ydubrovensky4
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- Sep 16, 2023
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I have tried to understand the problem, but I am getting stuck in the following areas:What are your thoughts? What have you tried? Where are you getting stuck?
Please re-read the "Read Before Posting" message, and reply with the requested information. Thank you!
Think about the path the center of the ball will follow, and add up the lengths of the segments and arcs that make up that path. Here is a picture of part of that path, in red:I am not sure how to calculate the distance that ball A has rolled along figure 1 when it returns back to its original position.
Without knowing that, you couldn't find the path. Look at the picture above.I am not sure what the significance of the fact that ball A is the same size as the two identical white balls is.
They determine part of the path.I am not sure what the significance of the fact that the two identical white balls are fixed to the box at a point is.
Dr Peterson,Think about the path the center of the ball will follow, and add up the lengths of the segments and arcs that make up that path. Here is a picture of part of that path, in red:
It doesn't say where it starts; you can take your choice. It doesn't matter, since it returns to wherever it starts.Dr Peterson,
Does the ball start at point D or 3.5 cm from point D?
Thank you,
Steven
OK, I see what you're saying. I too realized that where it starts didn't matter. I was just curious why you chose to start at DIt doesn't say where it starts; you can take your choice. It doesn't matter, since it returns to wherever it starts.
I would probably take it as starting at D for simplicity, if I paid any attention to that at all. I didn't bother showing that in the last picture. Is this clearer?
Um ... because that's (near) where the ball is in the picture I used?OK, I see what you're saying. I too realized that where it starts didn't matter. I was just curious why you chose to start at D
On the 1/2O, I got 1/2 * 3.14 * 7Without knowing that, you couldn't find the path. Look at the picture above.
They determine part of the path.
But there's one really big thing you are misunderstanding, as shown by your drawing:
They tell you that the ball rolls anti-clockwise around the entire figure, not just back and forth along the top. So the path is more like this:
Does that help you visualize it?
What do you mean by that? Please provide more details of your solution.On the 1/2O, I got 1/2 * 3.14 * 7
If you're talking about my arc BC, you may be almost thinking correctly. What is the radius of that arc? How do you find its length?On the 1/2O, I got 1/2 * 3.14 * 7
I have no idea where to start.If you're talking about my arc BC, you may be almost thinking correctly. What is the radius of that arc? How do you find its length?
You can start by labeling some of the distances in either of my pictures, so we can see what you don't understand:I have no idea where to start.
Anything can show of your own thinking will help us find ways to help.What is the radius of that arc? How do you find its length?