Calculator · Engineering Mechanics
Newton's Second Law Calculator
ΣF = m·a for a planar point particle. Each mode solves for exactly one unknown; nothing is inferred from an inconsistent set of values.
Solve for
Known values
A particle mass must be greater than zero.
Applied forces
F1
F2
The forces are summed with the same resultant routine used by the Statics tools, then divided by the mass.
Results
| Resultant force ΣF | (6, 8) N |
|---|---|
| |ΣF| | 10 N |
| Direction of ΣF from +x | 53.13° |
| Mass m | 2 kg |
| Acceleration a | (3, 4) m/s² |
| |a| | 5 m/s² |
| Direction of a from +x | 53.13° |
Technical reference
ΣF = m·a
- ΣF
- vector resultant of every applied force[N]
- m
- particle mass, m > 0[kg]
- a
- acceleration of the particle[m/s²]
Valid in an inertial reference frame with constant mass. When solving for acceleration, ΣF is the vector sum of every listed force, computed with the same resultant routine as the Statics tools. Solving for mass uses |ΣF|/|a| and only applies when ΣF and a are parallel; a warning is shown otherwise.
Assumptions
- · Point particle: ΣF = m·a with no moment equation and no rotation.
- · The mass is strictly positive; a zero or negative particle mass is rejected.
- · Solving for the mass uses |ΣF|/|a| and warns when ΣF and a are not parallel.
- · A zero resultant means constant velocity, not a stationary particle.
Continue
Open in Particle Motion Lab
The same mass and forces as a dynamic particle model, starting from rest at the origin.