EXPERIMENTAL UNCERTAINTIES II (EU II) Sometimes when you measure the same quanti

Question

EXPERIMENTAL UNCERTAINTIES II (EU II) Sometimes when you measure the same quantity, you can get different results each time you measure it. That happens because different uncontrollable factors affect your results randomly. This type of uncertainty, random uncertainty, can be estimated only by repeating the same measurement several times. Consider the following experiment being performed by yourself in the physics laboratory. A ramp is clamped near the edge of a table. A ball is released from a height h above the table as shown in the diagram. The ball leaves the slope horizontally and lands on the floor a distance R, (referred to as the range) from the edge of the table. Special paper is placed on the floor on which the ball makes a small mark when it lands and you use a long ruler to measure the range, R and h. You have been asked to investigate how the distance d on the floor changes when the height h is varied. You decide to roll the ball once from the top end of the ramp. You then see a single spot on the paper where the ball landed. You measure the range, R (distance from the point directly under the end of the ramp to the landing spot) with a ruler. Say that your first reading is Ri -650.4 mm. Then you roll the ball a second time and observe that the ball lands at a slightly different position. You now see two spots on the paper 62 63 64 68 You measure the distance to the second spot and you have your reading R2- 660.6 mm Question 1 - Write down what you now think is the best value for Rben Clearly a value halfway in between is the best estimate for "true" range. You decide to roll the ball a third time from the same height and observe that the ball again lands at a slightly different place. You have now three readings form rolling the ball from the same height: R: = 650.4mm, R2-660.6mm, and R3-659.1 mm Question 2 - Write down what you now think is the best value for Rbea You can see that the average changes as we take more and more readings.

Explanation / Answer

Question 1 : after second reading which was R2 = 660.6 mm

Rbest = 1/2 * (R1 + R2 ) = 1/2 * (650.4 + 660.6) = 655.5 mm

Question 2: After third reading which was R3 = 659.1 mm

Rbest = 1/3 * ((R1 + R2 + R3 ) = 1/3 * (650.4 + 660.6 + 659.1) = 656.7 mm

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