constant accelerated motion 等加速度運動と自由落下
Mechanics Lesson Plans Introduction to constant accelerated motion Please catch this ball. ( Dropping a ball close to student’s hands) Please catch this ball, again.( Dropping a ball about a half meter high )Compare them! How do you feel?“Hmmm. Higher one hit me stronger , so it might have a big energy.”Good! which ball is faster?“ Higher one? ”Cool! A ball became faster as it dropped. Do you remember that kind of motion?Open your notebook, and review your last lesson.What do you call it?“ constant accelerated motion”Sure! I’ll explain you about constant accelerated motion.Please write down today’s topic.等加速度直線運動I’d like to ask you constant accelerated motion’s three equations.What kind of relationship between velocity, time, acceleration, and starting velocity?“ V = V0 + a*T ”yeah, perfect! V means velocity. V0 means starting velocity. a means an acceleration constant. t means time. Each quantities have unit. please say them. What is the unit of acceleration?“ m/s2”Exactly!! please tell me other equations.“ X = V0 *t + 1/2 * a*t*t ”“ 2*a*X = V*V ? V0*V0 ”V; velocity (m/s)V0; starting velocity (m/s)a; acceleration (m/sec2)t; time (sec)X; displacementGreat! I’d like to integrate constant accelerated motion.Here are two balls. Right? One is light, another is heavy.If I drop them at the same time, which one will reach faster on the ground?Discuss it and choose your group’s hypothesis with your reason.1, they reach on the ground at the same time.2, Light ball is faster.3, Heavy ball is faster.4, case by caseLet’s try! Confirm your hypothesis.Listen carefully, and pick out suitable equation from these.1, V = V0 + a*T ”2, X = V0 *t + 1/2 * a*t*t ”3, 2*a*X = V*V ? V0*V0 ”Do you use which equation? No.1? No.2? No.3?“ 1, V = V0 + a*T “In this experiment, x displacements are same. Time is also same. So, accelerations are the same constant. All materials have almost same acceleration constant. It is called “the gravity acceleration” It stand for G. Its quantity is 9.8m/s2.I will change a little these equations.We dropped balls gently, so starting velocity is 0 m/sec.Imagine math graph. It moves horizontally, you use X axis. So we use X as a displacement. It moves vertically, you use Y axis. So we use Y as a displacement of free fall.then, write down free fall equations. Understand free fall and constant accelerated motion are theoretically equal.V = g*tY = 1/2 * g*t*t2*g*Y = V*V ? V0*V0