A 10 kg box sits on a horizontal table. A person pushes DOWN on the box with an additional 20 N of force. What is the normal force on the box? (g = 9.8 m/s²)
A98 N — just the weight, since the normal force always equals mg
B78 N — the applied force partially replaces the normal force
C118 N — the normal force must balance both gravity and the applied downward force
D20 N — the normal force only balances the externally applied force
The box has zero vertical acceleration, so the net vertical force is zero: N − mg − F_applied = 0, giving N = mg + F = (10)(9.8) + 20 = 118 N. The normal force adjusts to balance ALL downward forces. Option A is the classic misconception: N = mg only when weight is the sole downward force. The normal force is a constraint force, not a fixed law.
Question 2 Multiple Choice
A student says: 'The normal force equals mg whenever the object is not accelerating vertically.' What is wrong with this reasoning?
ANothing — Newton's Second Law requires N = mg whenever vertical acceleration is zero
BZero vertical acceleration means net vertical force is zero, but other vertical forces (a hand pushing down, a rope pulling up) also contribute; N adjusts to balance all of them, not just weight
CThe object could be accelerating horizontally even if N = mg, making the statement incomplete
DThe student forgot to include the object's mass in the calculation
Zero acceleration means the NET force is zero — not that only weight and normal force are present. If a string pulls up with tension T, then N + T − mg = 0, so N = mg − T. If a hand pushes down with force F, then N = mg + F. The normal force compensates for ALL other forces in the perpendicular direction. Setting N = mg as a rule ignores every other possible force.
Question 3 True / False
On a frictionless 30° inclined plane, the normal force on a block is less than the block's weight mg.
TTrue
FFalse
Answer: True
On an incline, the normal force balances only the component of gravity perpendicular to the surface: N = mg·cos(θ). Since cos(30°) ≈ 0.87 < 1, the normal force is less than mg. The remaining component mg·sin(30°) acts along the surface and — with no friction — accelerates the block down the slope. The normal force cannot act along the surface, so it cannot prevent this motion.
Question 4 True / False
The normal force is a fundamental force of nature with its own governing law, like gravity or electromagnetism.
TTrue
FFalse
Answer: False
The normal force is a constraint force — it takes whatever value is required to prevent two objects from occupying the same space. It has no governing law of its own: its magnitude is determined by Newton's Second Law applied in the perpendicular direction, given all other forces. At the microscopic level, it arises from electromagnetic repulsion between electron clouds, but in classical mechanics it is treated as an emergent constraint, not a fundamental interaction.
Question 5 Short Answer
Why is it incorrect to state 'the normal force equals the weight' as a general law, and what actually determines the normal force?
Think about your answer, then reveal below.
Model answer: N = mg holds only in the special case of an object on a horizontal surface with no other vertical forces and no vertical acceleration. In general, the normal force is a constraint force determined by Newton's Second Law in the direction perpendicular to the surface: its value is whatever is needed to make the perpendicular acceleration equal to the actual perpendicular acceleration (typically zero, since objects don't pass through surfaces). Any other force with a perpendicular component — a hand pushing down, a rope pulling up, or the component of gravity on an incline — changes what N must be.
The key insight is that normal force is reactive, not prescriptive. It doesn't push with a fixed strength; it pushes with exactly the strength needed to enforce the constraint that two objects can't overlap. This is why free-body diagrams work: list all known forces, apply F = ma in the perpendicular direction, and N falls out as whatever value satisfies the equation.