Answers · Measuring and the pendulum
Measuring and the pendulum — return questions key
Check meaning, not exact wording. These are teaching points, not official Cambridge marks.
1. SR1 · Return
Model answer. Stack, say, 20 identical coins and stand the ruler beside the pile. With your eye level with the top, read the height, starting from a clear mark (subtract if it is not zero). Thickness of one coin = height of the pile ÷ 20. Measuring many coins makes the reading big enough to read well, and dividing shares the reading error over all of them.
A full answer includes
- I stacked many identical coins (for example 20) and measured the height of the pile, eye level with the marks and starting at a clear mark.
- I divided the height of the pile by the number of coins to get the thickness of one.
Also accept
- Measure the height of a stack of n coins, divide by n, reading at eye level from a clear mark.
Watch for
- “Measure one coin carefully several times and average.” — Averaging helps with random errors, but a coin is only about 2 mm thick, close to the smallest division. Measuring a stack makes the reading much larger compared with the division.
- “Multiply the height of the pile by the number of coins.” — The pile is many coins thick, so one coin is the height divided by the number of coins.
2. SR2 · Return
Model answer. (a) Period = 16.0 s ÷ 10 = 1.60 s. (b) period / s. (c) The reaction-time error at the start and the stop is shared over 10 oscillations, so the period is about 10 times more precise than timing one. (d) Light gates and an electronic timer: the fall takes only about 0.3 s, about the same as a reaction time, so a hand-held stop-clock would measure mostly reaction error.
A full answer includes
- (a) I calculated 16.0 s ÷ 10 = 1.60 s.
- (b) I wrote a heading with the quantity and the unit, such as “period / s”.
- (c) I said the reaction-time error at the start and stop is shared over 10 oscillations, so the error in one period is smaller.
- (d) I chose light gates (an electronic timer), because the fall lasts about 0.3 s, as short as a reaction time.
Also accept
- (a) 1.60 s (1.6 s); (b) “period / s” or “T / s”; (c) the reaction error is divided by 10.; (d) light gates.
Watch for
- “The heading is “period (1.60)”.” — A heading names the quantity and its unit, like “period / s”; the numbers go in the column.
- “Timing 10 oscillations removes the reaction time.” — It shares the same reaction error over 10 oscillations, so it is 10 times smaller per oscillation; it is not removed.