Force probes are versatile tools in the physics lab, but their internal workings can introduce artifacts when measuring rapidly changing forces. The Dual-Range Force Sensor by Vernier (Fig. 1) uses strain gage technology to measure force, based on the bending of a beam. Strain gages along the length of the beam change resistance as the beam bends (Fig. 2). The elasticity of the beam leads to oscillations that persist after being excited by an impulsive force. How quickly the force probe freely returns to zero is thus related to the rigidity of the beam and the total mass attached to it. By varying the added mass and measuring the resulting frequency of the probe's internal free oscillations, the effective mass and spring constant of the probe's moveable parts can be found. Weighing of the probe parts and conducting a Hooke's law experiment provide static verification of these parameters. Study of the force sensor's behavior helps students to learn about damped harmonic motion, mathematical modeling, and the limitations of measuring devices.

## References

*F*-versus-

*t*curve during the first quarter-period, even though the time scales differ. In a representative experiment, the popper gained 0.046 kg·m/s of momentum, while the integral of force with respect to time was 0.043 N·s for the first quarter-cycle of the graph—reasonably close agreement despite damping and the impulse occurring over a finite time.

^{9}N/m. See http://www.pcb.com/TestMeasurement/Force/GenPur.aspx.

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