**Goal:** Recognize sources of measurement error.

**Source:** UMPERG

Using a stopwatch to measure the time for a ball to fall a distance of 1

meter, and based upon 3 measurements of the time, a student obtained a

value for the gravitational constant of g = 9.4 +/- 0.2 m/s^{2}.

What can be done to improve the accuracy of the data?

- Take more data
- Allow the ball to fall a larger distance
- Use a digital timer
- Allow the ball to roll down a slope rather than freefall
- Use a heavier ball
- More than one, but not all, of the above would improve the accuracy
- All of the above would improve the accuracy
- None of the above would improve the accuracy
- Cannot be determined

## Commentary:

## Answer

Several factors, such as air resistance and reaction time, can affect

the accuracy of the measurement. Without more details, we do not know

which factors have the largest effect. For example, if the ball falls

over a larger distance the factor of reaction time becomes less

significant, but the factor of air resistance becomes more significant.

The impact on the overall accuracy is undetermined. A ball rolling

down a slope would move slower and would decrease the effects of air

resistance and reaction time. But new factors such as rolling friction

and moment of inertia (radius) need to be considered. Students will

make assumptions. Getting students to state their assumptions is what

is most important.

## Background

Issues to consider: (1) Do students think that merely collecting more

data or using a digital timer will improve accuracy? (2) Can students

identify factors that could impact the accuracy of measuring the

gravitational constant using the method described? (3) Can students

describe how the factors impact the accuracy and how the proposed

modifications would increase/decrease the accuracy.

## Questions to Reveal Student Thinking

How do we know that the measured value for g is inaccurate? What factors

impact the accuracy? What factor impacts the accuracy the most?

Does increasing the distance the ball falls impact the accuracy? Why?

How?

Consider some of the other factors.

## Suggestions

Have different groups of students measure the time for an object to fall

one meter. Have each group consider a different object: (1) crumpled

paper, (2) small metal ball, (3) two objects of the same size and shape,

but different weight, etc.