Friction: Block 1 and block 2 have the same mass, m, and are...

Name: Friction: Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?
Uploaded: 2021-11-01T17:38:45-08:00
Duration: 5 min 35 s
Channel: Rajesh Kumar
Description: Friction: Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

Friction: Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

Transcript

00:01 We're given two situations.

00:02 This is the situation number one, which you can see from here.

00:06 This is the situation number one, wherein a block is at a height edge and it is sliding down the inclined plane.

00:15 The angle is given as 30 degree and coefficient of friction is given as mu.

00:20 And other situations, the same object of the same mass is falling from an inclined plane.

00:26 The important thing is the height of the plane is same.

00:29 It is also h in this case.

00:32 All right.

00:33 So now the angle is 60 degree and we have to find in which case the speed of the object would be more.

00:40 So that can be done very easily.

00:43 So what we can see is from here the potential energy is getting lost, right? when the object is coming from here to here or from here to here, potential energy is getting lost.

00:55 So that amount of potential energy which is getting lost is mgh in both cases.

01:00 It is mgh because it is falling from the same height now this potential energy is getting converted into two things one is the kinetic energy so half of m i'm calling the speed v1 here so half m v1 square so some part of the potential energy which we are giving is getting converted into the kinetic energy and some of them some of the energy that we are supplying is getting lost in the form of the work done by friction so in the form of the work done by friction or we can simply if we want to avoid this term here we can simply like right here the loss of we can write here it is loss of energy okay this is the loss of energy i'm calling this loss of energy one similarly here the potential energy is getting converted into the kinetic energy which is half of m b2 square plus there is also a loss happening here so loss of energy is happening here, which is mainly in the form of heat, basically.

02:07 So i'm calling this loss of energy two, basically.

02:11 So now from here we can see that the half of mb square, half of mv1 square, which is kinetic energy, is equal to what, is equal to m gh minus loss one...

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