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Contact [7]
4 years ago
14

A rigid dam is composed of material of SG = 5 . The dam height is 20 m . What is the minimum thickness b of the dam necessary to

prevent it from tipping about the point O when the water reaches the top of the dam considering unit width? Assume that the maximum hydrostatic pressure acts over the bottom of the dam.
Physics
1 answer:
Kay [80]4 years ago
3 0

Answer:

b = 5.164 m is the minimum thickness of the dam

Explanation:

Given

SG = 5

h = 20 m

b = ?

w = 1 m

γw = 9800 N/m³

We  can get the forces as follows

Fp =  γw*(h/2)*(h*w)

⇒ Fp = (9800 N/m³)*(20 m/2)*(20 m*1 m) = 1.96*10⁶N

W = (SG*γw)*(h*b*w)

⇒  W = (5*9800 N/m³)*(20 m*b*1 m) = (9.8*10⁵N/m)*b

Then, we apply

∑M₀ = 0  (counterclockwise)

- Fp*(h/3) + W*(b/2) = 0

⇒   - 1.96*10⁶N*(20 m/3) + (9.8*10⁵N/m)*b*(b/2) = 0

- 13.066*10⁶N-m + (4.9*10⁵N/m)*b² = 0

⇒  b = 5.164 m is the minimum thickness of the dam

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Explanation:

The correct question statement is :

A floor polisher has a rotating disk that has a 15-cm radius. The disk rotates at a constant angular velocity of 1.4 rev/s and is covered with a soft material that does the polishing. An operator holds the polisher in one place for 4.5 s, in order to buff an especially scuff ed area of the floor. How far (in meters) does a spot on the outer edge of the disk move during this time?

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From this we have

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