Friction — Question 3

Question 3

Zero acceleration does not identify the friction regime

A 2 kg sled is pulled right with 5 N and has zero acceleration. The supporting belt can move independently. Three possible observations are listed below; in every case the ground-frame sled velocity is +2 m/s. There are no other horizontal forces.

1. Find friction in every dynamically possible case.

2. Classify friction for cases A and B.

3. Explain why case C cannot satisfy all the stated observations under ordinary sliding friction.

Question 3 - Solution

Zero acceleration does not identify the friction regime

(a) Use the measured acceleration.

For any dynamically admissible case, $$\sum F_x=P+f=ma=0\Longrightarrow\boxed{f=-5\ \mathrm N}.$$ The required friction is leftward; the contact regime must also permit that direction.

(b) Compare contact velocities.

The two admissible relative velocities are $$v_{{\mathrm{rel}},A}=2-2=0,\qquad v_{{\mathrm{rel}},B}=2-0=+2\ \mathrm{m/s}.$$ A permits static friction $f_s=-5$ N if $f_{s,\max}\geq5$ N. B requires kinetic friction $f_k=-5$ N to balance the pull.

(c) Check the direction in C.

For C, $$v_{{\mathrm{rel}},C}=2-4=-2\ \mathrm{m/s}\Longrightarrow f_k>0.$$ Consequently $a=(5+f_k)/2>0$, contradicting the measured $a=0$. Ordinary sliding friction cannot satisfy all of case C’s observations.