Formula Used
Vertical drop from angle: h = L × (1 - cos θ)
Impact velocity: v = √(2gh)
Kinetic energy: KE = 0.5 × m × v²
Momentum: p = m × v
Average force from energy: F = KE ÷ d
Average force from impulse: F = m × v × (1 + e) ÷ Δt
Contact pressure: P = F ÷ A
Safety margin: Margin = Allowed force ÷ Selected force
How to Use This Calculator
- Enter the pendulum bob mass in kilograms.
- Enter pendulum length and release angle.
- Use drop height only when measured directly.
- Enter stopping distance or deformation after contact.
- Enter estimated impact time for impulse comparison.
- Set coefficient of restitution for rebound behavior.
- Choose a force method or use conservative mode.
- Press the calculate button and review results above the form.
- Download CSV or PDF for records.
Example Data Table
| Case |
Mass (kg) |
Length (m) |
Angle |
Stop Distance (m) |
Impact Time (s) |
Approx Force Focus |
| Small lab bob |
2 |
1.2 |
45° |
0.020 |
0.015 |
Classroom comparison |
| Medium impact arm |
8 |
1.8 |
60° |
0.030 |
0.012 |
Energy and impulse review |
| Heavy test bob |
20 |
2.5 |
75° |
0.050 |
0.020 |
Conservative planning |
Understanding Pendulum Strike Force
A pendulum strike looks simple, yet it can produce high load. The bob stores gravitational potential energy when it is raised. That energy becomes kinetic energy at the lowest point. The strike then converts motion into deformation, heat, sound, and rebound. Force is not a fixed value. It depends on stopping distance, impact time, bob mass, and material behavior.
Why Energy Matters
The calculator first finds the vertical drop of the bob. For a release angle, the drop is found from the pendulum length and cosine of the angle. The impact speed follows from conservation of energy. A heavier bob, a longer swing, or a larger release angle increases kinetic energy. More energy usually means a stronger strike, if the stopping distance stays small.
Impact Distance and Time
Average striking force can be estimated two ways. The work energy method divides kinetic energy by stopping distance. It is useful when crush depth, dent depth, or travel after contact is known. The impulse method divides momentum change by impact time. It is useful when sensor data, high speed video, or contact duration is known. A conservative report can compare both values.
Rebound and Target Response
The coefficient of restitution changes the impulse estimate. A value near zero means the bob stops with little rebound. A larger value means the bob bounces back, so momentum change increases. Target mass helps estimate acceleration. Contact area helps estimate pressure. These values are planning aids, not proof of structural safety.
Reading the Result
The final force is an average estimate, not a peak load. Real impacts have sharp peaks. Stiff materials can create short contact times and high spikes. Soft pads can lengthen stopping distance and reduce average force. The safety margin compares your selected force with a limit. A margin above one is better than a failed limit.
Practical Use
Use measured values when possible. Enter a realistic stopping distance. Small distances create large forces. Review both energy and impulse outputs. Check the safety limit field against your expected force. Use the exported report for lab notes, design reviews, or teaching examples. For critical machinery, weapons testing, lifting devices, or public safety work, consult an engineer and use test equipment.
FAQs
What does this calculator estimate?
It estimates average striking force from pendulum motion. It also reports velocity, energy, momentum, pressure, safety margin, and target acceleration.
Which force method should I use?
Use work energy when stopping distance is known. Use impulse when impact time is known. Use conservative mode when you want the higher estimate.
Why does stopping distance matter so much?
The same energy spread over a shorter distance creates a larger average force. Small dents, stiff targets, and rigid stops can raise force quickly.
What is coefficient of restitution?
It describes rebound after impact. Zero means little bounce. Higher values mean the bob reverses more strongly, increasing momentum change and impulse force.
Can this predict peak impact force?
No. It estimates average force. Peak force depends on stiffness, vibration, shape, materials, sensors, and contact wave behavior.
What units should I enter?
Use kilograms, meters, degrees, seconds, square centimeters, and newtons. The calculator keeps results in standard metric units.
Is the result safe for design approval?
No. Use it for study, early planning, and comparison. Critical designs need tests, codes, safety factors, and engineering review.
Why include target mass?
Target mass estimates acceleration caused by the selected force. It helps compare strikes against movable carts, blocks, or simple lab targets.