The work done on the bowling ball is 576 J to accelerate an 8.0-kg bowling ball from rest to a speed of 12 m/s and a distance of 2.5 m to reach a speed of 12 m/s if the average force on the bowling ball is 230 N.
What is the calculation of the work done?Work = 1/2 × m × [tex]v^2[/tex]
( m =8 kg=is the mass, v= 12 m/s= is final velocity)
Work = 1/2 × 8.0 kg × [tex](12 m/s)^2[/tex] = 576 J
As per work-energy principle, the work done on an object = the change in its kinetic energy
Work = ΔKE
(ΔKE = change in kinetic energy, initial kinetic energy=0)
final kinetic energy is,
KE = 1/2 × m × [tex]v^2[/tex] = 1/2 × 8.0 kg × [tex](12 m/s)^2[/tex] = 576 J
the change in kinetic energy,
ΔKE = KE - 0 = 576 J (work is equal to force here)
So, Work = Force × Distance
Distance = Work / Force = 576 J / 230 N = 2.5 m
As a result, the work done on the bowling ball is 576 J to accelerate and travel 2.5 m with an 8.0-kg bowling ball.
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a marathon runner starts her race at a speed of 3 m/s. by the end of the race, 5 hours later, her speed is 2.8 m/s. what was her average acceleration?
Answer: Acceleration, a= -1.11*10^-5
Explanation:
Using a= (V(final speed)- U(Initial speed) )/ TIME IN SECONDS
5hr to seconds is 5*60*60=18,000s
(2.8m/s-3m/s)/ 18,000s = -1.11*10^-5
I'm sorry I wasn't able to explain well, but I hope this helps.
A cord is used to vertically lower an initially stationary block of mass M kg at a constant downward acceleration of g/4. The block has fallen a distance d. (Use any variable or symbol stated above as necessary.)
(a) Find the work done by the cord's force on the block.
WF = __________
(b) Find the work done by the weight of the block.
Wg = ___________
(c) Find the kinetic energy of the block.
K = _________
(d) Find the speed of the block.
v = __________
(a) Work done by the cord's force on the block [tex](WF) = Mg/4\times d[/tex]
(b) Work done by the weight of the block [tex](Wg) = Mg/4 \times d[/tex]
(c) Kinetic energy of the block [tex](K) = Mg/2\times d[/tex]
(d) Speed of the block [tex](v) = sqrt(gd/2)[/tex] where g is the acceleration due to gravity and d is the distance the block has fallen.
What is Kinetic energy?Kinetic energy is the energy that an object possesses due to its motion. In other words, if an object is moving, it has kinetic energy. The amount of kinetic energy an object has depends on its mass and velocity. The formula for calculating kinetic energy, K, is:
K = 1/2 mv^2
where m is the mass of the object and v is its velocity. The factor of 1/2 in the formula is due to the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. If a force is applied to an object to put it in motion, work is done on the object, and its kinetic energy increases.
The units of kinetic energy are joules (J). One joule is defined as the amount of work done when a force of one newton (N) is applied over a distance of one meter (m). Since work and energy are measured in the same units, the unit of kinetic energy is the same as the unit of work, which is the joule.
Kinetic energy is a scalar quantity, which means it has magnitude but no direction. The kinetic energy of an object increases as its mass and velocity increase.
(a) The work done by the cord's force on the block can be found using the formula:
[tex]WF = force\times distance[/tex]
The force applied by the cord is equal to the tension in the cord, which is equal in magnitude to the weight of the block. Therefore, the force applied by the cord is:
[tex]F = Mg[/tex]
where M is the mass of the block, and g is the acceleration due to gravity.
The distance over which the force is applied is d, the distance the block has fallen. Therefore, the work done by the cord's force on the block is:
[tex]WF = Fd = Mg \times d[/tex]
Substituting g/4 for g
[tex]WF = M(g/4) \times d = Mg/4 \times d[/tex]
Hence, the work done by the cord's force on the block is Mg/4 × d.
(b) The work done by the weight of the block can be found using the formula:
[tex]Wg = force \times distance[/tex]
The weight of the block is equal to its mass times the acceleration due to gravity, which is:
[tex]W = Mg[/tex]
The distance over which the weight is applied is again d. Therefore, the work done by the weight of the block is:
[tex]Wg = Wd = Mg\times d[/tex]
Substituting g/4 for g:
[tex]Wg = M(g/4) \times d = Mg/4 \times d[/tex]
Hence, the work done by the weight of the block is also [tex]Mg/4 \times d.[/tex]
(c) The change in the kinetic energy of the block can be found using the work-energy principle:
Wnet = ΔK
where Wnet is the net work done on the block, and ΔK is the change in the kinetic energy of the block.
