Different types of granular material settle at different angles when stored in c

Question

Different types of granular material settle at different angles when stored in cone-shaped piles. This angle when stored in cone-shaped piles. This angle is called the angle of repose. If your material is stored in a cone-shaped pile of height 5T=__ft. with a diameter of the pile's base of 8R=__ft., determine: A bouy oscillates in a simple harmonic motion. The high point is observed to beT=__ft. above the normal water level and the low point is M=__ ft. below the normal water level. It takes 3R=__ seconds to go from the high point back to the high point. Determine: A pendulum's bob, mass=T+7=__ grams, is released from the left of its rest position at a distance of 0.R__ meters. If the period is M=2R=__ sec and the damping factor is MT/100=__ grams/sec, determine the Displacement Model and the displacement from rest for the following values.

Explanation / Answer

Q. V

angle of repose = tan(theta) = height/radius

height H = 30ft

diameter d =72ft

radius = d/2 = 36ft

tan theta = 30/36

theta = 39.80 degrees

now

If diameter is 60ft then new height h

h/30 = 30/36

h = 25ft

Q no. from given data for SHM

amplitude

A = 4+10 = 14/2 = 7ft

Time period T = 10seconds

angular frequency w = 2*pi/T = 0.2pi

equation of motion

D = 7 sin(0.2pi*t) ft

Part B

at t = 15 seconds

D = 7 sin(0.2*pi*15)

D = 0ft

so heght of bouy is 10-7=3ft above the water level

Part C

at t= 79 seconds

D = 7 sin(0.2*pi*79)

D = -4.11ft

so height of bouy is 1.11 ft below water level

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