You need to design the shipping area for a local delivery business that handles

Question

You need to design the shipping area for a local delivery business that handles packages up to 500 pounds. At the main distribution center, boxes will slide down a ramp between the loading dock and the sorting area. You must determine the angle this ramp should have so that a box will take 4 seconds to slide down the ramp when starting from rest at the top. When the box arrives at the bottom of the ramp, you decide that its speed should be no more than 10 ft/s or the contents may be damaged. The ramp will be extremely smooth so that boxes slide easily. ((also need the diagram for this problem))

Explanation / Answer

given,

mass = 500 pounds or 226.796 kg

time = 4 sec

maximum speed = 10 ft/sec or 3.048 m/s

acceleration of the block will be = g * sin(theta)

v = u + at

3.048 = 0 + 9.8 * sin(theta) * 4

theta = 4.46 degree

angle of the ramp should be 4.46 degree

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