The flatbed truck carries a large section of circular pipe secured only by the two fixed blocks A and B of height h. The truck is in a left turn of radius rho. Determine the maximum speed for which the pipe will be restrained. Use the values rho = 60 m, h = 0.1 m, and R = 0.8 m.

The maximum speed for which the pipe will be restrained is 18.05 m/s.

Explanation:

We note that the

Securing blocks have height, h = 0.1 m

The radius of travel, rho = 60 m

The radius of the circular pipe, R = 0.8 m

We note that the weight of the pipe is acting at the centroid of the pipe

Therefore, for the pipe to slip, it has to climb the wedge h

Taking moments about h, we have  

mg × R sin α = ma × R cos α  

a/g  =  Tan α

But a =

Therefore   = g tanα

Since height of the block, h = 0.1 m therefore,

R cos α = R - h

That is 0.8 cos α = 0.8 - 0.1 = 0.7

Therefore α = cos⁻¹ (0.7/0.8) = 28.96 °

From which V² = rho × g× tanα = 60 × 9.81 × tan 28.96

= 325.66 m²/s²

∴ V = √(325.66 m²/s²)  = 18.05 m/s

Maximum speed = 18.05 m/s.

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