Balanced and Unbalanced Forces Simulator

What Is the Balanced and Unbalanced Forces Simulator?

How to Use the Simulator

1. Read the four cards before you touch anything. They sit at the top of the panel and are already answering for a dead-even rope pull: The forces balanced, Net force 0 N, Velocity now at rest, and What happens next stays at rest.
2. Read the sub-line under each one, because that is where the card shows its working. They read left 60 N, right 60 N, the two cancel exactly, at t = 0.0 s and zero net force leaves the velocity alone. The last of those is the rule the whole lab turns on, and it does not mention standing still.
3. Pull Force pushing left down one step at a time and watch where the call flips. At 55 N against 60 N it has already gone to unbalanced, with the second card reading 5 N right; there is no band of near-enough values, because the two forces are compared exactly. At 40 N that card reads 20 N right over 20 N is left over, to the right.
4. Now look at the four-row grid under the drawing, and read the third row. With the block still untouched at at rest it has gone to unbalanced, but momentarily at rest. That row is the one this lab exists for, and it has only three possible values.
5. Press Run and watch what it does and does not move. The button flips its own label to Pause, animates the clock to 10.0 s and stops there by itself. The two forces, the mass and the starting velocity are left exactly where you put them: the clock is the only thing a run advances.
6. Press Coasting, forces even and leave the clock alone. The call comes back balanced over a block already doing 5.00 m/s right, the trap row reads balanced, and still moving, and What happens next reads keeps the same velocity. Run it to 10.0 s and the velocity card has not changed a character.
7. Press Pushed back while rolling and drag Time since the start through 4.0 s. At 4.0 s the velocity card reads at rest while the call still reads unbalanced, with the position at 16.00 m. Carry on to 6.0 s for 4.00 m/s left at 12.00 m, and to 8.0 s for 8.00 m/s left back at 0.00 m.
8. Check the last grid row on that preset before you trust it. It reads at t = 4.00 s, x = 16.00 m at every one of those instants, including 8.0 s. It names the moment this run passes through zero velocity, worked out from the starting velocity, rather than a halt still ahead of the block.
9. Press Reset when you have finished. It puts the five sliders back to 60 N, 60 N, 20 kg, 0.0 m/s and 0.0 s, and replays the opening settle, so the scene grows back rather than cutting straight to the answer.

Dragging is the right way to find out which readings move together and a poor way to hit an exact figure, because the force sliders step five newtons at a time and the clock a tenth of a second. The five preset buttons above exist for that reason: they write the sliders for you and leave every number to the simulation. The written guide to balanced and unbalanced forces is where both terms are defined properly and the problems are worked through with every step shown.

One thing this panel will not decide for you is which forces belong on the block in the first place. That judgement is upstream of every reading on the screen, and it is where most wrong answers are actually made: leave a force off and the two values still compare perfectly while telling you nothing true. The force diagram lab is the place to settle it, and then this panel will tell you what the pair you ended up with means.

Worked Example: Two Blocks Sitting Perfectly Still

Nothing in the three tables below was worked out here. Each row is a setting the lab was put into through its own sliders and then read back from, cell by cell, so every string in them is the panel’s own. The first table is the pair this whole lab was built around.

One: the same stillness, the opposite call

Press Tug of war, dead even and then Tug of war, one side wins, and read the first two rows before you touch the clock. Both blocks are motionless, both have gone nowhere, and the panel gives them opposite answers.

Read the first two rows across, then stop. Columns four and five are identical in both: at rest and 0.00 m. Column two is not. Whatever the panel used to tell these two settings apart, it was not the motion, because at this instant there is no difference in the motion to use.

Now read rows three and four, which are the same two settings two seconds later. The dead-even rope pull has not moved a character: still at rest, still 0.00 m. The one-sided pull is doing 2.00 m/s right and has covered 2.00 m. The difference the arrows showed at the start has become a difference you could see.

The last column is where the two rows at the start are worth keeping. One reads neither trap on show and the other unbalanced, but momentarily at rest, from identical readings in every motion column. Signed velocity is the quantity all of this turns on, and the guide to velocity against speed is where the distinction between it and a bare speed is set out.

Two: the five presets, and what each one is for

These are the buttons above with the readings they produce at t = 0.0 s. The fifth column is the What happens next card and the last two are the third and fourth rows of the grid under the drawing.

The second and third columns never disagree, and that is worth checking yourself. Wherever column two says balanced, column three says 0 N; wherever it says unbalanced, column three has a magnitude and a direction. Both readings come from the same comparison of the two slider values, so the panel cannot print one without the other.

The last column is the one to read carefully, because three of its five entries are refusals. never moves belongs to a block with no left-over force and no starting velocity; never to one that is moving and has nothing to change it; never (already moving away) to one being pushed the way it is already going. Only the two settings with a real crossing give a time.

Three: the same clock, run on two of them

Press Coasting, forces even and then Pushed back while rolling, and read them at the same five instants. Both start the run moving; one of them is still doing exactly what it started with ten seconds later.

