Title: GR8677.006 [tagged] Post by: conantee on January 02, 2011, 09:56:03 AM 6. อนุภาคอันหนึ่งอยู่นิ่งบนยอดของรางโค้งไร้แรงเสียดทาน พิกัด x และ y ของรางสัมพันธ์กันตามสมการ
![]() (A) ![]() (B) ![]() (C) ![]() (D) ![]() (E) ![]() [tag: กลศาสตร์ดั้งเดิม, กฎของนิวตัน, กลศาสตร์ลากรานจ์, ปรนัย, ระดับมัธยม, ระดับปริญญาตรีตอนต้น, คำนวณทั่วไป] Title: Re: GR8677.006 Post by: conantee on February 07, 2011, 04:30:59 AM What do you need to answer this question? Normal force? Lagrange's equation with a constraint? Not at all! It turns out that you can use asymptotic behavior of the answer.
First, you can eliminate choice (A) and (B) since the acceleration of the particle is not constant (otherwise, it just same as free fall or no acceleration). Then, imagine when the particle goes very far. The tangent direction get closer and closer to y-direction. That is as if there is no track at all. The answer should converges to free fall acceleration, ![]() ![]() The correct answer is (D). 39 of 100 people got it correctly. To solve this question properly. One must project the gravitational force into tangential direction. (Note that the normal force due to the track is always normal to the motion). One can find the direction of tangential direction at point ![]() ![]() In this case, it equals to ![]() ![]() The projection of gravitional force ![]() ![]() ![]() The norm of this tangential component equals to ![]() ![]() The tangential acceleration can be found by just dividing the mass ![]() |