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Chapter 9: Problem 43

You fill a bucket half full of water and swing it in a vertical circle. When the bucket is at the top of its arc, the bucket is upside down but the water does not spill on your head. What direction is "up" for the water? Explain.

Short Answer

Expert verified
'Up' for the water is towards the center of the circular path.

Step by step solution

01

Understand the Situation

You are swinging a half-filled bucket of water in a vertical circle. At the top of the swing, the bucket is upside down.
02

Identify Forces Acting at the Top

At the top of the arc, two main forces are acting on the water: gravity (acting downwards) and the centripetal force (which is necessary to keep the water in a circular path).
03

Centripetal Force and Gravity Relationship

Both the centripetal force and gravity are pulling the water towards the center of the circle. This combined force is directed downwards towards the center of the circle.
04

Direction of 'Up' for the Water

Since the water is being held in place and not spilling, the direction 'up' for the water corresponds to the direction of the force keeping the water in the bucket, which is towards the center of the circular path.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Centripetal Force
When you swing the bucket of water in a vertical circle, it remains in the bucket without spilling. This is because of centripetal force. Centripetal force is a real force that acts on an object moving in a circular path, pulling it towards the center of the circle.
The main purpose of this force is to keep the object constantly changing direction so it can follow a circular trajectory. Without centripetal force, the object would fly off in a straight line due to inertia.
So, in this example, centripetal force is responsible for keeping the water in the bucket while you swing it around.
Gravity
Gravity is the force that pulls objects towards the Earth. When you swing the bucket at the top of the arc, gravity acts downwards towards the ground.
But, in this position, the direction of gravity is also aligned with the centripetal force needed to keep the water following the circle. This downward force towards the center of the circle helps prevent the water from spilling.
Inertia
Inertia is an object's tendency to resist changes in its motion. In the bucket example, the water, due to inertia, wants to move in a straight line. However, the continuous change of direction due to the circular motion means that the water feels an inward pull.
This inward pull, created by centripetal force and gravity, keeps the water secured in the bucket, counteracting its inertial tendency to move straight ahead.
Centripetal Acceleration
Centripetal acceleration is the rate of change of tangential velocity of an object moving in a circular path. This acceleration always points towards the center of the circle.
In our example, centripetal acceleration ensures that the water constantly changes direction, keeping it on the circular path without spilling. The combination of gravity and centripetal force provides the necessary centripetal acceleration to keep everything moving smoothly.

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