Column two is a single string repeated five times. 5.00 m/s right at the start and 5.00 m/s right at 10.0 s, with the position climbing steadily to 50.00 m underneath it. That is the lab’s stated frictionless surface doing what it was told to do, not a claim about any floor you have met.

Column four changes sign without the panel ever printing one. It goes 8.00 m/s right, at rest, 4.00 m/s left, 8.00 m/s left, 12.00 m/s left, and the only minus sign in the whole table is in column five, where the position reaches -20.00 m. The two forces that slowed the block are the two that then sped it up the other way.

Column six holds the trap for exactly one row. It is the same string the one-sided tug of war printed at the start, arrived at from the opposite direction: that block had never moved, this one has been brought to a halt. The guide to acceleration in physics is where a velocity changing sign while the acceleration holds steady is set out at length.

Formula and Symbol Reference: Every Slider and Every Readout

The line at the head of this page is the whole of the test: compare the two forces, and the answer is one word. The net force is the subtraction behind it, and the acceleration is that net force shared out over the mass.

What the lab does with the answer is the second half, and it is the half that people get wrong. A net force of zero leaves the velocity exactly as it was, which is a statement about change and not about standing still. How large the acceleration becomes once there is a left-over force is a separate question with its own tool: the force, mass and acceleration calculator works that figure out from typed values.

If you read one row twice, make it the last. The row that says when the run reaches zero velocity is the only reading on the panel that describes an instant other than the one the clock is on, and it keeps its answer as the clock moves past it.

Reading the Diagram: Arrows, Bands and Units

The drawing is laid out as three bands and the bands are reserved before anything is placed, so no part of it is ever painted across another. The top band carries the call, the middle band carries the block and its arrows, and the bottom band carries a position axis.

The three force arrows share one scale, and that is the only thing their lengths are good for. On the dead-even pull the two are the same length; on the one-sided pull the 60 N arrow is exactly half as long again as the 40 N one, and the net arrow is the difference. At the page’s full width the shared factor is 110 pixels per 100 newtons, and on a narrower canvas all three shrink together, so the proportions hold and the pixel figure does not.

The velocity arrow sits in its own row with its own label and its own, different scale. It is a different quantity in different units, so its length is a statement about velocities only, and the row label says velocity for exactly that reason. Read the figure printed beside each arrow and treat the lengths as a comparison within a row, never across two.

There is no minimum width in this picture, and no caption claims one. A 5 N force, the smallest the sliders can ask for, comes out at five and a half pixels at the full width and is drawn at exactly that; nothing is propped up to stay visible. A force of 0 N is drawn as no arrow at all, which is what the right-hand side of the braking preset looks like, and the velocity arrow disappears on exactly the test the velocity card uses.

The three predicates behind all of this are short enough to state outright. The forces are called balanced when the two values are equal; the block is called at rest when its speed rounds to 0.00 m/s; and the trap row is computed from those two answers and nothing else. The forces you feed in are a separate question, and the guide to the types of forces covers what you might be adding up before you get here.

The Physics: Why the Motion Cannot Tell You the Verdict

Two blocks sitting perfectly still can be in opposite states, and two blocks moving at speed can be in opposite states. That is the whole claim, and both halves of it are a button press away: the first two presets are the stillness pair and the third and fourth are the moving pair.

The moving pair is the one that takes longer to believe. At 4.0 s the coasting block is doing the 5.00 m/s right it started with and the braking block has stopped dead at 16.00 m, and the thing that separates them was visible from the first frame: one pair of arrows matched and the other did not. Nothing about the two blocks at t = 0.0 s would have told you.

Be blunt about what the simulator is doing here, because a panel that keeps agreeing with itself can look like a panel that has found something out. It has not. The simulator does not measure anything: it is told the two forces and works out the rest, so matching forces leave the velocity alone is built into its arithmetic rather than discovered by it, and the honesty strip under the drawing says so in its own words.

What the sliders are genuinely for is the other direction. They let you build the two states that look wrong — still but unbalanced, moving but balanced — and then watch what each one actually does next, which is a thing you cannot do by staring at a photograph of a block. That is also why the clock is a slider rather than only a Run button: every frame is a state you can set and read.

One consequence is worth saying plainly. A left-over force does not need the block to be stationary to start with, and it does not stop acting when the block happens to be passing through zero speed: on the braking preset the net force reads 30 N left at 0.0 s, at 4.0 s and at 10.0 s without changing a character, while the velocity goes from right, through nothing, to left.

Where It Breaks Down

Every slider position this lab can reach is answered, and the arithmetic is not where it can let you down. What it cannot do is model a real surface, and what it chooses not to do is treat its own idealisations as facts. Six limits sit under the readings on this page.

There is no friction anywhere in the model, and that is the big one

The panel says so in its fixed line, and it is the single most important thing to carry away from the coasting preset: on a real floor that block would slow and stop. Worse for the lab, a real crate pushed along at a steady speed is balanced — the friction opposing the push is one of the forces that match — and this lab does not draw that force at all, so a two-arrow picture of that crate would be wrong. The friction calculator is where the missing force gets a size, and it takes the kind of figures this panel prints.

