Forces: Complete A Level H2 Physics Cheatsheet
A Level Physics (H2), Chapter 4 · Read time: ~10 minutes
Key Formulas
Free-body diagrams and types of force
A free-body diagram shows every force acting on a single object, weight, normal contact force, tension, friction, upthrust, viscous drag/air resistance, drawn as arrows starting from that object.
It must NOT include any force the object exerts on something else, only forces acting on the object being analysed.
Trap: A common transition error from O Level: including a Newton's Third Law pair force that belongs to a *different* object in the free-body diagram of the object being studied. If a book rests on a table, the book's free-body diagram shows the table's normal reaction on the book, not the book's weight pressing down on the table, that force acts on the table, not the book.
Conditions for equilibrium
Translational equilibrium: the vector sum of all forces on an object is zero. In practice, resolve every force into perpendicular components and require each direction's components to sum to zero separately.
Rotational equilibrium: the sum of clockwise moments about any point equals the sum of anticlockwise moments about the same point (the Principle of Moments).
A rigid, extended object is only fully in equilibrium when both conditions hold. Zero resultant force alone does not rule out the object spinning.
Trick: For exactly three coplanar forces in equilibrium, they form a **closed triangle** when drawn head-to-tail (since they sum to zero). Sketching this triangle and applying the sine rule is often faster than resolving into x- and y-components algebraically.
Hooke's Law and elastic behaviour
Hooke's Law: extension is directly proportional to the applied force, F = kx, valid only up to the limit of proportionality. k is the force constant (or spring constant), in N/m.
Beyond the elastic limit, deformation becomes permanent (plastic), the object no longer returns to its original length once the force is removed.
The elastic potential energy stored equals the area under a force-extension graph. Within the Hooke's Law region, this area is a triangle, giving the shortcut E = ½Fx = ½kx².
Trap: ½kx² only works while the force-extension graph is a straight line through the origin. If the extension goes beyond the limit of proportionality, the graph curves, and the energy stored must be found from the actual area under that curved graph, not the shortcut formula.
Worked Example
A spring of natural length 20.0 cm and force constant 50 N/m hangs vertically from a fixed support. A mass of 250 g is attached to the free end and hangs in equilibrium. Take g = 9.81 N/kg.
(a) Calculate the weight of the mass. [1]
W = mg
= 0.250 × 9.81
= 2.45 N
(b) Calculate the extension of the spring when the mass hangs in equilibrium. [2]
Since the mass hangs in equilibrium, the spring's tension force equals its weight: F = 2.45 N
F = kx, so x = F / k
= 2.45 / 50
= 0.049 m (4.9 cm)
(c) Calculate the elastic potential energy stored in the spring at this extension. [2]
E = ½kx²
= ½ × 50 × (0.049)²
= 0.060 J
Why this question is a good test of the topic: knowing F = kx isn't enough on its own, the question only becomes solvable once you recognise that 'hangs in equilibrium' is what tells you the spring's tension force must exactly equal the mass's weight, linking this chapter's equilibrium condition to Hooke's Law.
Frequently Asked Questions
What must a free-body diagram include?
Only the forces acting on the object being studied, never a force that object exerts on something else.
What are the two conditions for an object to be in equilibrium?
Zero resultant force (translational equilibrium) and zero resultant moment (rotational equilibrium).
What is Hooke's Law and when does it stop applying?
F = kx, extension is proportional to applied force, valid only up to the limit of proportionality. Beyond that, the force-extension relationship is no longer linear.
How do I find the elastic potential energy stored in a spring?
It's the area under the force-extension graph. Use ½kx² only if that graph is a straight line through the origin, i.e. within the Hooke's Law region.
Which paper is this tested in?
Paper 1 MCQs often test free-body diagrams and Hooke's Law graphs. Paper 2 and Paper 3 typically include a full equilibrium, moments, or elastic energy calculation similar to the worked example above.
Free-body diagrams and equilibrium conditions feeling shaky?
Small group A Level H2 Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, taught by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author.