Newton's laws of motion

The law that launched rockets

• Every rocket, every car, every falling apple obeys the same rule: $F = ma$.
• Newton's second law is the foundation of all mechanics. Master it and you can predict the motion of anything.

Newton's second law

• The key law: resultant force 合力 = mass × acceleration:

• Weight 重力 is the force of gravity: $W = mg$ (take $g = 10\text{ m s}^{-2}$).
• Forces include weight, friction, tension 张力 in a string, and the push in a rod.

Slopes and inclined planes 斜面

• On an inclined plane: split forces along and perpendicular to the slope, then apply $F = ma$ along the slope.
• Component of weight along slope: $mg\sin\theta$. Component perpendicular: $mg\cos\theta$.

Connected particles 连接质点

• For connected particles (joined by a string): apply $F = ma$ to each body, or to the whole system.
• The string has the same tension throughout (if light and inextensible 不可伸长).
• Both bodies have the same acceleration.

Connected particles share one tension T and one acceleration; apply F = ma to each mass.

Worked example — connected particles

• A 3 kg and 2 kg mass are connected by a light string over a smooth pulley. Find the acceleration.
• For the 3 kg mass (moving down): $3g - T = 3a$.
• For the 2 kg mass (moving up): $T - 2g = 2a$.
• Adding: $3g - 2g = 5a \Rightarrow a = \dfrac{g}{5} = 2\text{ m s}^{-2}$.
• Newton's laws of motion give $F=ma$; forces may include thrust and air resistance.

You've got it

Write from an acceleration of 3 metres per second squared

• A resultant force of 18 N acts on a 6 kg body.
• Find the acceleration.