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3 years ago

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The compression strength of concrete (the maximum pressure that can be exerted on the base of the structure) is 1.7 × 107 Pa. Wh

at is the height of the tallest cylindrical concrete pillar with a radius of 46 cm that will not collapse under its own weight?

1 answer:

yarga [219]3 years ago

8 0

<h2>Height of cylinder = 679.70 m</h2>

Explanation:

Compression strength = 1.7 x 10⁷ Pa

Normal force = Compression strength x Area

Radius = 46 cm = 0.46 m

Area of cylinder = π x 0.46² = 0.665 m²

Normal force = 1.7 x 10⁷ x 0.665 = 1.13 x 10⁷ N

So weight of cylinder = 1.13 x 10⁷ N

Density of concrete = 25 kN/m³ = 25000 N/m³

Volume of cylinder = Base area x Height = 0.665 x h

Weight of cylinder = 25000 x 0.665 x h

Equating

25000 x 0.665 x h = 1.13 x 10⁷

h = 679.70 m

Height of cylinder = 679.70 m

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Answer:

h=12.41m

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N=392

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So the weight of the wheel is the force N divide on the gravity and also can find momentum of inertia to determine the kinetic energy at motion

$N=m*g\\m=\frac{N}{g}\\m=\frac{392N}{9.8\frac{m}{s^{2}}}$

$m=40kg$

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$M_{I}=0.8*40.0kg*(0.6m} )^{2}\\M_{I}=11.5 kg*m^{2}$

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$K_{r}=\frac{1}{2}*I*W^{2}\\K_{r}=\frac{1}{2}*11.52kg*m^{2}*(24\frac{rad}{s})^{2}\\K_{r}=3317.76J$

Kinetic energy translational

$K_{t}=\frac{1}{2}*m*v^{2}\\v=w*r\\v=24rad/s*0.6m=14.4 \frac{m}{s}\\K_{t}=\frac{1}{2}*40kg*(14.4\frac{m}{s})^{2}\\K_{t}=4147.2J$

Total kinetic energy

$K=3317.79J+4147.2J\\K=7464.99J$

Now the work done by the friction is acting at the motion so the kinetic energy and the work of motion give the potential work so there we can find height

$K-W=E_{p}\\7464.99-2600J=m*g*h\\4864.99J=m*g*h\\h=\frac{4864.99J}{m*g}\\h=\frac{4864.99J}{392N}\\h=12.41m$

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Since initial velocity is zero, the second term goes away:

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