Tension in accelerating cord calculator
On a smooth floor, pulling a 3 kg block with 10 N while it tows a 2 kg block gives both an acceleration of 2 m/s² and a cord tension of 4 N. Enter the two masses and the force to get both values. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- M1
- 2
- M2
- 3
- F
- 10
- Mass1
- 2
- Mass2
- 3
- Force
- 10
- Total mass
- 5
A tension in accelerating cord calculator turns the classic two-mass, one-force homework problem into a reliable deterministic solver for classrooms, labs, and automation scripts. The ideal model assumes a frictionless horizontal surface and a massless inextensible cord, with F applied to m2 so that free-body analysis on the trailing mass yields T equal to m1 times a.
What the two-mass accelerating cord model is and which formulas apply
Consider two blocks resting on a smooth horizontal surface and joined by a light, inextensible cord. An external horizontal force F is applied to mass m2, the mass on the side that is pulled; mass m1 trails and feels only the cord tension as its horizontal force. Because the cord does not stretch, both masses share one common acceleration a along the line of the force.
Newton’s second law on the system as a whole says the net external force F equals the total mass times that acceleration, so a equals F divided by m1 plus m2. Newton’s second law on the trailing mass alone says the tension T equals m1 times a, which expands to T equals m1 times F over m1 plus m2. That single connecting cord is the only segment whose tension is unknown: the applied force itself is an input, not a free tension to solve for.
Masses must be non-negative finite numbers; a negative mass is not physical in this classical model and is rejected. Callers keep m1, m2, and F in one coherent unit system—for example kilograms and newtons—so that a comes out in metres per second squared and T in newtons when SI is used. The calculator does not model friction, cord stretch, pulley redirection, or vertical hanging weights; those setups need different free-body diagrams and different capabilities such as an Atwood machine solver when gravity drives the motion over a pulley.
Practical tips, limits, and related searches
Use one consistent unit system end to end before calling; this landing does not convert between SI and imperial units. Pair classroom examples deliberately: m1 equals two, m2 equals three, and F equals ten yields a equal to two and T equal to four, a clean check that T equals m1 times a and that T is less than F whenever m2 is positive. Setting m1 to zero with positive m2 yields zero connecting tension, which matches free-body intuition that nothing trails behind the pulled mass.
When teaching free-body diagrams, derive a from the system and T from the trailing mass first, then confirm the numeric result here. This page targets people searching for a tension in accelerating cord calculator, two-mass rope tension under force, or accelerating string segment tension online; it is not a multi-body friction suite, not an Atwood pulley model, and not a unit converter.
Prefer this capability when the surface is smooth, the cord is light, and only one external horizontal force pulls the pair; if your source problem includes kinetic friction, subtract friction from F or fold it into an effective net force before calling. Round-trip checks are easy: recompute F over the mass sum by hand and confirm it equals the published a within the same twelve-decimal rounding used in the response.
What you can do with it
Homework checks for two-mass cord problems
Students enter m1, m2, and F from textbook accelerating-cord problems and compare common acceleration, connecting tension, and substitution steps against a deterministic result before submitting.
Lab pre-check on frictionless air tracks
Pipelines compute ideal a and T first, then compare against motion-sensor runs on air tracks or low-friction carts to quantify residual drag as error against the ideal cord model.
FAQ
What formulas does the tension in accelerating cord calculator use?
For an ideal frictionless two-mass system with F applied to m2 it uses a = F / (m1 + m2) for common acceleration and T = m1 · F / (m1 + m2) for connecting-cord tension.
Which mass is pulled by the force F?
By convention F is applied to m2. Mass m1 is the trailing mass connected only by the cord, so free-body analysis on m1 gives T = m1 · a.
Does this include friction or a pulley?
No. The ideal model assumes a frictionless horizontal surface and a massless inextensible cord. Atwood-style hanging masses need a different calculator.
Is the tension in accelerating cord calculator free?
The browser tool is free and runs locally.
What is the tension when 10 N pulls masses of 2 kg and 3 kg?
The cord carries 4 N. Both blocks accelerate at 2 m/s², the force divided by the total mass, and the trailing 2 kg block needs 4 N to keep up with that acceleration.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/mech/tension-accelerating-rope \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"m1":2,"m2":3,"F":10}'const res = await fetch("https://api.kit.forhosting.com/mech/tension-accelerating-rope", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"m1": 2,
"m2": 3,
"F": 10
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/tension-accelerating-rope",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"m1": 2,
"m2": 3,
"F": 10
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/tension-accelerating-rope", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"m1":2,"m2":3,"F":10}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"m1":2,"m2":3,"F":10}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/tension-accelerating-rope", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"m1": 2,
"m2": 3,
"F": 10
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.tension_accelerating_rope",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Zero total mass is rejected with a clear invalid_input error so bad forms never invent a number. Pricing is a flat $0.002 per successful API request; failed validation is never charged.
What the two-mass accelerating cord model is and which formulas apply
The sum m1 plus m2 must be strictly greater than zero—if both masses vanish, the acceleration formula divides by zero and the task fails with invalid_input rather than returning Infinity.
How to call the API and what comes back
Absolute values must stay within the published limit of one trillion; each mass must be non-negative, and the sum of the masses must be greater than a tiny positive epsilon so that division remains well defined. Sign of F is free: a negative pull reverses both acceleration and tension signs in the same linear model, which is useful for checking that graded scripts treat direction consistently. Send a JSON body with the three required finite fields m1 (aliases mass1 and m_1), m2 (aliases mass2 and m_2), and F (aliases force, f, and pull). On success the response echoes rounded m1, m2, and F, mirrors them as mass1, mass2, and force, sets total_mass to the sum, sets a and acceleration to the common system acceleration, sets T and tension to the connecting-cord tension, and exposes segments as a one-element array describing the m1–m2 cord with its tension, formula, and substituted equation. Symbolic formula_a and formula_T strings, fully substituted equation_a and equation_T lines, a short message, and an ordered steps array complete the payload for worksheets and automated tests. Failed validation—missing fields, non-finite numbers, values outside absolute limits, negative mass, or total mass equal to zero—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item. Prefer JSON numbers when you control the client; string numbers are accepted only when they match a strict finite numeric pattern for homework-form paste paths.
Practical tips, limits, and related searches
Keep m1, m2, and F inside the published absolute range so products and quotients remain finite in IEEE double precision on the Worker and in the browser. Setting both masses to zero demonstrates the hard invalid_input path that protects clients from division by zero. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately pass a zero total mass.
Integration use cases
Unit tests for physics helpers
Generate known-good a and T cases plus deliberate zero-total-mass rejections for coding kata expected values in simulators, LMS graders, or game physics sandboxes.
Technical questions
What happens if total mass is zero?
The task fails with invalid_input. When m1 + m2 is zero the acceleration formula would divide by zero, so the solver refuses the request and does not bill it.