Question

When you stand with bare feet in a wet bathtub, the grip feels fairly secure, but yet a catastrophic slip is quite possible?

With the help of a suitable graph of force versus time, briefly explain this phenomenon in terms of the two coefficients of friction.

Answer 1

I wasn’t expecting the sting in the tail, but it should be possible!

Explanation:

First the words, then we’ll build a graph (may need to be a photo of a sketch.)

When you stand upright in the bath your feet exert sufficient pressure to exclude the vast majority of the water, leaving a very good seal between skin and bathtub, hence the static friction is surprisingly high.

Once you lift a foot, or even tilt the foot, you allow a layer of water to enter between the two surfaces and the friction falls dramatically and suddenly.

I’d guesstimate the static friction to be about 0.7 (similar to a road when wearing shoes) and the dynamic friction to be 0.1 to 0.01 (similar to ice.) The transition time is certainly below 0.25 sec (average reaction time is around here.)

I’ll now attempt a sketch...

Hope this helps, sorry it’s not very specific. You could try looking up better coefficients here:

https://www.engineeringtoolbox.com/friction-coefficients-d_778.html