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Astronomy Ch04.9: Process of Science: Testing the Law of Gravity

Part A
Each diagram shows a single experimental trial in which you will drop a ball from some height. In each case, the ball’s size, mass, and height are labeled. Note that two diagrams show a basketball, one diagram shows a bowling ball of the same size but larger mass, and one diagram shows a much smaller marble with the same mass as the basketball. You have a timer that allows you to measure how long it takes the ball to fall to the ground. Which pair of trials will allow you to test the prediction that an object’s mass does not affect its rate of fall?

– mass:5.0kg ; size:bowling ball ; height:20m
– mass:5.0kg ; size:basketball ; height:20m

The simplest way to test the effects of mass is to compare the results of two trials that are identical except for the mass of the balls. In the language of experimental design, we say that the mass is the “variable of interest” for this experiment, and we therefore hold the other variables (size and height) constant so that they cannot affect the results.

Part B
Assume you have completed the two trials chosen in Part A. Which of the following possible outcomes from the trials would support Newton’s theory of gravity? Neglect effects of air resistance.

– Both balls fall to the ground in the same amount of time.

Newton’s theory of gravity predicts that, in the absence of air resistance, all objects on Earth should fall with the same acceleration of gravity, regardless of mass. This means that balls dropped from the same height should take the same amount of time to reach the ground.

Part C
Consider again the experimental trials from Part A. This time, you wish to test how the size of an object affects the rate of its fall. Which pair of trials should you compare?

– mass:0.5kg ; size:marble ; height:30m
– mass:0.5kg ; size:basketball ; height:30m

The variable of interest is now size, so appropriate trials to compare are those in which size differs but other variables are constant.

Part D
If you actually performed and compared the two trials chosen in Part C, you would find that, while the basketball and marble would hit the ground at almost the same time, it would not quite be exact: The basketball would take slightly longer to fall to the ground than the marble. Why?

– Because air resistance has a greater effect on the larger ball.

The larger size and lower density of the basketball means it will encounter more air resistance than the marble, so it will take slightly longer to reach the ground.

Part E
Einstein’s theory, like Newton’s, predicts that, in the absence of air resistance, all objects should fall at the same rate regardless of their masses. Consider the following hypothetical experimental results. Which one would indicate a failure of Einstein’s theory?

– Scientists dropping balls on the Moon find that balls of different mass fall at slightly different rates.

Dropping the balls on the Moon removes any potential effects due to air resistance, so a result in which mass affects the rate of fall would directly contradict the prediction of Einstein’s theory.

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