A bucket filled with water is tied to a piece of string and whirled in a vertical plane.(I)at which position (x or y) will the bucket be heavier and explain.(II) give a reason why the water does not pour out of x.
Well, heavier ?
I think you mean the tension in the string
at the bottom it is m g + m v^2/R
at the top it is m g - m v^2/R
if m v^2/R is greater than m g, the tension remains positive and neither the bucket or the water in it fall.
Of course if v is too small, the bucket will not make it to the top and the water in it will spill.
I. The position at which the bucket will be heavier can be determined by analyzing the forces acting on the water and the bucket. Let's consider two positions: x and y.
In position x:
1. The bucket is at its highest point, pointing directly upwards.
2. Gravity is acting vertically downwards, pulling both the bucket and the water downwards.
3. The tension in the string is directed towards the center of the circular path.
In position y:
1. The bucket is at its lowest point, pointing directly downwards.
2. Gravity is acting vertically downwards, pulling both the bucket and the water downwards.
3. The tension in the string is directed towards the center of the circular path.
Since the forces acting on both the bucket and the water are the same in positions x and y, the weight of both the bucket and the water remains constant. So, the bucket will be equally heavy in both positions.
II. The reason why the water does not pour out of position x is due to the centripetal force acting on it. As the bucket is being whirled in a circular path, the string exerts a centripetal force towards the center of the circle, preventing the water from pouring out. This force acts perpendicular to the direction of motion and keeps the water contained within the bucket. However, it's important to note that if the speed of rotation is too high or the string breaks, the water may spill out.
(I) In order to determine at which position, either x or y, the bucket will be heavier, we need to consider the forces acting on the bucket.
When the bucket is at position x (below the string), the weight of the bucket and the water inside act downwards, while the tension in the string acts upwards. However, the centripetal force is also acting inwards towards the center of the circular motion.
When the bucket is at position y (above the string), the weight of the bucket and the water act downwards, while the tension in the string still acts upwards. However, the centripetal force is now acting outwards, away from the center of circular motion.
The net force at position x is the sum of the downward force (weight) and the inward force (centripetal force). At position y, the net force is the sum of the downward force (weight) and the outward force (centripetal force).
Since the net force at position x is greater (downward force + inward force), the bucket will be heavier at position x compared to position y. This is because the inward centripetal force adds to the weight, making it feel heavier.
(II) The reason why the water does not pour out of position x is due to the concept of centripetal force. When an object is in circular motion, there is always a force acting towards the center of that motion, called the centripetal force.
In this case, the tension in the string between the bucket and the hand provides the centripetal force. It continuously pulls the bucket towards the center of the circular motion, preventing the water from spilling out. The combination of the centripetal force and the weight of the water creates a downward force, which keeps the water in the bucket even when the bucket is upside down at position x. As long as the centripetal force is strong enough, the water will stay inside the bucket.