A researcher at a Martian exploration outpost is attempting to determine the local acceleration due to gravity, gMg_MgM, using two different experimental setups.
Method A: Vertical Drop A dense steel sphere is released from rest from a height of 2.50 m2.50\text{ m}2.50 m. The researcher measures the fall time using a manual digital stopwatch.
Method B: Inclined Track A low-friction hover-pod model is released from rest from the top of an air-track of length 3.000 m3.000\text{ m}3.000 m, inclined at an angle of 15.0∘15.0^\circ15.0∘ to the horizontal. The researcher measures the time taken to slide to the bottom using the same manual digital stopwatch.
Single measurements from these setups are recorded below:
| Method | Distance / m\text{m}m | Angle / ∘^\circ∘ | Time / s\text{s}s |
|---|---|---|---|
| Method A (Vertical Drop) | 2.502.502.50 | −-− | 1.181.181.18 |
| Method B (Inclined Track) | 3.0003.0003.000 | 15.015.015.0 | 2.482.482.48 |
Compare and discuss the uncertainties associated with the values of gMg_MgM calculated from these single sets of measurements.
Describe how the researcher should analyze a full range of data for both methods (by varying the independent variables) to obtain more reliable values for gMg_MgM and estimate their uncertainties.