The net work done on the block is equal to the sum of the work done by the cord's force and the work done by the weight of the block:
[tex]Wnet = WF + Wg = Mg/4 \times d + Mg/4 \times d = Mg/2 \times d[/tex]
The change in the kinetic energy of the block is equal to the net work done on the block:
ΔK = Mg/2 × d
Since the block starts from rest, its initial kinetic energy is zero. Therefore, the final kinetic energy of the block is equal to the change in kinetic energy:
[tex]K = Mg/2\times d[/tex]
(d) The final speed of the block can be found using the equation for the final kinetic energy:
[tex]K = 1/2 mv^2[/tex]
where m is the mass of the block, and v is its final speed.
Substituting Mg/2 × d for K and M for m
[tex]Mg/2\times d = 1/2 Mv^2[/tex]
Simplifying and solving for v, we get:
[tex]v = sqrt(gd/2)[/tex]
Therefore, the speed of the block is[tex]sqrt(gd/2)[/tex], where g is the acceleration due to gravity and d is the distance the block has fallen.
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A pool ball moving 1.83 m/s
strikes an identical ball at rest.
Afterward, the first ball moves
1.15 m/s at a 23.3° angle. What is
the x-component of the velocity of
the second ball?
Answer:n to the right to the right
Explanation:
A parallel plate capacitor with plates of area A and plate separation d is charged so that the potential difference between its plates is V. If the capacitor is then isolated and its plate separation is decreased to d/2, what happens to the potential difference between the plates? A) The final potential difference is 4V B) The final potential difference is 2V. C) The final potential difference is 0.51 D) The final potential difference is 0.25V E) The final potential difference is V.
The new potential difference when the distance between the plates vary is calculated to be 0.5 V. Correct option is C.
The parallel plate capacitor's area is denoted by the letter A.
Distance between the plates is d.
Potential difference is V.
If the distance is reduced to d/2, the potential difference is to be found out.
We know that, Q = C V
To find out potential difference, make it as subject,
V = Q/C
From the above equation, it is seen that, capacitance is inversely proportional to potential difference.
So, V C = k
where,
k is contant
The parallel plate capacitor's capacitance is stated as,
C = εA/d
When the distance apart is d. Then, C₁ = εA/d
When the distance is half d/2
C₂ = εA/(d/2)
C₂ = 2εA/d
Then, applying V C = k
V₁ is voltage of the full capacitor V1 = V
V₂ is the required voltage let say V'
Then,
V₁ C₁ = V₂ C₂
V × εA/d=V' × 2εA/d
VεA/d = 2V'εA/d
Then the εA/d cancels on both sides and remains
V = 2V'
Then, V' = V/2
Thus, the potential difference is half when the distance between the parallel plate capacitor was reduce to d/2.
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A 5-kg block is suspended by a rope from the ceiling of an elevator that accelerates downward at 3.0 m/s2 . The tension force of the rope on the block is: (specify magnitude and direction)
The tension force is 15 N.
What is the tension force?Tension force is a pulling force transmitted through a flexible medium, such as a rope or cable, when it is pulled at both ends. It is directed along the length of the medium and is equal in magnitude at both ends.
In this case we have been told that A 5-kg block is suspended by a rope from the ceiling of an elevator that accelerates downward at 3.0 m/s2 .
We know that the tension force is the force that acts along the rope hence;
Tension = ma
= 5 Kg * 3.0 m/s2
= 15 N
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A pan is used to boil water by placing it on a stove, from which heat is transferred at a fixed rate q0. There are two stages to the process. In Stage I, the water is taken from its initial (room) temperature Ti to the boiling point, as heat is transferred from the pan by natural convection. During this stage, a constant value of the convection coefficient h may be assumed, while the bulk temperature of the water increases with time, T infinity = T infinity(t). In Stage 2, the water has come to a boil, and its temperature remains at a fixed value, T infinity = Tb, as heating continues. Consider a pan bottom of thickness L and diameter D, with a coordinate system corresponding to x = 0 and x = L for the surfaces in contact with the stove and water, respectively. Write the form of the heat equation and the boundary/ initial conditions that determine the variation of temperature with position and time, T(x, t), in the pan bottom during Stage 1. Express your result in terms of the parameters qo, D, L, h, and T infinity, as well as appropriate properties of the pan material.
