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CWatters

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- Homework Statement:
- See Below

- Relevant Equations:
- F = ρgAd

My son and I are having a problem with part c that suggests our answer for part a and b are wrong..

**Part a)**. If we've understood the teaching notes correctly the force on the gate acting through its centroid perpendicular to the gate and is given by

F = ρgAd

where

ρ is the density of water 997 kg/m^3

g is 9.81m/s^2

A is the area of the gate

d is the depth of the centroid of the gate

The area of the gate A is

A = 1.1 * 0.8/cos(45)

= 1.24 sqm

The centroid is half way up the gate so at a depth d below the surface of

d = 2-0.4

= 1.6m

So the Force F acting through the centroid is

F = 997 * 9.81 * 1.24 * 1.6

= 19,405 N

**Part b)**The centroid of the gate is at..

y = 0.5 * 0.8/cos(45)

so the moment M acting on the gate due to water pressure is

M = 19,405 * 0.5 * 0.8/cos(45)

= 10,977 Nm

**Part c)**If the gate isn't accelerating the net moment must be zero.

The clockwise moment due to the mass Q is

= 0.8*Q*g

The anti clockwise moment due to water pressure is 10,977 Nm from above.

Equating these gives

0.8*Q*g = 10,977

and

Q = 10,977/(0.8*g)

= 1,398 kg

So we have failed to prove mass Q needs to be 1,527 kg

Where are we going wrong?

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