Problem — Ranking Accelerations

Problem

Ranking. Three blocks lie on identical frictionless surfaces. A horizontal force acts on each. (A) Mass $2\;\text{kg}$, force $6\;\text{N}$. (B) Mass $1\;\text{kg}$, force $5\;\text{N}$. (C) Mass $4\;\text{kg}$, force $4\;\text{N}$. Rank the accelerations from smallest to largest.

Solution

Step 1 — Rule. The surfaces are smooth, so the only horizontal force is the applied one and $a = F/m$. There is no need to compute everything precisely: it is enough to compare the ratios $F/m$.

Step 2 — Computing the ratios.

$a_A = \frac{6\;\text{N}}{2\;\text{kg}} = 3\;\text{m/s}^2 \qquad a_B = \frac{5\;\text{N}}{1\;\text{kg}} = 5\;\text{m/s}^2 \qquad a_C = \frac{4\;\text{N}}{4\;\text{kg}} = 1\;\text{m/s}^2$

Step 3 — Ranking. From smallest to largest: $a_C = 1 < a_A = 3 < a_B = 5$.

$\ev{C < A < B}$

Note that the block with the largest force (A, $6\;\text{N}$) is not the one with the largest acceleration: what matters is the ratio of force to mass, not the force alone.

Links

Topics: Dynamics Concepts: Newton’s second law Skills: Ranking reasoning