{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"frontierscience","formal_name":"FrontierScience","introduction":"専門的な科学課題を解く能力を評価するベンチマークです。公開データはolympiadとresearchに分かれ、競技問題と研究課題を区別して扱います。\n\nFrontierScience evaluates the ability to solve expert-level scientific tasks. Its public data separates olympiad and research problems so that competition and research tasks can be examined independently.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/openai/frontierscience","indexing_mode":"noindex"},"task_id":"00e3ab86-93c7-58ab-8d17-a25f6d62c5c5","task_key":"olympiad--test--6e9aca19~2d46c4~2d46ea~2d9643~2d86b138e8f2f5","task_revision_id":"1","upstream_id":"6e9aca19-46c4-46ea-9643-86b138e8f2f5","short_description":"Consider a flat billiards table with a round spherical ball kept on it. The…","config":"olympiad","split":"test","body":"{\"problem\":\"Consider a flat billiards table with a round spherical ball kept on it. The billiards table is a horizontal plane, represented by the Cartesian coordinate system as the plane  `\\\\(z = 0\\\\)` with the x and y axes lying in the plane of the table. The coefficient of kinetic friction between the ball and the table is  `\\\\(\\\\mu\\\\)`, the radius of the ball is  `\\\\(R\\\\)`, and the mass of the ball is  `\\\\(m\\\\)`, with the mass uniformly distributed. In this question, the ball is hit with a cue stick.\\n\\nConsider the collision between the cue stick and the ball: Assume the point of contact (at this moment) between the ball and the table is `\\\\(P\\\\)`, the center of the ball is  `\\\\(C\\\\)`, and the point of impact (point where the stick hits the ball) is  `\\\\(T\\\\)`. Initially, the ball is at rest. It is assumed that after the collision, the ball remains in contact with the table and does not lift off: The collision is instantaneous.\\n\\nThe impulse given is along the vector `\\\\(\\\\vec {TA}\\\\)` where `\\\\(A\\\\)` (not the same as `\\\\(P\\\\)`) is any general point on the table\\n\\nIdentify the direction of the velocity of the ball after the ball begins to roll purely. Give your answer in the form of `\\\\(\\\\vec{Px}\\\\)` where the vector starts at point `\\\\(P\\\\)` and ends at \\\\(x\\\\)` which represents any one of the points mentioned above `\\\\( (A, T, P, C) \\\\)`.\\n\\nThink step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.\",\"subject\":\"physics\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/openai/frontierscience","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}