How fast would a bowling ball have to be moving for it to clear the gap in the elevated alley and continue moving on the other side?

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Universal Gravitation

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Presentation transcript:

How fast would a bowling ball have to be moving for it to clear the gap in the elevated alley and continue moving on the other side?

A body in free fall falls 4.9m in the first second of fall. 16 ft 1 sec

8 km 4.9 m

How fast would a bowling ball have to be moving for it to clear the gap in the elevated alley and continue moving on the other side? 8 km/sec. In fact, you could remove the whole alley!

Ball launched horizontally from a cannon with no gravity

Add in gravity…

Now with a slightly larger velocity…

V = 8 km/s

V > 8 km/s

Would a cannon ball fired upward at 8 km/s go into Earth orbit? No! It would simply act as a projectile and crash back into the Earth at 8 km/s. To circle the Earth it must have a tangential speed of 8 km/s

Every body in the universe attracts every other body with a mutual force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Law of Universal Gravitation Where: G = 6.67x N m 2 /kg 2 The Universal Gravitation Constant

He is obviously attracted to her. But, how much force of attraction is there? Assume: His mass = 80. kg Her mass = 52 kg.

He is obviously attracted to her. But, how much force of attraction is there? Assume: His mass = 80 kg Her mass = 52 kg. 0.75m = 4.9x10 -7 N

Example: A satellite is orbit around the Earth makes one complete revolution every 3 days. At what altitude is the orbit? (Mass of Earth = 6.0 E 24 kg, Radius of Earth = 6.4 E 6 m)

The altitude of the distance above the surface of the Earth. Altitude = 8.80x x10 6 Altitude = 8.16x10 7 m

How do the Tides work?

But what about the bulge on the other side?

What we already know: The water under the moon is closer to the moon then the center of the Earth is. So the moon’s gravity pulls harder on the water and the water “heaps up” under the moon.

The New Part: The center of the Earth is closer to the moon then the water on the OPPOSITE side of the Earth. The moon pulls the Earth away from the water, and it appears to “heap up” too.