At a glance
A block feels several forces at once. This sim lets you add, drag and remove forces on a frictionless table, then tilt the surface into a slope, to see how the forces together set the block's motion.
What you'll learn
- How several forces combine into one, and what that combination decides.
- How a force is related to the block's acceleration, velocity and path.
- What it means for forces to balance, and what happens when one disappears.
- How mass, slope angle and friction change the motion on a slope.
Three forces act on one block.
What's on screen
- Force arrows F₁, F₂, F₃…: each has its own colour and its size in newtons. Drag a tip to change one.
- Fnet (violet), a (green) and v (cyan): the net force, the acceleration and the velocity. They appear with show net force. A faint violet trail marks the path.
- Incline scene: gravity mg (red), the normal force N (blue) and friction (amber).
- Readouts: |Fnet| and |a|. They show a placeholder until the first ▶ Play.
See itRelease the 2 kg block with its three starting forces. Watch for: the readouts filling in as the block starts to move.
The controls
Press ⌖ on a row to see where that control sits in the sim.
| Control | What it changes | Range | |
|---|---|---|---|
| Scene | Flat (top view): a frictionless table, where you choose the forces. Incline (side): a slope with gravity, the normal force and optional friction. | 2 buttons opens on Flat | |
| mass m | The block's mass. Changing it while the block is running restarts the run from rest. | 2–5 kg opens at 2 kg | |
| incline θ | The slope angle, measured from the horizontal. Incline scene only. | 0°–60° opens at 30° | |
| friction | Switches friction between the block and the slope on or off. Incline scene only. | μ = 0.30 opens off | |
| + Force | Adds a force arrow (up to 6). Drag its tip to set its direction and size; drag a tip onto the block to remove that force. | up to 10 N flat steps of 0.25 N | |
| ⟲ Re-place block | Puts the block back at its start, at rest. The forces stay as they are. | button | |
| show components | Draws gravity's two parts, mg·sin θ and mg·cos θ, as dashed arrows. Incline scene only. | on / off | |
| show net force | Draws the net force Fnet, the acceleration a and the velocity v as arrows, and fills in the readouts. | on / off | |
| Readouts | The size of the net force and of the acceleration, live. | panel | |
| Status | Names the surface and says whether friction is acting. | panel | |
| ▶ Play / ⏸ Pause | Releases the block, or freezes it so you can read the arrows. | top bar | |
| Speed | Plays the motion faster or slower on screen. The physics stays the same. | 0.25×–4× opens at 0.5× | |
| ↻ Reset | Restores the starting forces and settings, and restarts the mode you are in. | top bar |
Fixed: g = 9.81 m/s², μ = 0.30 (used for both sticking and sliding), no air drag. The flat table has no friction.
Forces add as vectors
A force has a size and a direction, so forces add as vectors, one component at a time. The net force is the vector sum of all the forces on the block.
Components add separately: x with x, y with y.
- For the opening forces, (5, 0) + (0, 4) + (−2, −1) = (3, 3) N. That is 4.24 N, at 45° to the x-axis.
- The block therefore does not move along the longest arrow, F₁. The sum sets the direction, and F₁ is only one part of it.
The three opening forces, and the same forces placed tip to tail.
Key idea. The block's motion follows the vector sum of all the forces, not the largest one.
See itRelease the block with the net force shown. Watch for: the violet Fnet arrow pointing between F₁ and F₂, with the trail leaving along it.
A force sets acceleration, not velocity
Newton's second law links the net force to the acceleration. The velocity then changes by a·Δt in each short time Δt, so it builds up gradually.
The law, and how velocity accumulates.
- For the opening forces, a = 4.24 N / 2 kg = 2.12 m/s². The block starts at rest, so its velocity grows from zero while a stays the same.
- If the net force turns mid-run, the acceleration turns at once. The velocity the block already has does not: it stays, and the new acceleration bends it. The path curves toward the new net force instead of kinking.
The net force is turned partway along. The old velocity carries on, and the path bends.
See itRelease the block with the net force shown. Watch for: the cyan velocity arrow growing while the green acceleration arrow keeps its length.
See itTry it yourself: press ▶ Play, pause after a second, drag the tip of F₂ round to point down, then press ▶ Play again. Watch for: the trail curving toward the new net force.
Balanced forces add up to zero
Forces balance when their vector sum is zero. Then a = 0, so the velocity stops changing: a block at rest stays at rest, and a moving block keeps its velocity.
