High Road, Low Road. Fact and conceptual
The Situation
Mr. Nichols has brought in a special race track like the one shown in the figure. Two balls are released from the same height on a short ramp, so they travel with the same speed along the first horizontal section. The ball on the horizontal track, colored red, continues to travel with the same speed until it bumps into a block at the end of the ramp. The second ball, colored blue, follows a downward slope along a ‘dip’ and then rises up again to the original height before reaching the end of the ramp. “So,” Mr. Nichols asks, “which ball wins the race?”
What is your prediction?
The Predictions
Cathy says the red ball will win because the blue ball has to travel a farther distance.
John says the blue ball wins because it moves faster when it travels into the dip.
Frank agrees that the blue ball moves faster when it enters the dip, but it must also slow down by
the same amount when it travels up the ramp again. Because these two accelerations cancel out,
he believes the race will end in a tie.
Any comments? Are any of these arguments clearly wrong? On what basis do you make that
determination?
The Answer
Mr. Nichols releases both balls, and the blue one following the dip in the track is the clear
winner. However, the class can also see that the blue ball did return to its original speed when it
came out of the dip, so Frank was correct in his reasoning.
Can you explain why Cathy was wrong, even though the blue ball does travel a farther distance?
Can you explain how Frank could be correct in his reasoning, but still make the wrong
prediction?
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Mr. Nichols has brought in a special race track like the one shown in the figure. Two balls are released from the same height on a short ramp, so they travel with the same speed along the first horizontal section. The ball on the horizontal track, colored red, continues to travel with the same speed until it bumps into a block at the end of the ramp. The second ball, colored blue, follows a downward slope along a ‘dip’ and then rises up again to the original height before reaching the end of the ramp. “So,” Mr. Nichols asks, “which ball wins the race?”
What is your prediction?
The Predictions
Cathy says the red ball will win because the blue ball has to travel a farther distance.
John says the blue ball wins because it moves faster when it travels into the dip.
Frank agrees that the blue ball moves faster when it enters the dip, but it must also slow down by
the same amount when it travels up the ramp again. Because these two accelerations cancel out,
he believes the race will end in a tie.
Any comments? Are any of these arguments clearly wrong? On what basis do you make that
determination?
The Answer
Mr. Nichols releases both balls, and the blue one following the dip in the track is the clear
winner. However, the class can also see that the blue ball did return to its original speed when it
came out of the dip, so Frank was correct in his reasoning.
Can you explain why Cathy was wrong, even though the blue ball does travel a farther distance?
Can you explain how Frank could be correct in his reasoning, but still make the wrong
prediction?
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