The call is an exact equality here and a threshold in the world

Two slider values either match or they do not, and five newtons apart is as unbalanced as a hundred. A real surface answers a softer question, with a range of pushes below which nothing happens at all, and nothing in this lab reproduces that range because nothing in this lab resists. If you are asking whether a push is enough to get something going, this panel is answering a different question from the one you asked.

The two forces never change during a run

That is what makes the velocity and the position exact here rather than stepped: with a constant net force the expressions are closed form and there is no integration error to accumulate. Real pushes vary, ropes stretch, and a hand tires, so the straight-line velocity on this panel is the cleanest possible version of the story. The clock slider is honest about this — every instant is computed, not reached by running.

Nothing here can turn, and the lab assumes it away rather than hiding it

Both forces act through the centre line, which is why the drawing is one axis and the answer is one word. A real pair of forces offset from each other can match for the purpose of moving the object along and still set it spinning, and this panel would call that pair balanced and be only half right. The formal word for the full condition, covering that case as well as this one, is set out in the guide to equilibrium in physics.

The block is a rectangle on a line

It has a mass and it has a width on screen and nothing else: no shape, no contact area, no deformation, no place where one force is applied rather than another. The 20 kg written inside it is a label, not a size, and the surface under it is a line rather than a material. Anything you want to conclude about a real object’s stiffness, grip or balance has to come from somewhere other than this picture.

The drawing is a drawing, and only one of its promises is geometric

The three force arrows are in proportion to one another, on a factor that shrinks with the canvas so that they stay inside a narrow column. That is the one thing a length tells you. The velocity arrow’s scale is a different number at every width, the position axis is rescaled per setting, and the mass chip is text. Read the figures; the picture is for seeing which way things point and which of two forces is bigger.

Where the Verdict Is Actually Used

A crane load that is already on its way up

A load of 500 kilograms weighs about 4,900 newtons — 500 kg at roughly 9.8 N per kilogram — and while a hoist raises it at a steady speed the rope is carrying exactly that: 4,900 N up against 4,900 N down. Two forces of nearly five kilonewtons each, an object plainly in motion, and the call on it is balanced. Neither the height it has reached nor the speed it is doing enters the comparison, which is the one structural thing this panel is built to make obvious.

A car at its top speed, where the call is what fixes the number

Top speed is not a property an engine has on its own: it is the speed at which the driving force has stopped being larger than everything resisting the car, so nothing is left over to change the speed. At 30 metres per second — 108 kilometres per hour — the call on such a car is balanced while it travels as fast as it can go. How big each side is depends on the shape of the car and the air it pushes aside, and this page will not hand you a figure for it. Lift off the accelerator and the call flips, with the left-over force now pointing backwards.

Knowing what an object is doing at the instant it stops

Load Pushed back while rolling and sit on 4.0 s. The velocity card reads at rest, the net force still reads 30 N left, and the acceleration row still reads 2.00 m/s2 left. That is the state behind anything that stops and then comes back — a ball at the top of a ramp, a trolley released on a slope — and two seconds further on the panel is reading 4.00 m/s left.

Recognising forces that come into balance while something is moving fast

The coasting preset is a laboratory version of a very common real case: something is moving quickly, the forces on it have become equal, and the velocity simply stops changing. The guide to terminal velocity is where that happens for real, with a falling object whose drag grows until it matches the weight and the speed levels off. This panel shows the end state of that story without the mechanism that gets there.

Trusting a set of scales, which only report a weight while the call is balanced

A weighing machine does not measure a weight at all: it measures how hard its pan has to push up, and that force equals the weight only while the two of them match. Stand still on bathroom scales and 70 kilograms reads as about 690 newtons, taking roughly 9.8 N for every kilogram. Step on quickly, or weigh something on a ship in a swell, and the figure wanders, because for those seconds the pan is doing more than holding the load up. The pair being compared there is the weight-and-support pair this lab assumes away and never draws.

Separating the call from the size of what follows

Once the answer is unbalanced, how fast the velocity moves is a second question, and the mass slider is where you see the two come apart: the call does not shift by a character as it travels from 1 kg to 50 kg, while the acceleration row does. The force and acceleration lab takes that second question as its whole subject, with the size of the effect in the foreground instead.

Where to Go Next

A panel can show you a state and let you run the clock on it, and that is the end of what a panel is for. Balanced and unbalanced forces is where the subject itself is written out: both terms defined separately, the procedure for deciding between them, and worked problems with every step shown.

Three guides sit around this one. The guide to the types of forces covers what you are adding up before any of this starts, the guide to drawing the forces on an object covers getting them onto the page correctly, and the overview of the laws of motion is where this one consequence sits among the rest.

Three more are about what happens after the answer is unbalanced. The guide to how much acceleration a net force produces is the one place the size of it is worked out, the guide to acceleration in physics is where a changing velocity gets its own treatment, and the guide to velocity against speed covers the signed quantity this lab reads. The guide to terminal velocity is the real case that lands in the coasting preset’s end state.

On the tool side there are the friction calculator, the force, mass and acceleration calculator and the acceleration calculator, with the force diagram lab and the force and acceleration lab for the drawn versions. Beyond them there is the simulation library, an index of calculators, and the blog for everything written out at length.