- #1
- 10,544
- 2,323
- 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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