Newton's laws of motion
Newton's laws
- The key law: resultant force = mass × acceleration:
$$F = ma$$
- Weight is the force of gravity: $W = mg$ (take $g = 10\,\text{m s}^{-2}$).
- Forces include weight, friction, tension in a string, and the push in a rod.
Practice
A resultant force gives a 5 kg mass an acceleration of 2 m/s². What is the force (F = ma), in N?
F = ma = 5 × 2 = 10 N.
Practice
Taking g = 10 m/s², what is the weight of a 2 kg object (W = mg), in N?
W = mg = 2 × 10 = 20 N.
Slopes and connected particles
- On an inclined plane: split forces along and perpendicular to the slope, then apply $F = ma$ along the slope.
- For connected particles (joined by a string): apply $F = ma$ to each body, or to the whole system.
Practice
To analyse motion on an inclined plane, you should:
Resolve along the slope (apply F = ma there) and perpendicular to it (for the normal reaction).
You've got it
Key idea
- F = ma; weight $W = mg$
- on a slope, resolve forces along and perpendicular to the slope
- for connected particles, apply $F = ma$ to each body or the whole system