# How far can the ant walk before slipping off the record?

by cdornz
Tags: centripetal, friction, record
 P: 40 1. The problem statement, all variables and given/known data A 1-mg ant is located near the center of a horizontal record (radius = 7 inches) which is rotating at 78rpm. The coefficient of friction between the ant and the record is 0.7. How far out towards the edge of the record can the ant walk before it will slip? 2. Relevant equations circumference = d$\Pi$ ΔV = circumference * rpm Fcentripetal = m(v2/r) $\Sigma$F=ma 3. The attempt at a solution I got all of my numbers into lowest form/metric units. So the radius is 0.1778 meters; rpm is now 78/60 or 1.3 rev/sec Circumference = 0.3556$\Pi$; circumference = 1.11 meters Velocity = 1.11/1.3; velocity = 1.45 m/s I then listed the forces involved: Fcentripetal; Fn; Fgravity; Ffriction I setup my free body diagram like this picture attached I can then do the forces in the x direction (cosine) and the forces in the y direction (sin). My question for now, is if I get a number for x and y, how will that tell me how long until the ant slips? We've never covered a question like this in my physics class before. Attached Thumbnails