AP Physics 1 · Exam guide
AP Physics 1 Forces and Free-Body Diagrams: An Incline Problem Step by Step
Force problems on the exam reward a clean diagram and a clear equation for each axis. Once the diagram is correct, the rest is algebra. This guide uses a block on a rough incline, with \(g = 10\ \mathrm{m/s^2}\).
The routine
- Draw the object as a dot or a box, and draw each force as an arrow from it: weight down, normal force perpendicular to the surface, friction along the surface, and any applied force.
- Choose axes along the incline and perpendicular to it, which keeps the motion on one axis.
- Resolve the weight into a component along the incline and one perpendicular.
- Write Newton's second law for each axis: the sum of the forces equals mass times acceleration.
- Solve, check the units, and ask whether the answer makes sense.
A worked example
A 4.0 kg block slides down a \(30^\circ\) incline. The coefficient of kinetic friction is 0.20. Find the acceleration of the block.
Perpendicular to the incline there is no acceleration, so \(F_N = mg\cos 30^\circ = (4.0)(10)(0.866) = 34.6\) N. The friction force is \(f = \mu F_N = 0.20 \times 34.6 = 6.9\) N, directed up the incline. Along the incline, the weight component is \(mg\sin 30^\circ = (4.0)(10)(0.5) = 20\) N, directed down the incline. Then \(ma = 20 - 6.9\), so \(a = \dfrac{13.1}{4.0} = 3.3\ \mathrm{m/s^2}\), down the incline.
It leaves out friction. The problem gives a coefficient, so it must be used.
It shows the normal force, the friction force, and Newton's second law along the incline.
Quick checks
- If friction were zero, the acceleration would be 5 m/s^2, so 3.3 is smaller, as it should be.
- The normal force is smaller than the weight (40 N) on an incline.
- The units of every term in the equation are newtons.
Common mistakes
- Drawing the normal force straight up instead of perpendicular to the surface.
- Using the weight in place of the normal force in the friction formula.
- Mixing the sine and cosine components.
- Leaving a force out of the diagram.
Frequently asked questions
Why is the normal force less than mg on an incline?
Only the component of the weight perpendicular to the surface is balanced by the normal force.
Do I always need to resolve forces?
When forces are not along the axes, yes, or choose axes that make them so.
Which direction should I make positive?
The direction of the acceleration, if you know it, which keeps the signs simple.
Where can I find the official scoring rules?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every lesson in the AP Physics courses ends with practice problems and an Exam focus box that shows how the topic is tested, and every unit has a review with worked answers. These free lessons also build the skills the free-response section tests:
- Free lesson 1.2: displacement, velocity, and acceleration
- Free lesson 1.4: the constant acceleration equations
See the AP Physics 1 course Free lessons and lesson list
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Multiple choice
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