What force does work on a ball as it is rotating down an inclined plane? Explain why the other forces the ball experiences do not do work.
I think the ball experiences gravitational, normal, and frictional forces. Is the force that actually does work on the ball just gravity? I'm having a...
Thank you very much. I solved for T in terms of the point that is 0.030 m from the center of the disc, then plugged that value into find the centripetal acceleration at the point that is 0.050 m from the center of the disc.
The numbers worked out very nicely and it came out to be 200 m/s2...
Homework Statement
A computer is reading data from a rotating CD-ROM. At a point that is 0.030 m from the center of the disc, the centripetal acceleration is 120 m/s2. What is the centripetal acceleration at a point that is 0.050 m from the center of the disc?
Homework Equations
ac =...
Homework Statement
The escalator that leads down into a subway station has a length of 30.0 m and a speed of 1.8 m/s relative to the ground. A student is coming out of the station by running in the wrong direction on this escalator. The local record time for this trick is 11 s. Relative...
Homework Statement
A ball is dropped from rest from the top of a building and strikes the ground with a speed vf. From ground level, a second ball is thrown straight upward at the same instant that the first ball is dropped. The initial speed of the second ball is v0 = vf, the same speed...
Would these intervals be correct?
Clockwise for t: (-\infty, \frac{1}{6})
Counter-clockwise for t: (\frac{1}{6}, \infty)
\frac{1}{6} is not included in the interval because the derivative of u (see below) is 0 at that point, so it is neither increasing nor decreasing. Right...
Homework Statement
For what values of p does the following integral converge or diverge?
\int^{\infty}_{2}\frac{dx}{x[ln(x)]^{p}}
The Attempt at a Solution
I have graphed y=\frac{1}{x[ln(x)]^{p}} for different values of p (negative, zero, positive), and it looks as though in all...
Homework Statement
Consider the parameterization of the unit circle given by x=cos(3t^{2}-t), y=sin(3t^{2}-t) for t in (-\infty,\infty).
In which intervals of t is the parameterization tracing the circle out in a clockwise direction?
In which intervals of t is the parameterization tracing...
I have attached my work with this post. I felt that I was heading in the right direction, but obviously I must have done something wrong near the beginning I would assume, since by the end I found that my integral diverged.
Homework Statement
Calculate \frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}x^{2}e^{-\frac{x^{2}}{2}}dx
Use the fact that \int^{\infty}_{-\infty}e^{-\frac{x^{2}}{2}}dx=\sqrt{2\pi}
Homework Equations
I'm assuming that integration by parts is the best way to solve this...
I also do not know many of the answers and am interested in what you find. Make sure to post your answers once you get them. It would make for a very interesting read.