Year 12 / Gravity and motion
Choose axes along the slope.
Choosing axes parallel and perpendicular to a slope simplifies the force sum. Weight resolves to mg down the slope and mg into it. The normal force is perpendicular to the surface.
On a smooth slope with no additional perpendicular force, N = mg . Include friction, tension and applied forces with their directions before finding acceleration along the slope. The normal force and weight are not a Newton’s third-law pair.
Down a smooth slope
Explore the relationship
The parallel component is mg sin θ; the normal force is mg cos θ when no other perpendicular forces act.
Down-slope weight / N
Tap or focus a plotted point to read its values.
View plotted data as a table
| Series | Slope angle / degrees | Down-slope weight / N |
|---|---|---|
| Down-slope weight / N | 0 | 0 |
| Down-slope weight / N | 1 | 0.684134 |
| Down-slope weight / N | 2 | 1.36806 |
| Down-slope weight / N | 3 | 2.05157 |
| Down-slope weight / N | 4 | 2.73445 |
| Down-slope weight / N | 5 | 3.41651 |
| Down-slope weight / N | 6 | 4.09752 |
| Down-slope weight / N | 7 | 4.77728 |
| Down-slope weight / N | 8 | 5.45559 |
| Down-slope weight / N | 9 | 6.13223 |
| Down-slope weight / N | 10 | 6.80701 |
| Down-slope weight / N | 11 | 7.47971 |
| Down-slope weight / N | 12 | 8.15014 |
| Down-slope weight / N | 13 | 8.81808 |
| Down-slope weight / N | 14 | 9.48334 |
| Down-slope weight / N | 15 | 10.1457 |
| Down-slope weight / N | 16 | 10.805 |
| Down-slope weight / N | 17 | 11.461 |
| Down-slope weight / N | 18 | 12.1135 |
| Down-slope weight / N | 19 | 12.7623 |
| Down-slope weight / N | 20 | 13.4072 |
| Down-slope weight / N | 21 | 14.048 |
| Down-slope weight / N | 22 | 14.6846 |
| Down-slope weight / N | 23 | 15.3167 |
| Down-slope weight / N | 24 | 15.9441 |
| Down-slope weight / N | 25 | 16.5666 |
| Down-slope weight / N | 26 | 17.1841 |
| Down-slope weight / N | 27 | 17.7964 |
| Down-slope weight / N | 28 | 18.4033 |
| Down-slope weight / N | 29 | 19.0045 |
| Down-slope weight / N | 30 | 19.6 |
| Down-slope weight / N | 31 | 20.1895 |
| Down-slope weight / N | 32 | 20.7728 |
| Down-slope weight / N | 33 | 21.3499 |
| Down-slope weight / N | 34 | 21.9204 |
| Down-slope weight / N | 35 | 22.4842 |
| Down-slope weight / N | 36 | 23.0412 |
| Down-slope weight / N | 37 | 23.5911 |
| Down-slope weight / N | 38 | 24.1339 |
| Down-slope weight / N | 39 | 24.6694 |
| Down-slope weight / N | 40 | 25.1973 |
| Down-slope weight / N | 41 | 25.7175 |
| Down-slope weight / N | 42 | 26.2299 |
| Down-slope weight / N | 43 | 26.7343 |
| Down-slope weight / N | 44 | 27.2306 |
| Down-slope weight / N | 45 | 27.7186 |
| Down-slope weight / N | 46 | 28.1981 |
| Down-slope weight / N | 47 | 28.6691 |
| Down-slope weight / N | 48 | 29.1313 |
| Down-slope weight / N | 49 | 29.5846 |
| Down-slope weight / N | 50 | 30.0289 |
| Down-slope weight / N | 51 | 30.4641 |
| Down-slope weight / N | 52 | 30.89 |
| Down-slope weight / N | 53 | 31.3065 |
| Down-slope weight / N | 54 | 31.7135 |
| Down-slope weight / N | 55 | 32.1108 |
| Down-slope weight / N | 56 | 32.4983 |
| Down-slope weight / N | 57 | 32.8759 |
| Down-slope weight / N | 58 | 33.2435 |
| Down-slope weight / N | 59 | 33.601 |
| Down-slope weight / N | 60 | 33.9482 |
Explore: Keep the angle fixed and double mass. Compare force with acceleration.
A 2 kg block slides down a smooth 30° slope; use g = 9.8 .
- Down-slope force = 2 × 9.8 × sin 30° = 9.8 N.
- a = = 4.9 down the slope.
Assumed knowledge
Sine, cosine and net force.
Learning checkpoints & source
YOUR LEARNING CHECKPOINT- Resolve weight on an inclined plane.
- Construct free-body diagrams and find net force.
READY TO TRY IT?