Properties of gravity ?
Mr. Nicholls explained to the class that Galileo wanted to study the properties of gravity but that
the acceleration of gravity was too large. Therefore, he studied the effects of gravity on a
‘gravity dilution device’: a simple inclined plane. Mr. Nicholls wanted the class to reproduce
Galileo’s investigations with their own inclined planes.
Each pair of students was given a marble and a 1.5 meter ramp with a groove cut down the
center. (You can do this experiment yourself on a board without a groove, or by placing two
meter sticks next to each other with the marble rolling down the groove between them). One end
of the ramp was raised up on a book; and an index card was taped to the other end of the ramp
and to the table to make a smooth transition for the marble between the two surfaces.
The class was asked to start the marble from rest at the top of the ramp and to observe its motion
traveling down the ramp and across the table. The class all agreed that the marble increased its
speed rolling down the ramp, and after some discussion, that the ball rolled with a constant speed
across the table top.
Next, Mr. Nicholls had the class start the ball from rest half-way up the ramp. Once again, all
agreed that the ball moved slower across the table top than before. “So does that mean that the
acceleration is less?”, he asked.
About half the class thought that the acceleration was less because the marble was moving
slower across the table. The other half thought the acceleration should be the same, but they
weren’t sure why.
After collecting position, time, and velocity data and calculating the acceleration, the class could
see that in fact the acceleration on the ramp was constant.
What was wrong with the reasoning that a smaller velocity implies a smaller acceleration?
All things being equal, a smaller velocity would imply a smaller acceleration, according to the
equation defining acceleration. But all things are not equal. What other factors have changed
besides the velocity at the bottom of the ramp? Can you show using the equations how these
changes cancel each other out, resulting in the same acceleration as before?
The class was then told to put a second book under the ramp and repeat the experiment with the
marble starting from the top of the ramp. Everyone agreed that the velocity was greater across
the table compared to the previous set-up. “So do you think the acceleration has changed, or
not?” Mr. Nicholls asked. The whole class agreed that the acceleration of the marble was larger.
“How do you know?”, the instructor asked.
“Because the marble is moving faster at the bottom of the ramp”, Beth said.
“But a different speed at the bottom of the ramp didn’t change the acceleration in the last
experiment. Why should it imply a different acceleration now?”
How would you respond to Mr. Nicholls’ question?
(In fact, after collecting more data, the class did prove that the acceleration of the ramp set at a
greater angle was larger.)
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the acceleration of gravity was too large. Therefore, he studied the effects of gravity on a
‘gravity dilution device’: a simple inclined plane. Mr. Nicholls wanted the class to reproduce
Galileo’s investigations with their own inclined planes.
Each pair of students was given a marble and a 1.5 meter ramp with a groove cut down the
center. (You can do this experiment yourself on a board without a groove, or by placing two
meter sticks next to each other with the marble rolling down the groove between them). One end
of the ramp was raised up on a book; and an index card was taped to the other end of the ramp
and to the table to make a smooth transition for the marble between the two surfaces.
The class was asked to start the marble from rest at the top of the ramp and to observe its motion
traveling down the ramp and across the table. The class all agreed that the marble increased its
speed rolling down the ramp, and after some discussion, that the ball rolled with a constant speed
across the table top.
Next, Mr. Nicholls had the class start the ball from rest half-way up the ramp. Once again, all
agreed that the ball moved slower across the table top than before. “So does that mean that the
acceleration is less?”, he asked.
About half the class thought that the acceleration was less because the marble was moving
slower across the table. The other half thought the acceleration should be the same, but they
weren’t sure why.
After collecting position, time, and velocity data and calculating the acceleration, the class could
see that in fact the acceleration on the ramp was constant.
What was wrong with the reasoning that a smaller velocity implies a smaller acceleration?
All things being equal, a smaller velocity would imply a smaller acceleration, according to the
equation defining acceleration. But all things are not equal. What other factors have changed
besides the velocity at the bottom of the ramp? Can you show using the equations how these
changes cancel each other out, resulting in the same acceleration as before?
The class was then told to put a second book under the ramp and repeat the experiment with the
marble starting from the top of the ramp. Everyone agreed that the velocity was greater across
the table compared to the previous set-up. “So do you think the acceleration has changed, or
not?” Mr. Nicholls asked. The whole class agreed that the acceleration of the marble was larger.
“How do you know?”, the instructor asked.
“Because the marble is moving faster at the bottom of the ramp”, Beth said.
“But a different speed at the bottom of the ramp didn’t change the acceleration in the last
experiment. Why should it imply a different acceleration now?”
How would you respond to Mr. Nicholls’ question?
(In fact, after collecting more data, the class did prove that the acceleration of the ramp set at a
greater angle was larger.)
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