Inclined Planes & Newton’s Second Law
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Newton’s second law: a = Fnet ÷ m, applied in each direction separately. On a ramp, tilt your axes so one runs along the slope. Then gravity splits into mg sin θ down the slope and mg cos θ into the slope.
1. Tilt the axes
2. A reliable method
1. Draw the free-body diagram.
2. Choose axes along and perpendicular to the motion.
3. Split any force that isn’t along an axis.
4. Write Fnet = ma for each axis and solve.
Check sin vs. cos with a flat ramp (θ = 0): the part along the surface, mg sin 0, must be zero. ✓
On a frictionless ramp, a = g sin θ: steeper ramp, bigger acceleration. The block’s mass cancels out.
3. Example, then try it
A block slides down a frictionless ramp tilted at 30°. What is its acceleration?
Along the slope, the only force is mg sin 30°, so ma = mg sin 30°.
a = g sin 30° = (10)(0.5) = 5 m/s² down the slope, for any mass.
A 4.0 kg block slides down a 37° ramp with μk = 0.25. Find its acceleration. (sin 37° ≈ 0.60, cos 37° ≈ 0.80)
Down the slope: mg sin θ = (40 N)(0.60) = 24 N.
Normal force: Fn = mg cos θ = (40 N)(0.80) = 32 N.
Friction (up the slope, opposing the slide): (0.25)(32 N) = 8 N.
Net force and acceleration: 24 − 8 = 16 N, so a = 16 ÷ 4.0 = 4.0 m/s².
Answer: 4.0 m/s² down the slope.
4. Common mistakes
A block slides down a frictionless ramp. If the ramp is made steeper, what happens to the block’s acceleration?
On a frictionless ramp, a = g sin θ. A larger angle gives a larger sin θ, so the acceleration increases.
Ready to practice?
5 questions on Inclined Planes & Newton’s Second Law, each with a hint and an explanation for every wrong answer.