Friction — Question 9

Question 9

A friction force can be inferred from motion without knowing a coefficient

A 2 kg puck slides right on a stationary horizontal surface. A force of 3 N acts left. At one instant the measured acceleration is 4 m/s$^2$ left. No other horizontal interaction acts.

1. Infer friction at that instant.

2. Find the reaction force exerted by the puck on the surface.

3. A second report gives acceleration 1 m/s$^2$ right with the same rightward slip and applied force. Can ordinary friction explain it?

Question 9 - Solution

A friction force can be inferred from motion without knowing a coefficient

(a) Use a signed force balance.

Take right positive and use the measured acceleration: $$-3+f=2(-4)\Longrightarrow\boxed{f=-5\ \mathrm N}.$$ The inferred 5 N leftward force agrees with kinetic friction opposing rightward slip.

(b) Reverse agent and recipient.

The tangential third-law pair is $$\vec f_{\mathrm{floor\to puck}}=-5\hat{\mathbf i}\ \mathrm N,\qquad\boxed{\vec f_{\mathrm{puck\to floor}}=+5\hat{\mathbf i}\ \mathrm N}.$$ The applied 3 N force is a separate interaction, not this force’s reaction partner.

(c) Audit signs before fitting parameters.

The alternative acceleration would require $$-3+f=2(+1)\Longrightarrow f=+5\ \mathrm N.$$ But rightward sliding on a stationary floor requires $f_k\leq0$. The positive inferred force contradicts ordinary kinetic friction; an observation or the force inventory must change.