00:01
So here we have been given that there is a parabolic dish and this parabolic dish is rotating at a constant rate.
00:10
And the equation of this parabolic dish is given to us as y equals to r square by 4.
00:17
And there is a block here which is kept and that block has the mass of 3kg.
00:23
And the distance of this block from the base in the horizontal direction, that's 2 meters, and there is static coefficient of friction that is 0 .5 which is offered by this floor.
00:40
So we need to figure out the maximum speed of this block.
00:44
So considering v as the maximum speed, let's draw the free body diagram.
00:49
There will be the weight here in this direction that will be its mass times acceleration due to gravity and there will be normal force.
01:00
In addition to that, there will be friction force because of rotation the block will have the tendency to go up which will be opposed by the friction force.
01:10
And this friction force is responsible for providing the necessary sentry -petal force.
01:16
So friction force will be mu -times n and let's complete the simple right angle triangle.
01:24
So here let's take this angle as theta because we need to project the force.
01:28
Forces such that the total force is pointing towards the center.
01:35
So for that we will project this friction force because this angle is theta as these two lines are parallel and this is the transversal.
01:43
So its projection along this side will be mu n cost theta and along this direction it will be mu n sine theta.
01:53
Similarly we can project this normal force as well.
01:57
Its projection here will be n cost theta and its projection here.
02:00
Here will be n sine theta...