Newtons Cannon or Mountain Ch 4 A projectiles

Newton’s “Cannon” or “Mountain” • Ch. 4: A projectile’s path is parabolic as it goes up & down. NEWTON’S IDEA (in the 1600’s!): Put a large cannon on a large mountain. Shoot cannon balls (projectiles) at faster & faster velocities. Eventually, the initial velocity is fast enough that the Earth's curvature must be taken into account in looking at the path. If the initial velocity continues to increase, the path extends farther & farther around the Earth. Finally, at some critical velocity (Newton estimated ~40, 000 km/h!) the path would go around the Earth all the way & eventually past the starting point & keep on going. It would keep on “falling” forever! The projectile would ORBIT the Earth! This is essentially what happens when a satellite is put into orbit. • Ch. 4: A projectile is in “free” fall in Earth's gravity. When an object orbits the Earth, it also is in “free fall”! Maybe it will be easier now to understand why objects in orbit are in “free fall”?

• To keep an object in orbit, the Gravitational Force provides the “Centripetal Force”! F = (mv 2)/r = G(m. ME)/r 2 • Figure: Newton’s “Cannon” showing parabolic projectile paths becoming orbits as the initial velocity increases. Many web pages (11, 000 hits on Google) are devoted to this. Some have animated illustrations, where the user can specify the initial velocity & see the path (orbit) it will follow. Typical web pages: http: //www. waowen. screaming. net/revision/force&motion/ncananim. htm http: //www. smaphysics. ca/phys 40 s/field 40 s/newtmtn. html http: //www. astronautix. com/lvs/newannon. htm