Question

A torque meter is calibrated to reference standards of mass, length, and time, each with 5% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of: ___________

Answer 1

The net accuracy of torque measured by a torque meter calibrated with a 5% accuracy each in mass, length, and time would be around 8.66%, calculated using the root-sum-square method assuming independent uncertainties.

Step-by-step explanation:

The accuracy of the torque measured by a torque meter calibrated with 5% accuracy in mass, length, and time will not be simply 5% but needs to be considered collectively, as these variables are typically multiplicative when computing torque. Torque (τ) is calculated by τ = rFsin(θ), where r is the lever arm length, F is the force applied, and θ is the angle between the force vector and the lever arm. Since both the force applied and the lever arm length could be affected by the calibration accuracy, the net accuracy of the measured torque must take into account the potential compound error.

The combined percentage uncertainty can be roughly estimated using the root-sum-square (RSS) method for independent errors: ∑(Δ⁡x/x)2, where x represents each contributing factor to the measurement. Given three calibration accuracies each at 5%, the net accuracy would be √(52+52+52)% = √(75)% ≈ 8.66%. Therefore, the net accuracy is expected to be around 8.66%, assuming independent uncertainties.