- Zero net force does not mean zero force. Every force is still acting; every component cancels.
- Take 5.00 N to the right plus two forces of 3.91 N, (−2.5, 3) N and (−2.5, −3) N. The pair adds to (−5, 0) N and cancels the 5.00 N exactly.
- Remove the 5.00 N force and nothing cancels the pair. The net force is 5.00 N to the left, so a = 5.00 N / 2 kg = 2.5 m/s² to the left.
See itRelease the balanced block, then the same block with F₁ removed. Watch for: |Fnet| reading 0.00 N with the block at rest, then 5.00 N once F₁ is gone.
Gravity on a slope splits in two
On the Incline scene, the weight mg splits into mg sin θ along the slope and mg cos θ into it. The surface answers the second part with the normal force N = mg cos θ, so, without friction, only mg sin θ is left to accelerate the block.
Along the slope, the mass cancels.
m
θ
These move the sim's sliders too.
- Without friction or applied forces, every mass slides alike. The pull mg sin θ and the inertia m both grow with m.
- The angle matters, but not in proportion: 30° gives 4.91 m/s², and 60° gives 8.50 m/s², not twice as much.
- This is special to the slope. On the Flat table you choose the forces yourself, so a = Fnet/m and the mass does matter.
See itShow gravity's two parts on the slope. Watch for: the dashed mg·sin θ and mg·cos θ arrows, and |a| matching g sin θ.
See itSlide a 2 kg block, then a 4 kg block, down 30°. Watch for: the card showing a different Fnet but the same |a|.
Friction on a slope decides if it slides
Friction pushes back up the slope, by at most μN. A block at rest gets exactly the friction it needs to balance mg sin θ, until that reaches the limit μN.
The block stays put while its pull down the slope does not exceed the friction limit.
- The mass cancels again, so the test needs only the angle: the block sticks while tan θ ≤ μ. For μ = 0.30 that means θ ≤ arctan 0.30 = 16.7°.
- While it sticks, the friction equals mg sin θ, not μN. At 15° with m = 2 kg that is 5.08 N, below the limit of 5.69 N.
- Above 16.7° the block slides, with friction μN = μmg cos θ (the sim uses the same μ for both). Then a = g(sin θ − μ cos θ), which is 2.36 m/s² at 30°.
See itPut the block on 15°, then on 30°, with friction on. Watch for: the block staying put at 15° (|a| = 0.000), then sliding at 30°.
Where it matters
- Towing and mooring. Several tugs can pull on one ship from different directions. Only the vector sum of their pulls accelerates it, so the tugs do not have to pull the same way.
- Galileo's ramps. Free fall was too quick to time, so Galileo slowed it down with a ramp, where gravity's pull along the slope is only g sin θ. A solid ball that rolls without slipping accelerates at only 5/7 of g sin θ, which slowed it further; the sim's block slides instead.
- Angle of repose. A dry pile of sand or scree can only be piled up to a certain steepness, set by the friction between the grains. Roughly, it is where tan θ reaches the friction coefficient; steeper than that and grains slide.
Go deeper: a force that pushes into or pulls off the slope
F⊥,in is an applied push into the slope. A pull away from it counts as negative.
- A push into the slope raises N, and with it the friction limit μN. A pull away lowers both.
- If the pull is strong enough, N reaches zero and the block leaves the surface. The sim then marks N = 0 — lift-off.
Summary
In one line. The vector sum of all the forces, divided by the mass, is the block's acceleration; the velocity then builds up from it.
Key points
- Forces add as vectors, so the largest force does not decide the direction.
- a = Fnet/m. A changing force bends the path, because the velocity it has already built up stays.
- Balanced forces give a = 0, not zero force.
- On a frictionless slope a = g sin θ for any mass. With friction, the block sticks while tan θ ≤ μ.
Common mix-ups
- "The block moves along the largest force." Only the sum counts. With F₁ stretched to 8 N the net force is (6, 3) N, 26.6° above the x-axis, not along F₁.
- "Heavier blocks slide faster down a slope." The pull and the inertia both grow with the mass, so they cancel. This still holds with friction.
- "Static friction is always μN." μN is only the largest it can be. A resting block gets just enough friction to balance mg sin θ.
Things to try on your own
- Drag F₁ out to (8, 0) N. Work out the net force by hand, then compare it with the |Fnet| readout.
- On the incline, switch friction on and find the steepest whole-degree angle at which the block stays at rest.
- Set m = 5 kg and θ = 60°, then compare |a| with g sin 60°.