3. (30 points) Assume the maximum rotating speed of the...

3. (30 points) Assume the maximum rotating speed of the drawworks' drum is 100 RPM and that its diameter is 6 ft. a. What is the maximum possible speed for the fast line, in ft/s (hint: the drum has a fully-cylindrical cross section)? b. Using the speed from part(a), build a table displaying the traveling-block speed in ft/s if the blocks are strung on 6, 8, 10, 12, and 14 lines. c. Complete the below schematic for a block-and-tackle configuration where 6 lines are strung. Crown Block Draw-Works (DC electrical drive) Travelling Block Hoist cable dead-end anchor Hook-load sensor

Transcript

00:01 Hello students, in this question we have given a schematic diagram of cable drum which can be treated as cylinder.

00:10 Now from the figure we have the equation of motion based on the free body diagram acted vertically i .e.

00:19 Summation of fy is equal to m a gy.

00:28 Here this can be written as 300 minus t that will be equal to 300 divided by 32 .2 a gy.

00:37 Here the reaction force is a gy which is equal to a.

00:42 Now the moment along the mass center of the drum g is given as, now taking the moment we have m a is equal to i g z a.

00:54 Here the moment of inertia i g z and here the acceleration is a.

01:01 Now we obtain moment as 3 t is equal to i g alpha.

01:10 Now to find the moment of inertia of the rectangular plate about the support a that is given as half m r square into alpha.

01:25 Now we have mass that is equal to 300 upon 32 .2 kg.

01:31 This will be given as mass is 18 .63 kg.

01:37 Now we have also given diameter that is equal to 18.

01:42 So the radius will be equal to 1 .5 divided by 2 that will be equal to 0 .75 feet.

01:51 Now substituting all the values here we get 3 into t that is here we have 3 t.

01:59 3 into 300 is equal to now substituting the values here we have mass 18 .63 into r square 0 .75 square into alpha.

02:14 Now after solving this we get alpha is equal to 171 .76.

02:21 Now to determine the time required to rotate the cable drum three revolutions we proceed this will be omega minus omega, omega square minus omega square is equal to 2 alpha theta minus theta naught...

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