In the given figure below, a 3.0 -kg block is sliding down a...

In the given figure below, a 3.0 -kg block is sliding down a 60°-rough incline. The speed of the block is 1.68 m/s at the instant it is 5.25 m from an uncompressed spring located at the other lower end of the incline. The spring has a spring or stiffness constant of 120 N/m and the coefficient of kinetic friction between the block and the incline is 0.35. At what speed (in m/s) will the block strike the spring? And what would be the maximum compression (in m) of the spring? 5.25 m 60° g = 9.8 m/s^2

Transcript

00:01 Question we are given that this is some inclined plane at an angle of 60 degree over here at bottom this is spring right this is block having some initial kinetic energy that is 1 .68 meter per second is the speed right so this distance between these two point is 5 .25 meters all right so as we know that if you try to draw the free body diagram downward is amline.

00:35 This is normal.

00:38 This would be mg sine theta and this would be mg pose theta.

00:45 And this is mu mg, pose theta will be frictional.

00:54 During from here position 1 to position 2, what will happen? some of the work will be done by the gravity and some work will be done by the friction.

01:04 Initial kinetic energy plus work done by gravity minus work done by friction would be equal to kinetic energy.

01:17 This would be the conservation of energy.

01:19 This always happens.

01:21 So we will write the equation into m into the initial 1 .6 sphere plus work done by gravity would be what? mg sine theta into the distance table.

01:37 Mg sine theta into the distance table is 5 .25.

01:42 Minus mu m gose theta into the distance level so 0 .35 into m g cos theta into 5 .25 that must be equal to half m v final square so m cancels out from everywhere also this half will be canceling out and here it multiplied by two multiplied by this vf square we are getting is 1 .68 square plus 2 into 9 .81 into 9 .81 into 960 into 5 .25 minus 0 .35 into 2 into 460 into 5 .25.

02:48 So this is coming out to be 90.

02:53 Just a second multiplied by 9 .81.

02:56 So this is coming out to be 90.

02:57 Just a second multiplied by 9 .8.

02:57 To be 74.

02:59 So vf would be under root 74.

03:03 So this is 8 .6 meter per second...

Question

Please give Ace some feedback