Physics: Motion and Forces
Motion and forces (運動と力) rarely appear as pure definitions in the Yamaguchi paper. They arrive as a recorded experiment - a trolley pulled by a rubber band, or a tape from a 記録タイマー - and you must read the motion off the tape and then explain it with force arrows.
Reading speed from a tape
- A recording timer prints dots at a fixed frequency. A 60-dot-per-second model (the type used in western Japan, including Yamaguchi) leaves successive dots 1/60 s apart; 50 Hz models give 1/50 s. Read the label before dividing.
- 平均の速さ = 距離 ÷ 時間. Take a block of five or six intervals so the time is a round number (6 intervals at 60 Hz = 0.10 s).
- Equal spacing means 等速直線運動; widening spacing means acceleration.
- 瞬間の速さ at a dot is approximated by the average speed of the short interval containing it.
Forces you must draw
力の三要素 are magnitude, direction and point of application; an arrow starting anywhere else loses the mark. On a slope: 重力 straight down, 垂直抗力 perpendicular to the slope, 摩擦力 along it.
Two rules are constantly confused. Forces are つり合っている only when they act on the same object, are equal in size, opposite in direction and along the same line. 作用・反作用 act on two different objects and never cancel.
Worked example. A 60 Hz tape is cut into 6-interval blocks of 0.10 s. Block 1 spans 6.0 cm, block 2 spans 9.0 cm. Block 1: 6.0 ÷ 0.10 = 60 cm/s. Block 2: 9.0 ÷ 0.10 = 90 cm/s. Spacing grows, so the trolley accelerates by (90 − 60) ÷ 0.10 = 300 cm/s².
Traps. Dividing one 1/60 s gap and calling it an average speed; treating 作用・反作用 as a balanced pair; dropping units; assuming zero force at the top of a thrown ball, when gravity still acts.