Recent content by andyfeynman

Homework Statement A uniform solid sphere of radius R rolls without slipping at velocity V on a level surface. It collides with a step of height h. Assume that after the collision, the sphere maintains contact with the step at point A with no slipping. Find the minimum value of V for the...

Homework Statement I'm doing the lab report questions for the centripetal force experiment using this apparatus: ftp://ftp.pasco.com/Support/Documents/english/ME/ME-8088/012-08478B.pdf. One of the lab questions asks whether using a larger "free mass" reduces the percentage error. Homework...

Homework Statement Suppose the sequence (xn) satisfies |xn + 1 - xn| < 1/n2, prove that (xn) is convergent. Homework Equations |xn - xm| < ɛ The Attempt at a Solution If m > n, then |xn - xm| < |xn - xn + 1| + |xn + 1 - xn + 2| + ... + |xm - 1 - xm| < 1/n2 + 1/(n+1)2 + ... + 1/(m - 1)2 <...

Just forgot it. I made a very stupid mistake. But I came up with the idea of letting bk = 21/k - 1. This means bk2 < 4[k(k-1)] for all k > 2. Therefore, xn = 1 + b22 + ... + bn2 < 1 + 4/[1(2-1)] + ... 4/[n(n-1)] = 1 + 4(1 - 1/2) + ... + 4[1/(n-1) - 1/n] = 5 - 4/n < 5 Since xn is monotone...

Homework Statement Show that the sequence {xn}: xn := (21/1 - 1)2 + (21/2 - 1)2 + ... + (21/n - 1)2 is convergent. Homework EquationsThe Attempt at a Solution If n > m, |xn - xm| = (21/n - 1)2 + (21/(n-1) - 1)2 + ... + (21/(m+1) - 1)2 < (21/n)2 + (21/(n-1))2 + ... + (21/(m+1))2 < (21/(m+1))2 +...

Thank you so much :smile:

Yes, I forgot that anything moving should be subject to kinetic friction, not static. So it should be m accelerates while 3m stays at rest?

This is what I thought: If the tension is larger than the maximum static friction of m but not of 3m, then only m would accelerate but 3m would stay unaccelerated.

Wow! I just notice how similar this problem is to Kleppner & Kolenkow 2.15. At least now I can be sure T is indeed 6/7(μk + 1)mg for case (2).

Homework Statement In the machine shown in the attached picture, all pulleys have negligible mass and rotational inertia. The coefficient of static friction μs between the table and either mass is larger than the coefficient of kinetic friction μk. The two masses 3m and m originally were held...