A rectangular container, of base dimensions 0.4 m ×0.2 m and height 0.4 m, is filled with water

step 1 This equation you have to find the angle of the border surface relative to the horizontal or ang

A rectangular container, of base dimensions 0.4 m ×0.2 m and...

A rectangular container, of base dimensions $0.4 \mathrm{m} \times$ $0.2 \mathrm{m}$ and height $0.4 \mathrm{m},$ is filled with water to a depth of $0.2 \mathrm{m} ;$ the mass of the empty container is $10 \mathrm{kg} .$ The container is placed on a plane inclined at $30^{\circ}$ to the horizontal. If the coefficient of sliding friction between the container and the plane is $0.3,$ determine the angle of the water surface relative to the horizontal.

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Key Concepts

Role of Friction in Static Equilibrium

The frictional force, characterized by the coefficient of static friction, determines how much of the gravitational component parallel to the inclined plane can be resisted. In a situation where the object is on the verge of sliding, comparing the downslope gravitational force with the maximum static friction helps decide if the system remains at rest. This analysis is vital for understanding the overall equilibrium of any object on an inclined surface.

Hydrostatic Equilibrium

A fluid at rest will adjust its free surface until it is perpendicular to the net acceleration acting on it, which, in the absence of any additional accelerations besides gravity, means the surface is horizontal relative to the Earth. This principle holds regardless of the container’s orientation, as the water finds a level position under gravity.

Force Decomposition on an Inclined Plane

When an object is resting on a slope, the gravitational force acting on it can be split into two components: one parallel to the plane and one perpendicular to it. This decomposition is essential for analyzing whether friction can balance the downslope force and thus maintain static equilibrium on the incline.

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