In the design of a conveyor-belt system. blocks are discharged with a velocity a

Question

In the design of a conveyor-belt system. blocks are discharged with a velocity a ramp by the upper conveyor belt shown. If the co-efficient of kinetic friction between the blocks and the ramp is 0.30, calculate the angle theta which the ramp must make with the horizontal so that the blocks will transfer without slipping to the lower conveyor belt moving at the speed of 0.14 m/s. theta = 16.62 degree The nest of two springs is used to bring the 0.5-kg plunger A to a stop from a speed of 5 m/s and reverse its direction of motion. The inner spring increases the deceleration, and the adjustment of its position is used to control the exact point at which the reversal takes place. If this point is to correspond to a maximum deflection delta = 200 mm for the outer spring, specify the adjustment of the inner spring by determining the distance s. The outer spring has a stiffness of 300 N/m and the inner one a stiffness of 150 N/m.

Explanation / Answer

115) acceleration net = g.sin (theta ) - u.g.cos (theta)

= 9.81 x ( sin (t) - 0.3 cos (t))

so, V^2 = u^2 + 2.a.s

so, 0.14^2 = 0.4^2 + 2 x ( 9.81 x ( sin (t) - 0.3 cos (t)) x 1.5

on solving theta = t = 16.62 degree

138)

deflection of oute spring is transversed to inner spring

so., 1/2 x 300 x .2^2 + 1/2 x 0.5 x 5^2 0.1633 m = 163.33 mm= 1/2 x 150 . X^2

so deflection of inner spring = x =

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