True or false on acceleration, velocity and friction

Problem

True or false?

• (a) In uniform circular motion the acceleration is zero.
• (b) In uniform circular motion the velocity changes direction but not magnitude.
• (c) Static friction can take any value between zero and $\mu_s N$.
• (d) Kinetic friction depends on speed.

Solution

(a) FALSE. In uniform circular motion the magnitude of the velocity is constant, but its direction keeps changing. Since $\vec a = \dd\vec v / \dd t$, a vector that changes direction has a non-zero derivative. The acceleration exists and is centripetal, of magnitude: $a_c = \frac{v^2}{r}$ directed towards the centre. Only the tangential component (which would change the magnitude of $v$) is zero.

(b) TRUE. This is precisely the definition of uniform circular motion: the velocity is a vector tangent to the path, with constant magnitude $v$ but a rotating direction. The change of direction is what requires the centripetal acceleration of point (a).

(c) TRUE. Static friction is an adaptive force: it takes exactly the value needed to prevent sliding, from $0$ (no tangential stress) up to the maximum value $f_{s,\max} = \mu_s N$. Only when the stress exceeds $\mu_s N$ does the body start to move. So $0 \le f_s \le \mu_s N$ holds.

(d) FALSE. Kinetic friction has (approximate) magnitude $f_d = \mu_d N$, independent of the magnitude of the sliding speed. It depends on the pressing force $N$ and on the materials in contact, not on how fast the body is sliding.

$\ev{\text{(a) F} \quad \text{(b) T} \quad \text{(c) T} \quad \text{(d) F}}$

Links

Topics: Dinamica · Attrito Concepts: Moto circolare uniforme · Accelerazione centripeta · Attrito statico · Attrito dinamico