1) A bucket of water can be whirled in a vertical circular path in such a way th

Question

1) A bucket of water can be whirled in a vertical circular path in such a way that the water does no spill. a. Describe in your own words how this is possible. b. Which forces act on the bucket when it is at the bottom? c. Which forces act on the bucket when it is at the top? Is any of these forces zero? If so, why? d. What is the minimum speed of the bucket at the top to guarantee that the water does not splash down on you? (Show your work). 2) Because of Earth’s rotation about its axis, you weigh slightly less at the equator than at the poles. Explain. 3) Since ancient times we have known of the existence of 6 planets in our Solar System: Mercury, Venus, Earth, Mars, Jupiter and Saturn. Because of their progressively greater distance, Uranus was not discovered until 1781, Neptune in 1846 and Pluto in 1930. Research the odd facts about the discovery of Neptune and write a summary of the physics principles behind this discovery.

Explanation / Answer

1. here the circular motion of bucket generates centrifugal force.

That force pushes the water against the bottom of the bucket, perpendicular to the center of   rotation.

If the bucket is going fast enough, the centrifugal force will be greater than the force
of gravity and the water will stay in the bucket even when upsidedown.

hence the answer.

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yes apple exerts force, that can be given by

F = (G*m1*m2) / r^2

F on earth due to apple = - force on apple due to earth

So they are exerting equal forces on each other,contitues - action and reaction pair

The difference is the earth has a whole lot more momentum than the apple,

so it resists moving a lot more, and the apple ends up getting pulled to the earth because it's so much easier to move

momentum of earth in very large due to its higher mass than than of apple( negligible)

he earth does actually move a tiny bit but this is negligible

or

1)

Newton's thrid law states that for an action, there is an equal and opposite reaction, in an inertial reference frame.
The bucket at the highest point experiences two types of acceleration. One is gravity pointing downwards. Another is centripetal acceleration, which deters it from moving either to the right or to the left. The centripetal acceleration also points downwards. The bucket, at zero vertical velocity, applies a force on the water, equal to the centripetal force yet inthe reverse direction.
Therefore, the water in the bucket feel zero instantaneous force at zero instantaneous velocity. According to newton's first law, it shouldn't fall at that point.

2)

The two reasons (centripetal acceleration and less g due to increased radius at the equator) have been given in the answers above, but only one answer referred to both of them, and then only suggested that it was one or the other. Well it's the combined effect of the two that reduces your equatorial weight. And (this shouldn't be too surprising) the reason Earth's equatorial radius is greater than its polar radius is in fact centripetal acceleration applied to the earth itself. Earth's huge size causes the solid materials like rock that it's made of, that are rigid on a smaller scale, to behave more like a thick liquid and be distorted in the direction of the centripetal acceleration.
Note that you won't see your weight difference on a weight-balance type scale, since those weights are subject to the same centripetal and gravitational accelerations as you are. Only a spring-based scale can measure these differences.

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