Do this problem on your own and turn it in at the beginning of Friday\'s class (

Question

Do this problem on your own and turn it in at the beginning of Friday's class (due 10/16/15). 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 starling 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. Your answer must be organized, clear, and include the elements of the problem solving path: Focus the Problem Describe the Physics Plan the Solution Execute and Evaluate.

Explanation / Answer

intial speed is u = 0 ft/s

final speed is v = 10 ft/s

time taken is t = 4 sec

accelaration a = ?

apply a = (v-u)/t = (10/4) = 2.5 ft/s^2

but net force ma = m*g*sin(theta)

a = g*sin(theta)

g is the accelaration due to gravity = 32.17 ft/s^2

sin(theta) a/g = 2.5/32.17

theta = 4.45 degrees is the required minimum angle of the ramp

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