During Stage 1, the heat equation that governs the temperature distribution T(x, t) in the pan bottom is given by:
ρc_p∂T/∂t = k∂^2T/∂x^2 + q_0/V
How to use heat equation ?where ρ is the density of the pan material, c_p is the specific heat capacity of the pan material, k is the thermal conductivity of the pan material, and V is the volume of the pan bottom.The first term on the right-hand side of the equation represents heat conduction within the pan material, while the second term represents heat transfer from the pan to the water by natural convection. The term q_0/V represents the heat input rate from the stove.The boundary conditions are:
At x = 0 (the surface in contact with the stove), the temperature is fixed at Ti, and there is no heat flux:
T(x=0,t) = Ti, ∂T/∂x = 0
At x = L (the surface in contact with the water), the heat flux is given by:
-k(∂T/∂x) = h(Tb - T)
where h is the convection coefficient, Tb is the boiling point of water, and T is the bulk temperature of the water, which varies with time.The initial condition is:
T(x, t=0) = Ti
The solution to this heat equation with the above boundary and initial conditions will give the variation of temperature with position and time, T(x, t), in the pan bottom during Stage 1.Note that the properties of the pan material, including ρ, c_p, and k, need to be specified in order to solve the heat equation.
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Suppose that a right-moving em wave overlaps with a left-moving em wave so that, in a certain region of space, the net electric field in the y direction and magnetic field in the z direction are given by Ey = E0 sin(kx-wt)+E0 sin(kx+wt) and Bz =B0 sin(kx-wt)+B0 sin(kx+wt). (a) Find the mathematical expression that represents the standing electric and magnetic waves in the y and z directions, respectively. (b) Determine the Poynting vector and find the x locations at which it is zero at all times.
The standing wave can be obtained by taking the sum of the two traveling waves with equal amplitude and opposite phase velocities. To do this, we can use the trigonometric identity:
How to use wave amplitude?sin(A) + sin(B) = 2 cos((A+B)/2) sin((A-B)/2)
Applying this identity to the electric field Ey, we get:Ey = 2 E0 cos(wt) sin(kx)
This represents a standing wave with nodes (zero amplitude) at x = nλ/2k, where n is an integer.
Similarly, for the magnetic field Bz, we have:
Bz = 2 B0 cos(wt) sin(kx)
This also represents a standing wave with nodes at the same positions as the electric field.(b) The Poynting vector represents the flow of energy of the electromagnetic wave and is given by:S = E x B
where x represents the vector cross product. Substituting the expressions for E and B, we get:
S = E0 B0 sin^2(kx) / μ0
where μ0 is the permeability of free space.
The Poynting vector is zero when sin^2(kx) = 0, which occurs at x = nπ/k for n an integer. This represents positions where the electric and magnetic fields are out of phase and the energy flow is momentarily zero.
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the sun is not located at the center of an elliptical orbit, but is offset somewhat toward one of its ends.T/F
The sun is not located at the center of an elliptical orbit, but is offset somewhat toward one of its ends - True.
The Sun is not relatively at the center of a earth's elliptical route. An cirque has a point a little bit down from the center called the" focus". The Sun is at the focus of the cirque. Because the Sun is at the focus, not the center, of the cirque, the earth moves near to and further down from the Sun every route. The close point in each route is called perihelion. The far down point is called aphelion.
The Sun isn't located at the center of an elliptical route, but is neutralize kindly toward one of its ends. The Greek champion Claudius Ptolemaeus ( Ptolemy) tutored that all heavenly bodies moved in perfect indirect routeways centered on the Earth.
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A student in a science lab is investigating heat transfer and thermal energy conservation as she mixes hot and cold water. She first measures out her desired amount of cold water into a Styrofoam cup. She then measures out hot water from the faucet or from a pot hot water on her stove. After she measures the temperature of the hot and cold waters, she pours the hot water into the cold water. She monitors the temperature of the mixed waters and records the final temperature. She uses a standard thermometer to record the temperatures. She does three trials, which are shown below:
Trial 1:
For her first trial, the student decided to mix 250 mL of water at 20 °C with 250 mL of water at 98 °C. After waiting some time, she recorded the temperature of the mix to be 56 °C.
Trial 2:
For her second trial, the student decided to mix 200 mL of water at 20 °C with 400 mL of water at 98 °C. After waiting some time, she recorded the temperature of the mix to be 72 °C.
Trial 3:
For her third trial, the student decided to mix 300 mL of water at 15 °C with 150 mL of water at 90 °C. After waiting some time, she recorded the temperature of the mix to be 41 °C.
