Answer:
a) 35.94 ms⁻²
b) 65.85 m
Explanation:
Take down the data:
ρ = 1000kg/m3
a) First, we need to establish the total pressure of the water in the tank. Note the that the tanks is closed. It means that the total pressure, Ptot, at the bottom of the tank is the sum of the pressure of the water plus the air trapped between the tank rook and water. In other words:
Ptot = Pgas + Pwater
However, the air is the one influencing the water to move, so elimininating Pwater the equation becomes:
Ptot = Pgas
= 6.46 × 10⁵ Pa
The change in pressure is given by the continuity equation:
ΔP = 1/2ρv²
where v is the velocity of the water as it exits the tank.
Calculating:
6.46 × 10⁵ =1/2 ×1000×v²
solving for v, we get v = 35.94 ms⁻²
b) The Bernoulli's equation will be applicable here.
The water is coming out with the same pressure, therefore, the equation will be:
ΔP = ρgh
6.46 × 10⁵ = 1000 x 9.81 x h
h = 65.85 meters
Orient the semi-circle arc such that it is symmetric with respect to the y-axis. Now, by symmetry, the electric field in the x-direction cancels to zero. So the only thing of interest is the electric field in the y-direction.
dEy=kp/r^2*sin(a) where k is coulombs constant p is the charge density r is the radius of the arc and a is the angular position of each point on the arc (ranging from 0 to pi. Integrating this renders 2kq/(pi*r^3). Where k is 9*10^9, q is 9.8 uC r is .093 m
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Answer:
the cost to leave the lights on 24 hours a day for one year is 31,536 cents or 315.36 dollars
Explanation:
Given that;
P = 300 watts = 300/1000 = 0.3
t = 24hrs a day
In a calendar year, we have 365 days
so;
E = 0.3 × 365 × 24
E = 2628 KWh
given that; 1 KWh = 12 cent
then 2628 KWh is x
x = 2628 × 12
x = 31,536 cents or 315.36 dollars
Therefore, the cost to leave the lights on 24 hours a day for one year is 31,536 cents or 315.36 dollars
Answer:
Torque = 1191.68 N-m
Explanation:
Given data
mass m = 76 kg
standingdistance r = 1.6 m
Solution
we get here torque that si express as
torque = force × distance ................1
torque = r × F sin(theta)
and we know that
F = mg .........2
and g = 9.8 m/s²
put here value in equation 1 we get
Torque = 76 × 1.6 × 9.8 × sin(90)
Torque = 1191.68 N-m
