Friction — Question 5

Question 5

A block can stop and remain stopped under a continuing pull

A 2 kg block initially slides left at 3 m/s on a fixed floor. A constant 4 N force pulls right. Kinetic friction has magnitude 6 N; static friction can be at most 8 N. Take right as positive.

1. Find acceleration until the block first stops.

2. Find stopping time and displacement.

3. Determine what happens immediately afterward; explain why extending the first acceleration is invalid.

Question 5 - Solution

A block can stop and remain stopped under a continuing pull

(a) Use the current slip direction.

Initially $v_x<0$, so kinetic friction acts right. Thus $$F_{\mathrm{net}}=4+6=10\ \mathrm N,\qquad\boxed{a_x=10/2=+5\ \mathrm{m/s^2}}.$$

(b) End this phase at zero velocity.

Use the sliding acceleration only until the first zero of velocity: $$0=-3+5t_s\Longrightarrow\boxed{t_s=.60\ \mathrm s},$$ $$\boxed{\Delta x=-3(.60)+\tfrac12(5)(.60)^2=-.90\ \mathrm m}.$$

(c) Test the rest constraint.

At rest the necessary static force is $$4+f_s=0\Longrightarrow f_s=-4\ \mathrm N,\qquad |f_s|=4<8\ \mathrm N.$$ The block remains at rest: $\boxed{a=0}$. Extending $a=5$ beyond the stop incorrectly retains a kinetic-friction law after sliding has ceased.