Recent content by Rippling Hysteresis

OK thanks for the tips! I was rushing a little with typing, so I'll check the signs. Appreciate it.

1) Car 1 is going 22.2 m/s and car 2 is -22.2 m/s, but the zero momentum frame is moving -9.9, so v1=-32.1 m/s, v2= 12.3 m/s w.r.t. the zero momentum frame 2) This might be where I'm getting confused. I would think here is where we say Integral (F dt ) = m*delta_v. Since F=ma is constant...

Oh right, it is supposed to be around 850, not 950. Erg. Which step am I going wrong in if I go down that path then? I had 1.2F =387000, so for car 1, a =387,000/(1.2*540) = 597 Then I'm getting t=m*delta_v * x /W. So for car 1 that's 540* (-32.1)((0.6)/387000 = 0.2687. From there...

Hmm, good point! I would imagine I need to do something like F_net = F_crumpling + F_elastic, which is why the suggestion for the second approach probably involved time. I still get some wonky numbers, but perhaps it's closer. Or maybe my equation is wrong for force, but I see what you mean...

80km/h = 22.2 m/s Through momentum: 1940(v_f) = 540 (22.2) + (1400)(-22.2) => v_f = -9.84 m/s I figured the work that the energy lost in a collision is equal to the work done to crumple the cars. So W = K_i - Kf = [1/2 (540)(22.2)^2 + 1/2(1400)(-22.2)^2] - 1/2(1940)(-9.84)^ 2 = 384110 J At...

⋅ Thanks for your patience. It's still a challenge for me to make sense of proofs in concrete terms-- work in progress. I went back earlier into the lecture and see now how (after computing the cross product) the binormal vector must be (0,0,1) in this particular case. The trouble all...

So would the α(s) (a circle) I've chosen be wrong or would it be the vector (1/sqrt(2)(1,1,0). It seems like the vector is constant and the circle has zero torsion which is what I'm hung up about. The proof makes sense, but there's a disconnect with a specific example. And further, I can see...

Couldn't the vector also be v= (1/sqrt(2), 1/sqrt(2), 0), which then wouldn't equal a constant? So the dot product would be 1/sqrt(2)(cos(t) + sin(t)). Or perhaps that choice of v violates a rule?

The lecturer has used α(s) in the past to be any curve in R^3. I'm not sure why dotting that curve with a constant value represents a plane. I can see how the dot product will equal a scalar constant, but think of a plane as something as ax+by+cz=d, but am having trouble envisioning that from...

I was watching a lecture that made the conclusion about the torsion being equal to zero necessitated that the path was planar. The argument went as follows: -Torsion = 0 => B=v, which is a constant -(α⋅v)'=(T⋅v)'= 0 => α⋅v= a, which is a constant (where α is a function describing the path and...

Thanks! I will check those links out. Might be cool to tackle some.

Thanks for your reply. In past searches I have found a lot of basic problems (calculate the line integral of this function, use the divergence theorem to solve some integral, take the cross product of these vectors). Rarer finds seem to be the sets that have less obvious paths forward. I did...

I've taken multivariable/vector calc and can do most of the basic operations and have an OK understanding of the fundamental concepts, but certainly can't "see it" like I can calc I and II. In those subjects, I often feel competent to take on any problem I come across because the concepts are...

OK cool! So I see it this way then: If z=r, it simplifies to r^k(e^(r^2)-1)/(4r^(2k). Using the expansion e^(r^2) ≈ 1 +r^2, we get the expression to become r^2/(4r^(2k)= 1/4(r^(2-k), where as long as 2-k>0, the limit is zero.

Wait, now I'm doubting myself and thinking I made a mistake with the z=0, r -> 0 part. Won't the numerator actually become 0(e^(r^2)-1)/r^(2k), which is again 0 and independent of k?