Problem — Box pushed without friction

Problem

A box of mass $m = 4{,}0\;\text{kg}$ is pushed across a frictionless floor by a horizontal force $F = 10\;\text{N}$. Find the magnitude of the acceleration.

Solution

Step 1 — Forces at play. The floor is frictionless, so the only horizontal force acting on the box is the push $F$. Vertically, weight and normal reaction balance and do not affect the horizontal motion.

Step 2 — Newton’s second law. Along the direction of motion the net force coincides with $F$, so

$F = m\,a \quad\Longrightarrow\quad a = \frac{F}{m}$

Step 3 — Numerical substitution.

$a = \frac{10\;\text{N}}{4{,}0\;\text{kg}} = 2{,}5\;\text{m/s}^2$

$\ev{a = 2{,}5\;\mathrm{m/s^2}}$

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Topics: Dinamica Concepts: Seconda legge di Newton · Accelerazione