Include a data table that organizes the data collected from the three trials.
Make another table, or add to your table, to show data calculations. You will calculate the change in temperatures of the cold and hot water, as well as the mass of the cold and hot waters.
Use the beginning temperature of the hot and cold water and the final temperature of the mixture to calculate the change in temperature of the cold water and the change in temperature of the hot water. For example, the temperature of the cold water was raised from its beginning temperature to the final temperature of the mixture.
Since one milliliter (mL) of water has a mass of one gram (g), it is very easy to determine the mass of the cold and hot water. For example: If you have 100 mL of water, then the mass of the water is 100 g. Remember, 1 kg = 1000 g. Convert the mass of the hot and cold water to kilograms.
Use the equation Q = (m)(c)(Δ T) to calculate the heat gained by the cold water for each trial. Show your work using the problem-solving method shown in previous rubrics. The specific heat for water (c) is 4186 J/(kg * C°).
Use the equation Q = (m)(c)(Δ T) to calculate the heat "lost" by the hot water for each trial. Show your work using the problem-solving method shown in previous rubrics. The specific heat for water (c) is 4186 J/(kg * C°).
Compare the values for heat gain and heat loss in questions 3 and 4.
In an isolated system, the total heat given off by warmer substances equals the total heat energy gained by cooler substances. Now look at your answer to Question 5. What might have caused the difference you have reported? Even though this data was provided to you, think of the errors the student could have encountered when collecting the data.
Write a complete conclusion for this activity.
The heats gained by cold water in trials 1, 2 and 3 are 3048.6 J, 4311.52 J and 3048.6 J respectively and the heat lost are -6858 J, -4307.84 J and -3593.9 J respectively.
How to find heat gained and lost?Calculation of Heat Gained by Cold Water:
Trial 1:
Q = (m)(c)(Δ T)
Q = (0.25 kg)(4186 J/(kg x C°))(36°C)
Q = 3048.6 J
Trial 2:
Q = (m)(c)(Δ T)
Q = (0.2 kg)(4186 J/(kg x C°))(52°C)
Q = 4311.52 J
Trial 3:
Q = (m)(c)(Δ T)
Q = (0.3 kg)(4186 J/(kg x C°))(26°C)
Q = 3048.6 J
Calculation of Heat Lost by Hot Water:
Trial 1:
Q = (m)(c)(Δ T)
Q = (0.25 kg)(4186 J/(kg * C°))(-52°C)
Q = -6858 J
Trial 2:
Q = (m)(c)(Δ T)
Q = (0.4 kg)(4186 J/(kg x C°))(-26°C)
Q = -4307.84 J
Trial 3:
Q = (m)(c)(Δ T)
Q = (0.15 kg)(4186 J/(kg x C°))(-75°C)
Q = -3593.9 J
Comparison of Heat Gain and Heat Loss:
In all three trials, the heat lost by the hot water is not equal to the heat gained by the cold water. This discrepancy is likely due to errors in the measurement of the temperature and volume of the water, or due to heat loss to the environment.
Conclusion:
This activity allowed the student to investigate heat transfer and thermal energy conservation. Through the measurement of the temperature of hot and cold water and the calculation of heat gained and lost by each, the student was able to gain a better understanding of these concepts. However, it is important to note that the results may have been affected by errors in measurement, so further experimentation and refinement of techniques may be necessary to obtain more accurate results.
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Which of the quantities are zero throughout the flight?
The horizontal component of acceleration is always zero is the quantities are zero throughout the flight.
What is acceleration?
Acceleration was the representation rate In a change of velocity because the acceleration always depends on the object's speed. Acceleration determines the rate of the particles. Acceleration is the vector quantity. It is a vector quantity, but it has both extent and movement. Newton's law also has the acceleration of the magnitude described. The m.s-2 is the standard unit for acceleration.
What is velocity ?
The most important metric for determining an object's position and rate of movement is its velocity. The distance that an object travels in a certain amount of time might be used to define it. The object's displacement in a unit of time is referred to as velocity.
Therefore, The horizontal component of acceleration is always zero is the quantities are zero throughout the flight.
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A capacitor consists of two metal plates each 10 cm by 20 cm; they are separated by a 2.0 mm thick insulator with dielectric constant 4.1 and dielectric strength 6.0107 V/m. What is the capacitance in pF(10 −12
F)?
The equation gives the capacitance of a parallel-plate capacitor:C = εA/d. Where C is the capacitance, ε is the permittivity of the dielectric material between the plates, A is the area of each plate, and d is the distance between the plates.
