Problem — True or False on Forces and Motion

Problem

True or false, with justification: (a) if no forces act on a body, it is necessarily at rest; (b) the forces of the third law act on the same body; (c) the weight of a body changes on the Moon, but its mass does not; (d) static friction always has magnitude $\mu_s R$.

Solution

(a) False. The first law states that, in the absence of forces (or with zero net force), a body maintains its state of motion: if it was at rest it stays at rest, but if it was moving it continues in uniform straight-line motion, with constant speed, direction and orientation. The state of rest is only a special case, the one with zero velocity. So “no force” does not imply “at rest”.

(b) False. The two forces of an action–reaction pair act on different bodies: if body A exerts a force on body B, body B exerts an equal and opposite force on A. Precisely because they are applied to distinct bodies, they never add up on the same body and never “balance” one another.

(c) True. Mass measures the amount of matter and is an intrinsic property of the body: it does not change when moving from one planet to another. Weight, on the other hand, is the gravitational force $P = m\,g$, which depends on the local acceleration of gravity. On the Moon $g_{\text{L}} \approx 1{,}6\;\text{m/s}^2$, about a sixth of the terrestrial value, so the weight becomes about a sixth as well, while the mass stays exactly the same.

(d) False. Static friction is a variable force: it adapts to the applied force to keep the body at rest, taking the value required for equilibrium. It can therefore range from zero up to a maximum, $f_s \le \mu_s R$. The quantity $\mu_s R$ represents only the maximum value, reached at the instant immediately before the body starts to slip (a body “on the verge of slipping”).

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

Links

Topics: Dynamics Concepts: First law of dynamics · Newton’s third law · Weight force · Static friction