Estimate the initial speed of a projectile that embeds in a stationary pendulum bob. Enter the projectile mass, the bob mass before impact and the vertical rise of their combined center of mass. The calculator uses a fixed gravitational acceleration of 9.80665 m/s².
Enter masses in kilograms and height in meters. For example, 10 g is 0.010 kg and 5 cm is 0.050 m. The projectile mass must be greater than zero. A zero projectile mass makes the initial-speed result unavailable because the formula divides by that mass; unavailable does not mean zero speed.
Measure height vertically from the combined center of mass immediately after capture to its highest point. Do not enter the distance traveled along the arc. The bob mass excludes the projectile.
The model assumes a stationary bob, complete capture without rebound or pass-through, a brief horizontal impact at the bottom of the swing, and negligible external impulse along the impact direction. It treats the bob and captured projectile as a translating lumped mass with negligible suspension mass. A rigid physical pendulum with significant rotational inertia requires a different model.
Kinetic energy is not conserved during capture. The subsequent swing assumes negligible air resistance and pivot friction. Energy lost during that swing generally makes this ideal calculation underestimate the projectile speed. A zero rise returns zero speed under the ideal model and cannot resolve motion below the measurement threshold.
For a 0.010 kg projectile captured by a 1.000 kg bob that rises 0.050 m, the combined speed immediately after impact is √(2 × 9.80665 × 0.050) ≈ 0.990 m/s. The mass ratio is (1.000 + 0.010) / 0.010 = 101, giving an initial projectile speed of approximately 100.019 m/s.
The calculation retains intermediate precision and rounds only the displayed results. Measurement uncertainty may justify reporting fewer digits.
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