Question

Suppose that when you measured D , you measured the fence at a slight angle, rather than straight across. (If you wanted to exaggerate this effect, suppose you measured the length from one corner to the opposite corner.) How would this affect your final measurement of g (for each part) - would you overestimate g , underestimate it, or neither? Quantitatively estimate the magnitude of the effect if the angle we were off by was one degree. How much would the magnitude of the effect differ between the two parts? Explain.

Answer 1

When measuring the fence at a slight angle, it introduces an error in the measurement of g due to the horizontal component of the force. The magnitude of the effect can be estimated using trigonometry. The error differs between the two parts due to different lengths and angles.

Step-by-step explanation:

When measuring the length of the fence (side D) at a slight angle instead of straight across, it would affect the final measurement of g. This would result in neither overestimating nor underestimating g, but rather introducing an error called component of the force along the horizontal direction.

If we are off by one degree, the magnitude of the effect on g can be estimated by calculating the error introduced due to the angle. This can be done using trigonometry to find the horizontal component of the force and subtracting it from the actual value of the force of gravity g.

The magnitude of the effect would differ between the two parts (A and B) because they would be measured at different angles, resulting in different errors. The error in part A would be larger than the error in part B, due to the difference in the lengths of the sides and the angles at which they are measured.