3. We wrap a light, non-stretching cable around a solid...

3. We wrap a light, non-stretching cable around a solid cylinder with mass (M = 12.0 kg) and radius (R = 0.3 m). The cylinder rotates with negligible friction abut a stationary horizontal axis. We tie the free end of the cable to a block of mass (m = 15.0 kg) and release the block from rest at a distance (h = 0.5 m) above the floor. As the block falls, the cable unwind without stretching or slipping. Take moment of inertia of the solid cylinder as I = 1/2MR^2. Find the a. speed of the falling block and b. the angular speed of the cylinder as the block strikes the floor. Vf^2 = Vo^2 +

Transcript

00:01 Hello students here it is given that the mass of the solid cylinder is given as 12 kg and radius of solid cylinder is equal to 0 .3 meters and mass of the block is given as 15 kg and it is given that height from the ground is given as 0 .5 meters and moment of inertia i is equals to m by 2 r square now we can calculate the force here the force acting on the block is equal to f is equal to weight acting on the mass w minus t tension t therefore f is equal to m g minus t this is equation t this is equal to m g minus t this is equation one and for a second it is given that for the solid cylinder it is given that here t is equal to m into a by 2 now substituting 2 in 1 we get that f is equal to ma m g minus capital m a divided by 2 and m a is equal to m g minus m g minus capital m a divided by 2 and m a is equal to m g minus capital m a divided by 2 therefore we get that a is equals to m g divided by small m plus capital m divided by two now from the relation we know that we need to find the velocity which is equal to v square minus u square equals to two a yes here s is equal to height of the block therefore v square and here u square is to 0 v square equal to 2 into a value is m g divided by m plus capital m divided by 2 into h.

02:25 Substituting the values we get that v square equals to here 2 into 15 into 9 .8 divided by 15 plus here 12 divided by 15 plus here 12 divided by 2 into 0 .5.

02:49 From this we get that v square equals to 147 divided by 21 into 2 into 0 .5.

03:03 Therefore the obtained value of v square equal to root over 7 v is equal to 2 .64.

03:11 Therefore, the speed of the following block can be given as 2 .64 meter per second.

03:21 Now we will calculate the value of angular speed which is given that we know that from the above relation for circular disk it is given that tension acting on the disk is t, radius is r, t into r is equal to here this is rotating in the direction are clockwise...

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