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Regarding Algebra based free response #1 I believe the answer for c) is incorrect. I believe since the question asks for the position relative to where the mass is on the spring at full compression the displayed answer for c) should be subtracted from the answer for b). Which would leave: square root((mgsintheta)squared + 2kmgdsintheta)/k
James, you are correct. The original intent of part c) was to ask where the block's speed was a maximum (F = ma = 0) relative to where it first hit the spring, but it was worded incorrectly. The wording is now changed so the answer is mgsintheta/k. A new version will be uploaded shortly. Thank you very much for your correction. John
James - the new version is now posted. - Melissa
In the free response for the calc based problems, why is the answer to a and b negative?
Annette - are you talking about a problem on the unit test? What is the question number? - Melissa
Sorry--I am looking at the calc based free response worksheet. specifically #3 a and b.
Annette - sorry, the problem is poorly written. It was intended to have you realize that the external force is the negative of the spring force, but that was not communicated properly. It is rewritten, so we're just asking for the work done by the spring force, and in that case, the negative sign goes away. A new version of the problem set will be loaded with the reworded question and the answer key. Thank you very much. John
Annette - new version is now posted. - Melissa
For 3c on calc free response, a) would be negative because x2 > x1 so then 1/x2 < 1/x1. This would mean that answer b) must be a positive value of the same magnitude.
Bill, we don't really ask which one is negative or positive. If you assume that x1 is the largest value (the amplitude), then x2 would be smaller and 1/x2 > 1/x1. If you make a different assumption about where x2 can be you get a different answer. But that would come out in the math - neither answer a nor b tell you if the parentheses are positive or negative. The important question in part c is that the work done in opposite directions is equal in magnitude and opposite in sign - just like you said in your comment. This reflects the conservative nature of the spring force - if you make a complete path and go back to where you started, the net work is zero. Zero is the answer to part c. John