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An open bucket of water is on a frictionless plane inclined at an angle ∝ to the horizontal. Find the equilibrium inclination to the horizontal of the free surface of the water when (a) the bucket is held at rest; (b) the bucket is allowed to slide down at constant speed (a = 0, v = constant); and (c) the bucket slides down without restraint (a = constant). If the plane is curved so that a ≠ constant, what will happen?

An open bucket of water is on a frictionless plane inclined at an angle ∝ to   the horizontal. Find the equilibrium inclination to the horizontal of the free surface of the water when (a) the bucket is held at rest; (b) the bucket is allowed to slide down at constant speed (a = 0, v = constant); and (c) the bucket slides down without restraint (a = constant). If the plane is curved so that a ≠ constant, what will happen?

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
8 years ago
(a)
The free body diagram of the bucket containing full of water when it is at rest is shown below:
235-2258_1.PNG
When the bucket is held at rest, there is no net force acting on it. Thus, the level of the water CD in the bucket is parallel to the horizontal AB.
Therefore, the equilibrium inclination of the free surface of the water to the horizontal is 00 when the bucket is held rest.
(a)
When the bucket is sliding down at constant speed, there is no net acceleration acting on it. Thus, there is not net force acting on the bucket containing water. Thus, the level of the water CD in the bucket is parallel to the horizontal AB.
Therefore, the equilibrium inclination of the free surface of the water to the horizontal is 00 when the bucket is sliding down the incline at constant speed.
(b)
The free body diagram of the bucket containing full of water when it is sliding down at constant acceleration is shown below:


235-1406_1.PNG
When the bucket is sliding down without restraint, there is not frictional force acting on the bucket. The acceleration of the sliding bucket is constant. The level of the water is along the direction of the motion of the bucket.
Thus, the net force acting on the bucket is
F = ma
Here, mass of the water in the bucket is m and acceleration of the bucket long the incline is a .
235-1864_1.PNG

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