BIZOMAT MAKEOS · Mechanics
Impulse, Momentum and Collisions
What average force changes this body’s velocity in the time available, and how do two bodies move after they collide?
Average force from the change in momentum over a time (linear impulse), and the velocities of two bodies after a direct central impact with a coefficient of restitution, with the kinetic energy lost.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Calculation | choice | Choose the calculation. |
| Mass (force mode) | kg | Mass of the body. |
| Initial velocity | m/s | Velocity at the start (signed along one line). |
| Final velocity | m/s | Velocity at the end (signed). |
| Time the force acts | s | Duration of the force (stopping or acceleration time). |
| Mass of body 1 | kg | Mass of the first body. |
| Velocity of body 1 before impact | m/s | Its velocity before impact (signed). |
| Mass of body 2 | kg | Mass of the second body. |
| Velocity of body 2 before impact | m/s | Its velocity before impact (signed). |
| Coefficient of restitution | 1 for a perfectly elastic impact, 0 for perfectly plastic (bodies move together); measure or estimate for your materials. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Calculation
- What it is
- Whether to find the average force that changes one body’s velocity over a known time, or the velocities of two bodies after they collide head-on.
- Units and format
- Choose one of 2 options from the list: Average force from a velocity change; Two-body collision.
- Example
- The form opens with “Average force from a velocity change” selected as a worked example. Choose the option that matches your case.
What this means: Mass (force mode)
- What it is
- The mass of the single body whose velocity is being changed by the force, used only in force mode.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The change in momentum and the average force rise in proportion to mass.
What this means: Initial velocity
- What it is
- The body’s velocity just before the force starts to act, along one straight line. Give it a sign: motion in the opposite direction is negative.
- Units and format
- Enter a number in m/s: metres per second. The form accepts -100000 m/s to 100000 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a body brought to rest, this is its speed and the final velocity is zero; for a rebound, the final velocity takes the opposite sign.
What this means: Final velocity
- What it is
- The body’s velocity once the force has finished acting, measured along the same line and with the same sign convention as the initial velocity.
- Units and format
- Enter a number in m/s: metres per second. The form accepts -100000 m/s to 100000 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The average force is proportional to the difference between final and initial velocity.
What this means: Time the force acts
- What it is
- How long the force acts to produce the velocity change, such as the stopping time of an impact or the duration of a push. The force found is the average over this time.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 100000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.1 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Halving the time doubles the average force for the same velocity change.
- Get it right
- Impact times are often a few milliseconds; enter them in seconds (milliseconds ÷ 1000).
What this means: Mass of body 1
- What it is
- The mass of the first of the two colliding bodies, used only in collision mode.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Velocity of body 1 before impact
- What it is
- The velocity of body 1 just before impact, along the line joining the two centres; positive in the chosen direction and negative if moving the opposite way.
- Units and format
- Enter a number in m/s: metres per second. The form accepts -100000 m/s to 100000 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The bodies only meet if body 1 moves towards body 2 faster than body 2 moves away; otherwise the tool reports that they do not meet.
What this means: Mass of body 2
- What it is
- The mass of the second of the two colliding bodies, used only in collision mode.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Velocity of body 2 before impact
- What it is
- The velocity of body 2 just before impact, using the same line and sign convention as body 1; zero if it is standing still.
- Units and format
- Enter a number in m/s: metres per second. The form accepts -100000 m/s to 100000 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Coefficient of restitution
- What it is
- The ratio of the speed at which the bodies separate after impact to the speed at which they approached: 1 is a perfectly elastic impact with no energy lost, 0 means the bodies move on together.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lower values increase the kinetic energy lost and bring the two final velocities closer together.
- Get it right
- It depends on the materials, shapes and impact speed; measure it with a drop or impact test on your parts where possible.
Method and formulas
- Linear impulse equals the change in momentum: F t = m (v_f − v₀).
- Collision: v₁′ = [m₁v₁ + m₂v₂ − m₂ e (v₁ − v₂)] ÷ (m₁ + m₂) and v₂′ = [m₁v₁ + m₂v₂ + m₁ e (v₁ − v₂)] ÷ (m₁ + m₂).
- Energy lost = initial minus final kinetic energy.
- Example: 10 kg from 0 to 5 m/s in 0.1 s needs an average force of 500 N.
Limitations
- Average force only; peak force in an impact is usually several times higher.
- Direct central impact along one line.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate the force on a stop or buffer from the stopping time
- Predict the rebound after two parts collide
- Estimate the energy absorbed in an impact
Who it is for
- Design engineers
- Mechanical engineers
- Engineering students
What you get
- Average force or velocities after impact
- Momentum
- Kinetic energy lost
Interpreting the result
- A softer buffer that lengthens the stopping time lowers the force in proportion.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 184–186. Topic reference; no source tables or recommended settings are reproduced.
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