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Problem 3.34

3.34. a)

b)

The components given in the tex2html_wrap_inline415 and tex2html_wrap_inline417 directions can be summed together and the resultant is given by

tex2html_wrap_inline419

at an angle of

tex2html_wrap_inline421 above the negative x axis.

Now, to find the radial component of this acceleration vector, we first need to find the angle that the resultant vector makes with the string on which the pendulum is swinging. This is given by subtracting the angle found for our resultant acceleration, tex2html_wrap_inline423 and the angle that the pendulum makes with the vertical, tex2html_wrap_inline425 from tex2html_wrap_inline427 . We then find that this angle is tex2html_wrap_inline429 . Now, to find the radial component of the acceleration we cn simply use vector decomposition.

tex2html_wrap_inline431

c)

To find the velocity of the ball, we can just use our equations for circular motion.

tex2html_wrap_inline433 at tex2html_wrap_inline435 above the x axis. (Tangent to the circle)



Jason George Zeibel
Fri Sep 26 03:10:45 EDT 1997