Newton’s Second Law

\sum F = m a = m v ˙

The resultant force on a particle equals mass times acceleration of the mass center. Weight is mg; mass is not weight. In US customary, W = mg with g = 32.2 ft/s², so m = W/g slugs.

$m$ (kg or slug): Mass
$a$ (m/s²): Acceleration of the mass center

Step-by-step solved example

A 1500 kg vehicle on level ground needs 3 m/s². Ignoring drag, required tractive force?

ΣF = ma: the resultant of the force polygon accelerates the mass.

1. Apply ΣF = ma
F = 1500 × 3 = 4500 N = 4.50 kN.
$F = 4.50 kN$

Answer: 4.50 kN

10 practice questions

0/10 correct

1.Force to accelerate 80 kg at 2.5 m/s² is

2.A 3220 lb car (g = 32.2 ft/s²) has mass

3.On a 30° frictionless incline, a =

4.If net force is zero, acceleration is

5.Weight of 10 kg at g = 9.81 is

6.Elevator accelerating upward at 2 m/s², 70 kg passenger apparent weight

7.Circular motion at constant speed still needs

8.Two masses 4 kg and 6 kg connected over a frictionless pulley (Atwood): a =

9.Impulse equals

10.A 0.2 kg ball, Δv = 40 m/s in 0.01 s: average force