Newton's three laws of motion, weight and the relationship between mass and force, resolving forces, friction and the coefficient of friction, and connected particles.

What this dot point is asking

Edexcel wants you to apply Newton's three laws of motion, use $F = ma$, work with weight $W = mg$, resolve forces into components, handle friction using $F \le \mu R$ and the limiting case, and analyse connected particles such as masses joined by a string over a pulley.

The answer

Newton's laws

Newton's first law says a body stays at rest or moves at constant velocity unless a resultant force acts. The third law says that if body $A$ exerts a force on body $B$, then $B$ exerts an equal and opposite force on $A$.

Resolving forces

Forces are resolved into perpendicular components, often horizontal and vertical or along and perpendicular to a slope. The body is in equilibrium when the resultant in each direction is zero, and accelerates when there is a non-zero resultant.

Friction

Connected particles

For two masses joined by a light inextensible string over a smooth pulley, write $F = ma$ for each mass using the same acceleration magnitude and the same tension, then solve the simultaneous equations. The string being inextensible is what forces both masses to share the same acceleration magnitude $a$, and the pulley being smooth is what forces the tension $T$ to be the same on both sides. If you let go of either assumption the two equations stop being coupled and the method collapses, so always state them.

A strategy for any force problem

The same routine handles almost every Edexcel forces question. First, draw a clear diagram and mark every force: weight $mg$ downward, the normal reaction $R$ perpendicular to the surface, any applied force, tension along strings, and friction opposing the direction of (attempted) motion. Second, choose convenient perpendicular directions to resolve in. On a slope it is almost always cleanest to use along-the-slope and perpendicular-to-the-slope rather than horizontal and vertical. Third, resolve perpendicular to the motion to find the normal reaction $R$, since that direction is usually in equilibrium. Fourth, write $F = ma$ along the direction of motion. Solving these gives the unknown.

Examples in context

Try this

Q1. A force of $12$ N acts on a $3$ kg mass on a smooth surface. Find the acceleration. [2 marks]

• Cue. $a = \dfrac{F}{m} = \dfrac{12}{3} = 4$ m per second squared.

Q2. A $5$ kg block on a rough horizontal surface has $\mu = 0.4$. Find the maximum friction. Take $g = 9.8$. [3 marks]

• Cue. $R = mg = 49$ N, so $F = \mu R = 0.4 \times 49 = 19.6$ N.