A rectangular box containing water is accelerated upwards at 3 m / s^2 on an inclined plane mak

A rectangular box containing water is accelerated upwards at...

Key Concepts

Non-Inertial Reference Frames

In a non-inertial reference frame, such as an accelerating container, fictitious forces must be introduced to account for the observed effects. This concept helps explain how, in an accelerating system, objects behave as if additional forces (beyond gravity) are acting on them, influencing phenomena like the orientation of liquid surfaces.

Effective Gravitational Field

The effective gravitational field is the vector sum of the true gravitational acceleration and the acceleration of the non-inertial frame. In an accelerating container, this results in a modified direction and magnitude of 'gravity' that dictates how fluids and other objects behave within the container.

Equilibrium of Fluid Free Surface

In fluid statics, the free surface of a liquid at rest always aligns perpendicular to the effective gravitational field. This principle is crucial when studying fluids in accelerating systems because it determines how the surface will tilt in response to both real gravity and the imposed acceleration.

Vector Decomposition

Vector decomposition is the process of breaking down a vector into its components along defined axes. In the context of an accelerating container on an inclined plane, it allows for the calculation of the effective gravitational direction by resolving both the gravitational and acceleration vectors into components along the plane's axes.

Transcript

00:01 In this question, it is given that there is an inclined plane which is making an inclination of 30 degree with respect to horizontal.

00:13 On this inclined plane, there is a rectangular box filled with water.

00:22 This rectangular box is moving upwards with an acceleration of 3 meter per second square.

00:35 Now we need to determine the slope of the free liquid surface.

00:40 Consider this is the free liquid surface on which let us consider a fluid particle.

00:52 Let us say o.

00:54 On this particle, what will the forces be acting? the force due to the acceleration, f, and the pressure force.

01:11 That is, the force due to the pressure is acting.

01:15 Apart from these two forces, the weight of the fluid particle will be acting in the vertically downward direction.

01:21 So there are three forces.

01:24 One is the force due to acceleration, we can say that f is equal to ma and w is the weight of the fluid particle, that is f is equal to moss -hid acceleration due to gravity and the force due to pressure.

01:43 P is equal to pressure multiply with area.

01:49 Okay.

01:53 This is the angle.

01:55 Theta which we need to determine.

01:56 Let us say the inclined plane is making an inclination of 30 degree to the horizontal which we will call it as 5 which is 30 degrees.

02:14 If this is theta then this will be theta.

02:22 Why because this is a horizontal line and this is the vertical end and this is an inclined plane or we can say that free liquid surface.

02:34 The free liquid surface is making an inclination of theta with respect to horizontal.

02:38 That is the case definitely because of the alternate angles.

02:43 This will be theta.

02:45 Now if we consider the force f, this force will have two components.

02:50 One will be the horizontal component fh and another will be the vertical component fy...

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