Collision of blocks
Using elastic collision formulas:






Verification step: Conservation of Energy (not required)
Since all the objects are level, (before falling off), we conveniently ignore gravitational potential energy.

Initial Energy:


Final Energy:


where

This step isn't required. It's just to check that energy is conserved to ensure no mistakes anywhere.

Step 3: Trajectory
Using linear motion formulas in the vertical direction:

[/0]

Wow neobeo! Thanks a heap!

I just don't understand how you got those momentum formulas though ? 

[Neobeo]

I just don't understand how you got those momentum formulas though ? 

Copied and pasted from the textbook . In any case http://en.wikipedia.org/wiki/Elastic_collision should be a good starting point, letting u₂ = 0.