A.2.6—Normal force

Normal means perpendicular

The normal force $N$ is the contact force exerted by a surface perpendicular to that surface. Its direction follows the local surface normal, not necessarily the vertical direction.

Find it from the force balance

Use the component of Newton’s second law perpendicular to the surface. In a curved path, the normal force may combine with a component of weight to provide the required centripetal resultant.

Do not assume $N=mg$

$N=mg$ applies only in situations where the perpendicular acceleration and other perpendicular force components make that balance valid. Inclines, lifts, loops and vertical acceleration change the normal force.

How it is assessed

The evidence asks for the normal force in a vertical loop and tests how the normal force changes as an incline angle increases.

Command terms

Determine / Identify

What earns marks

Draw the normal perpendicular to the local surface and apply Newton’s second law along that direction. In a loop, include the relevant component of weight and the centripetal term; on an incline, use the perpendicular component of weight.

Watch for

Setting N equal to weight without considering curvature, acceleration or the component of weight perpendicular to the surface.

Representative question

[Maximum number: 3]

Determine the normal force exerted by the loop on the car at P .

$\begin{aligned} N+m g=\frac{m v^{2}}{r} N=0.12 \times\left(\frac{1.72^{2}}{0.15}-9.81\right) N=1.2 \text { «N» } \end{aligned}$

Allow 1.1 or 1.2 depending on g and rounding of v.

Award [0] for answers based on N=W.

A.2.6—Normal force

Model Normal Force Perpendicular to the Surface

A.2.6 Exam Analysis

Assessment in practice

Question 1