The water side of the wall of a 60-m-long dam is a quarter-circle with a radius of 7 m. Determine the hydrostatic force on the dam and its line of action when the dam is filled to the rim. Take the density of water to be 1000 kg/m3.
Answer:
[tex]26852726.19\ \text{N}[/tex]
[tex]57.52^{\circ}[/tex]
Explanation:
r = Radius of circle = 7 m
w = Width of dam = 60 m
h = Height of the dam will be half the radius = [tex]\dfrac{r}{2}[/tex]
A = Area = [tex]rw[/tex]
V = Volume = [tex]w\dfrac{\pi r^2}{4}[/tex]
Horizontal force is given by
[tex]F_x=\rho ghA\\\Rightarrow F_x=1000\times 9.81\times \dfrac{7}{2}\times 7\times 60\\\Rightarrow F_x=14420700\ \text{N}[/tex]
Vertical force is given by
[tex]F_y=\rho gV\\\Rightarrow F_y=1000\times 9.81\times 60\times \dfrac{\pi 7^2}{4}\\\Rightarrow F_y=22651982.59\ \text{N}[/tex]
Resultant force is
[tex]F=\sqrt{F_x^2+F_y^2}\\\Rightarrow F=\sqrt{14420700^2+22651982.59^2}\\\Rightarrow F=26852726.19\ \text{N}[/tex]
The hydrostatic force on the dam is [tex]26852726.19\ \text{N}[/tex].
The direction is given by
[tex]\theta=\tan^{-1}\dfrac{F_y}{F_x}\\\Rightarrow \theta=\tan^{-1}\dfrac{22651982.59}{14420700}\\\Rightarrow \theta=57.52^{\circ}[/tex]
The line of action is [tex]57.52^{\circ}[/tex].
How does the size of a wind turbine affect its energy output?
A.)Smaller turbines spin slower.
B.) Larger turbines have a greater storage capacity.
C.) Larger turbines generate more electricity.
D.)Smaller turbines are better for capturing strong winds.
Answer:
Larger tubines generate more electricity.
Explanation:
Larger blades allow the turbine to capture more of the kinetic energy of the wind by moving more air through the rotors. However, larger blades require more space and higher wind speeds to operate. This distance is necessary to avoid interference between turbines, which decreases the power output.
The three inclines have the same height and they are all frictionless, but they have different angles. Which object will have the highest speed at the bottom of the incline
Answer:
the speed of the body must be the same for the three hills regardless of their slope
v = [tex]\sqrt{2gy}[/tex]
Explanation:
To shorten the answer to this exercise, let's use the concept of conservation of energy
starting point. Highest point of the hill
Em₀ = U = m h y
final point. Lower part of the hill
Em_f = K = ½ m v²
as there is no friction the mechanical energy is conserved
Em₀ = Em_f
mg y = ½ m v²
v = [tex]\sqrt{2gy}[/tex]
Let's analyze this result, we see that the speed at the bottom of the hill depends only on the height of the hill, not on the slope, so the speed of the body must be the same for the three hills regardless of their slope
The average marathon runner can complete the 42.2-km distance of the marathon in 3 h and 30 min. If the runner's mass is 85 kg, what is the runner's average kinetic energy during the run
Answer:
the runner's average kinetic energy during the run is 476.96 J.
Explanation:
Given;
mass of the runner, m = 85 kg
distance covered by the runner, d = 42.2 km = 42,200 m
time to complete the race, t = 3 hours 30 mins = (3 x 3600s) + (30 x 60s)
= 12,600 s
The speed of the runner, v = d/t
v = 42,200 / 12,600
v = 3.35 m/s
The runner's average kinetic energy during the run is calculated as;
K.E = ¹/₂mv²
K.E = ¹/₂ × 85 × (3.35)²
K.E = 476.96 J
Therefore, the runner's average kinetic energy during the run is 476.96 J.
On a sunny day, a rooftop solar panel delivers 60 W of power to the house at an emf of 17 V. How much current flows through the panel
Answer:
3.53 amps
Explanation:
Given data
Power= 60W
Voltage= 17V
The expression relating current, power, and voltage is
P= IV
substitute
60= I*17
I= 60/17
I= 3.53 amps
Hence the current that flows is 3.53 amps
The skater lowers her arms as shown in the adjacent
figure decreasing her radius to 0.15 m. Find her new speed.
Answer:
is there more?
Explanation:
The power in our homes and buildings cycles at a frequency of 60Hz. If someone accidentally dropped a power line into a holding tank for frogs their muscles would immediately become stiff. This is because the high frequency stimuli is causing
Answer:
The answer is "Rigor mortis".
Explanation:
When the very large volume will be that the progress of its postponed by calcium and magnesium. The causes brain intensification of a liver due to the change throughout the myofibrils within a week of dying of its organism. When anyone accidentally spilled a power cable into a rank for toads, one's tissue will be disrupted instantly by stringent deaths.
This is because the high frequency stimuli of the power line is causing rigor
mortis.
Rigor mortis is referred to as the stiffening of the body of animals when they
die and is usually caused by the body's glycogen and ATP concentration
diminishing.
Rigor mortis can also be caused by a high frequency stimuli such as
exposure to electric current which hastens the conditions that causes it to
occur.
