Answer:
The gate will open if the height of water is equal to or more than 0.337m.
Explanation:
From the diagram attached, (as seen from the reference question found on google)
The forces are given as
Force on OA
Here
- ρ is the density of water.
- g is the gravitational acceleration constant
is the equivalent height given as
is the area of the OA part of the door which is calculated as follows:
The Force is given as
![F_1=0.6\rho g[h+0.3]](https://tex.z-dn.net/?f=F_1%3D0.6%5Crho%20g%5Bh%2B0.3%5D)
Force on OB
Here
- ρ is the density of water.
- g is the gravitational acceleration constant
- is the equivalent height given as
- is the area of the OB part of the door which is calculated as follows:
The Force is given as
![F_2=0.4\rho g[h+0.8]](https://tex.z-dn.net/?f=F_2%3D0.4%5Crho%20g%5Bh%2B0.8%5D)
Now the moment arms are given as
![\bar{y}_a=\bar{h}+\frac{I}{A\bar{h}}\\\bar{y}_a=h+0.3+\frac{\frac{1}{12}\times 0.6^3 \times 1}{0.6 \times[h+0.3]}\\\bar{y}_a=h+0.3+\frac{0.03}{h+0.3}](https://tex.z-dn.net/?f=%5Cbar%7By%7D_a%3D%5Cbar%7Bh%7D%2B%5Cfrac%7BI%7D%7BA%5Cbar%7Bh%7D%7D%5C%5C%5Cbar%7By%7D_a%3Dh%2B0.3%2B%5Cfrac%7B%5Cfrac%7B1%7D%7B12%7D%5Ctimes%200.6%5E3%20%5Ctimes%201%7D%7B0.6%20%5Ctimes%5Bh%2B0.3%5D%7D%5C%5C%5Cbar%7By%7D_a%3Dh%2B0.3%2B%5Cfrac%7B0.03%7D%7Bh%2B0.3%7D)
![\bar{y}_b=\bar{h}+\frac{I}{A\bar{h}}\\\bar{y}_b=h+0.8+\frac{\frac{1}{12}\times 0.4^3 \times 1}{0.4 \times[h+0.8]}\\\bar{y}_b=h+0.8+\frac{0.0133}{h+0.8}](https://tex.z-dn.net/?f=%5Cbar%7By%7D_b%3D%5Cbar%7Bh%7D%2B%5Cfrac%7BI%7D%7BA%5Cbar%7Bh%7D%7D%5C%5C%5Cbar%7By%7D_b%3Dh%2B0.8%2B%5Cfrac%7B%5Cfrac%7B1%7D%7B12%7D%5Ctimes%200.4%5E3%20%5Ctimes%201%7D%7B0.4%20%5Ctimes%5Bh%2B0.8%5D%7D%5C%5C%5Cbar%7By%7D_b%3Dh%2B0.8%2B%5Cfrac%7B0.0133%7D%7Bh%2B0.8%7D)
Taking moment about the point O as zero
=0.4\rho g[h+0.8](0.2+\frac{0.0133}{h+0.8})\\0.6[h+0.3](0.3-\frac{0.03}{h+0.3})=0.4[h+0.8](0.2+\frac{0.0133}{h+0.8})\\0.18h -0.054-0.018=0.08h+0.064+0.00533\\h=0.337 m](https://tex.z-dn.net/?f=F_1%28h%2B0.6-%5Cbar%7By%7D_a%29%3DF_2%28%5Cbar%7By%7D_b-h%2B0.6%29%5C%5CF_1%28h%2B0.6-h-0.3-%5Cfrac%7B0.03%7D%7Bh%2B0.3%7D%29%3DF_2%28h%2B0.8%2B%5Cfrac%7B0.0133%7D%7Bh%2B0.8%7D-h-0.6%29%5C%5CF_1%280.3-%5Cfrac%7B0.03%7D%7Bh%2B0.3%7D%29%3DF_2%280.2%2B%5Cfrac%7B0.0133%7D%7Bh%2B0.8%7D%29%5C%5C0.6%5Crho%20g%5Bh%2B0.3%5D%280.3-%5Cfrac%7B0.03%7D%7Bh%2B0.3%7D%29%3D0.4%5Crho%20g%5Bh%2B0.8%5D%280.2%2B%5Cfrac%7B0.0133%7D%7Bh%2B0.8%7D%29%5C%5C0.6%5Bh%2B0.3%5D%280.3-%5Cfrac%7B0.03%7D%7Bh%2B0.3%7D%29%3D0.4%5Bh%2B0.8%5D%280.2%2B%5Cfrac%7B0.0133%7D%7Bh%2B0.8%7D%29%5C%5C0.18h%20-0.054-0.018%3D0.08h%2B0.064%2B0.00533%5C%5Ch%3D0.337%20m)
So the gate will open if the height of water is equal to or more than 0.337m.
Hi! In order for me to help you, I need the answer choices. Thanks! -AmbitiousAndProud
Answer:
The ball and the wall experience the same force.
Explanation:
According to the third law of Newton, which states that "for every action, there is an equal and opposite reaction", this means that when an object 1 acts on object 2 with a certain force, object 2 also acts on object 1 with the same magnitude of force but in an opposite direction.
According to this question, a ball hits a wall with a certain force. This means that the wall will react on the ball with the same force magnitude, but in an opposite manner. Hence, the ball and the wall experience the same force.
1. The time taken for the car to reach a velocity of 60 m/s is 8.57 s
2. The distance travelled during the time is 257.14 m
<h3>What is acceleration? </h3>
The acceleration of an object is defined as the rate of change of velocity which time. It is expressed as
a = (v – u) / t
Where
- a is the acceleration
- v is the final velocity
- u is the initial velocity
- t is the time
1. How to determine the time
- Initial velocity (u) = 0 m/s
- Acceleration (a) = 7 m/s²
- Final velocity (v) = 60 m/s
- Time (t) =?
a = (v – u) / t
Thus,
t = (v – u) / a
t = (60 – 0) / 7
t = 8.57 s
2. How to determine the distance
- Initial velocity (u) = 0 m/s
- Acceleration (a) = 7 m/s²
- Final velocity (v) = 60 m/s
- Distance (s) = ?
v² = u² + 2as
60² = 0² + (2 × 7 × s)
3600 = 0 + 14s
3600 = 14s
Divide both sides by 14
s = 3600 / 14
s = 257.14 m
Learn more about acceleration and velocity:
brainly.com/question/491732
brainly.com/question/19466392
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