Formula Grids · Mechanics · M-07

F = ma Newton's second law

Calculation grid60 cellsTarget: 8 min

\(F_{\text{net}} = ma\)

\(F_{\text{net}}\): net (resultant) force in N  ·  \(m\): mass in kg  ·  \(a\): acceleration in m/s²

  • Use the net force: add forces in the same direction, subtract forces in opposite directions.
  • Units are in the column and row headings, so write numbers only in the cells.

A Find the acceleration \(a\) \(a = F \div m\)  (answers in m/s²)

mass ↓  force → pull 10 N pull 20 N spring 30 N pull 50 N,
friction 20 N		 no horizontal force
1 kg
2 kg
5 kg
10 kg

Notice: Down a column, the mass doubles, so the acceleration . Compare the spring and friction columns.

B Find the net force \(F\) \(F = m \times a\)  (answers in N)

mass ↓  accel. → at rest: 0 m/s² 2 m/s² lifted up: 3 m/s² 4 m/s² 5 m/s²
1 kg
2 kg
3 kg
5 kg

Notice: “At rest” means \(F_{\text{net}}=0\), not “no forces”. For “lifted up”, \(F\) is the net force, not the string’s pull.

C Find the mass \(m\) \(m = F \div a\)  (answers in kg)

accel. ↓  force → pull 10 N pull 20 N spring 30 N pull 40 N (left) pull 50 N,
friction 20 N
1 m/s²
2 m/s²
5 m/s²
10 m/s²

Notice: Put grid C next to grid A. Which answers appear in both? Why?

Think about it Concept check · circle one answer

Concept: net force and constant velocity

1. A box is pushed along the floor at constant velocity. Which is true?

  1. push > friction
  2. net force = 0
  3. no forces act
  4. it is slowing down

Constant velocity → \(a = 0\) → \(F_{\text{net}} = 0\): push = friction. Forces still act; they cancel.

Concept: how \(a\) depends on \(m\)

2. The same net force acts on X and Y. X has twice the mass of Y. Then \(a_X\) is

  1. \(2a_Y\)
  2. \(a_Y\)
  3. \(\tfrac12 a_Y\)
  4. \(\tfrac14 a_Y\)

\(a = F/m\): with \(F\) fixed, \(a \propto 1/m\). Double the mass → half the acceleration (look down a column of grid A).

Concept: velocity vs. acceleration

3. A ball is thrown straight up. At the top, the net force on it is

  1. zero
  2. upward
  3. down, = weight
  4. down, > weight

The velocity is zero for an instant, but the acceleration is not: only gravity acts, so \(F_{\text{net}} = mg\) downward.

Formula Grids · M-07 F = ma · Set 1Calculator: not needed