The formula
- Vector form
ΣF = ma- Component form
ΣF_x = ma_x and ΣF_y = ma_y- Weight, the force of gravity on a mass
w = mg
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
ΣF | Net external force on the object | N (1 N = 1 kg·m/s²) |
m | Mass of the object | kg |
a | Acceleration, in the direction of the net force | m/s² |
w | Weight | N |
g | Acceleration due to gravity near Earth's surface | 9.80 m/s² |
When it applies
- Mass stays constant and speeds are far below the speed of light. A rocket burning fuel needs the momentum form instead.
- Count external forces only. Forces between parts inside the system cancel in pairs.
- Work in components. One vector equation becomes one scalar equation per direction, which is what makes inclines and pulleys tractable.
Worked example
Problem. A 5.0 kg box is pushed horizontally with a 20 N force while friction resists with 8.0 N. What is its acceleration?
- List the forces along the direction of motion: 20 N forward and 8.0 N of friction backward. Vertically the weight and the normal force cancel.
- Find the net force: ΣF = 20 - 8.0 = 12 N forward.
- Apply the second law: a = ΣF / m = 12 N / 5.0 kg.
- a = 2.4 m/s², in the direction of the push.
Answer. 2.4 m/s² in the direction of the push.
Common mistakes
- Using the applied force where the net force belongs.
- Substituting mass where weight is needed. A 5.0 kg box weighs 49 N.
- Expecting a constant force to give a constant velocity. A constant net force gives a constant acceleration.
- Putting an action and reaction pair on the same free-body diagram. Those two forces act on different objects and never cancel for one of them.
Related formulas
- Kinematics equations:
v = v₀ + at - Tension formula:
T = mg - Centripetal force formula:
F_c = mv² / r