Question #eae36

1 Answer
Feb 20, 2017

Answer:

The acceleration is #a=gsintheta#

Explanation:

The forces acting on the pendulum will be #vecF_g# and #vecT#, this second being the tension in the cord.

webassign.net/labsgraceperiod/ncsulcpmech2/lab_7/manual.html

As the diagram shows, we can resolve #vecF_g# into two components, namely #mgsintheta# and #mgcostheta#.

Because the rope does not stretch, it must be that #T=mgcostheta#, and these forces cancel.

Therefore, the net force acting on the pendulum is the "restoring force", #mgsintheta#

From Newton's second law

#F_"net" = mgsintheta#

#ma = mgsintheta#

and finally,

#a=gsintheta#

If you prefer, you can express the acceleration as an angular acceleration:

#alpha=a/L#

in which case the angular acceleration of the pendulum bob, moving in a circular arc, is

#alpha=g/L sintheta#