Calculating Force on a Rat Attached to a Spinning Rod: Physics Homework Solution

[mybrohshi5]

Homework Statement

A wooden rod of negligible mass and length 77.0 cm is pivoted about a horizontal axis through its center. A white rat with mass 0.480 kg clings to one end of the stick and a mouse with mass 0.180 kg is placed at the other end of the rod (the end away from the rat), and the system is released from rest with the rod horizontal.

what is the magnitude of the force on the rat by the rod as the rod swings through a vertical position?

Since the spin rate of the rod will be maximum as it swings through a vertical position, therefore the tangential acceleration of the rat (at that location) will be zero.

Homework Equations

f=ma
conservation of energy

The Attempt at a Solution

First off i thought since it is the force when it is swinging through the vertical it should be 0, but that is incorrect :(

From an early part of the question i had to find the speed of the mouse and the rat.
v = 1.85 m/s

so i thought maybe i should use this to find acceleration and then use f=ma

v_f²=2ad

1.85²=2a(.77/2)

a = 4.445 m/s²

then...

f = 0.480(4.445)

f = 2.1335 N

I have a feeling this is wrong though. Can anyone confirm that this is right or tell me where i am going wrong?

Thank you

 

[mybrohshi5]

I just checked and that is wrong :(

I thought maybe the distance traveled instead of .77/2 was 1/4 the circumference of a circle so i tried using 1/2pi(.77/2) but that does not work either.

any suggestions?