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student builds a simple circuit with a single resistor with resistance R and measures an electric potential difference ΔV across the resistor. Then, the student replaces the resistor with a new one of resistance 2R and keeps the electric potential difference the same. What is the current (I2) through the new circuit in terms of the original current(I1)? 6mks
Answer:
i₂ = ½ i₁
Explanation:
Let's write ohm's law for the first statement
V = i₁ R
i₁ = V / R
tells us that we change the resistance to R '= 2R
let's write ohm's law
V = i₂ R’
indicates that V remains constant
i₂ = V / R '
i₂ = V / 2R
i₂ = ½ V/R
we substitute
i₂ = ½ i₁
Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field acting perpendicularly to its axis of rotation. Coil 1 has a radius of 4.5 cm and rotates in a 0.21-T field. Coil 2 rotates in a 0.39-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2
Answer:
Explanation:
Torque acting on a coil in a magnetic field = MBsinθ where M is magnetic moment , B is magnetic field and θ is inclination of the normal to coil with direction of field.
For maximum torque sinθ = 1
Maximum torque = MB
M = NIA where N is no of turns , I is current and A is area of the coil
Maximum torque = NIAB
As maximum torque is same
N₁I₁A₁B₁ = N₂I₂A₂B₂
N₁ = N₂ , I₁ = I₂
A₁B₁ = A₂B₂
π R₁² B₁ = π R₂² B₂
4.5² x .21 = R₂² x .39
R₂² = 10.9
R₂ = 3.3 cm .
Potential energy is
stored in a state of readiness.
conserved.
energy of motion.
not measurable.
Answer:
stored in a state of readiness.
Explanation:
Potential energy is stored in a state of readiness.
Potential energy can be defined as an energy possessed by an object or body due to its position.
Mathematically, potential energy is given by the formula;
[tex] P.E = mgh[/tex]
Where, P.E represents potential energy measured in Joules.
m represents the mass of an object.
g represents acceleration due to gravity measured in meters per seconds square.
h represents the height measured in meters.
which form of energy is an example of kinetic energy
Answer:
1. realizing of arrow
2. kicking of ball
3. punching the punching bag
A hot piece of copper is placed in water in an insulated cup. What is the final
temperature of the water and copper?
(Use
me AT: + copperfcoppe, Acoppe: = 0]
m = 0.50 kg water = 4.18 kJ/kg-'c,
m.copper = 0.50 kg, Cropper = 0.386 kJ/kg-°C, Ti copper = 115°C
Tower = 22°C
O A. 30°C
B. 45°C
O C. 39°C
O D. 52°C
Answer:
38.7 °C.
The final temperature (reached by both copper and water) is 38.7 °C.
So the answer is probably C.
The heat energy lost by the metal piece is equal to the heat gained by the water in the cup. From this concept using calorimetric equation, their final temperature is equal to 30°C.
What is calorimetric equation?Calorimetric equation states the relation between heat energy absorbed or released by a system with the mass, specific heat capacity and temperature difference of the matter as written below:
q = m c Δ
Given, mass of copper piece = 0.50 kg
mass of water = 0.50 kg
c for Cu = 0.386 KJ/Kg °C
c for water = 0.418 KJ/Kg °C
The heat energy lost by copper metal is equal to the heat energy gained by water. Let T be the final temperature.
then,
0.50 kg × 0.386 KJ/Kg °C × (115°C - T) = 0.50 kg × 0.418 KJ/Kg °C × (T - 22°C).
2.09 (115°C - T) = 0.193 (T - 22°C).
2.09 T - 45.98 + 0.193 = 22.195
T = 30°C
Therefore, the final temperature of water and copper piece is 30 °C.
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I can give you 50 points.
Freddy is participating in a pumpkin lifting contest. The 68 kg pumpkin starts at rest on the ground. If Freddy exerts a 720N force on the pumpkin, what is the acceleration of the pumpkin as he lifts it off the ground?
Draw a Force Diagram for the pumpkin. Indicate the direction of the sum of the forces.
Draw a Motion Diagram for the pumpkin. Is your motion diagram consistent with your force diagram?
Use Newton’s 2nd Law to find the pumpkin’s acceleration.
Answer:
Freddy is participating in a pumpkin lifting contest. The 68 kg pumpkin starts at rest on the ground. If Freddy exerts a 720N force on the pumpkin, what is the acceleration of the pumpkin as he lifts it off the ground?
Explanation:
7. Consumers can be predators, prey, scavengers, herbivores omnivoree, or carnivore: What is the common characteristic of all consumer: A Create their own food B. Must eat to get energy C. Hunt for live animals D. Will eat anything
Answer:
B. Must eat to get energy
Explanation:
The common characteristics of all consumers is that they must eat to get energy. This way, they are termed heterotrophs.
Heterotrophs are organisms that cannot make their own food. They must eat other organisms to obtain nutrition for energy needs.
Plants do not do this. They are autotrophs in that they simply make their own food.
They use this food to obtain energy for their living activities.
Is water a element or compound
Answer:
compound
Explanation:
water is made up of oxygen (O) and hydrogen (H) therefore making it a compound (H2O)
Calculate the magnetic field at 2m from a straight wire carrying a current of 5 A. (K = 2 x 10 ^-7)
Answer:
[tex]B=5\times 10^{-7}\ T[/tex]
Explanation:
Given that,
Current in a wire, I = 5 A
We need to find the magnetic field at 2m from a straight wire carrying a current of 5 A.
The magnetic field due to a wire is given by :
[tex]B=\dfrac{\mu_0I}{2\pi r}\\\\B=\dfrac{4\pi \times 10^{-7}\times 5}{2\pi \times 2}\\\\B=5\times 10^{-7}\ T[/tex]
So, the required magnetic field is [tex]5\times 10^{-7}\ T[/tex].
Currents exist in the ocean without the need of electric fields.
True
False
Answer:
True
Explanation:
which of the following can cause skin cancer and which can't?
Campfire
Flashlight
Lamp
Sun
Tanning bed
fluorescent light bulbs