In this case, the area of each plate is 10 cm × 20 cm = 200 cm^2 = 0.02 m^2. The distance between the plates is 2.0 mm = 0.002 m. The permittivity of the dielectric material is ε = ε0εr, where ε0 is the vacuum permittivity (8.85 × 10^-12 F/m), and εr is the relative permittivity or dielectric constant (4.1).
So, substituting these values into the equation, we get:
C = εA/d
= (ε0εr)(0.02)/(0.002)
= (8.85 × 10^-12)(4.1)(0.02)/(0.002)
= 7.26 × 10^-11 F
= 72.6 pF
Therefore, the capacitance parallel-plate capacitor is 72.6 pF.
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A 10,000 kg railroad car is rolling at 8.00 m/s when a 6000 kg load of gravel is suddenly dropped in. What is the car's speed just after the gravel is loaded? Express your answer with the appropriate units.
The car's speed just after the gravel is loaded is 4.00 m/s.
The momentum of the system (railroad car + gravel) is conserved before and after the gravel is dropped.
Therefore, we can use the law of conservation of momentum to find the velocity of the combined system just after the gravel is loaded.
Before the gravel is dropped, the momentum of the railroad car is:
p1 = m1v1 = (10000 kg)(8.00 m/s) = 80000 kg*m/s
where m1 is the mass of the railroad car and v1 is its velocity.
When the gravel is dropped, the total mass of the system becomes:
m2 = m1 + m_gravel = 10000 kg + 6000 kg = 16000 kg
where m_gravel is the mass of the gravel.
The momentum of the system just after the gravel is dropped is:
p2 = m2v2
where v2 is the velocity of the combined system just after the gravel is loaded.
Since momentum is conserved, we can equate p1 to p2:
p1 = p2
m1v1 = m2v2
Solving for v2, we get:
v2 = (m1v1) / m2
Substituting the given values, we have:
v2 = (10000 kg)(8.00 m/s) / 16000 kg
v2 = 4.00 m/s
Therefore, the car's speed just after the gravel is loaded is 4.00 m/s.
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The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy E_a = 30.0 kJ/mol. If the rate constant of this reaction is 5.0 times 10^4 M^-1 s^-1 at 201.0 degreeC, what will the rate constant be at 172.0 degreeC? Round your answer to 2 significant digits.
The rate constant be at 172.0°C is 1.11 x10⁵ m⁻¹s⁻¹
We employ the Arrhenius equation, which is: to determine the rate constant for the reaction at two different temperatures.
Ln(k 172.0°C/ k 201°C) = Ea/R (1/T₁ - 1/T₂)
where,
k 201°C = equilibrium constant at 201°C = 5x 10⁴m⁻¹s⁻¹
k 172.0°C = equilibrium constant at 172.0°C = ?
Ea = Activation energy = 30.0 kJ/mol = 30000 J/mol (Conversion factor: 1 kJ = 1000 J)
R = Gas constant = 8.314 J/mol K
T₁ = initial temperature = 201°C = 474°K
T₂ = final temperature = 172.0°C = 445 °K
Putting the value
Ln(k 172.0°C/ k 201°C) = 30000 J/mol /8.314 J/mol K (1/ 474°K - 1/445 °K)
k 172.0°C = 1.11 x10⁵ m⁻¹s⁻¹
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A student a model of isostatsy by placing a block of soon in a beaker
To answer the question: "A student made a model of isostasy by placing a block of wood in a beaker of water how can a student demonstrate isostaic rebound using her model?" If she "Press the block down and let go
What is Isostasy?The state of gravitational equilibrium between the Earth's crust and mantle known as isostasy or isostatic equilibrium causes the crust to "float" at an elevation that is dependent on its thickness and density.
This idea is used to explain how various topographic heights can occur on the surface of the Earth.
Hence, to test the model she has, she should press the block down and let go
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A student made a model of isostasy by placing a block of wood in a beaker of water how can a student demonstarte isostaic rebound using her model
A. Blow vigorously on the block
B. Press the block down and let go
C. Add water until the beaker overflow
D. Pour out all the water
Sound is emitted by a point source. You wish to compare the sound intensity and sound intensity level from this source at two different sites. If the distance to the second site is a factor of 8 greater than the distance to the first, determine the following.
(a) Determine the multiplicative factor by which the sound intensity decreases as you go from the first to the second site. (Assume the intensities at the first and second sites are I1 and I2, respectively.)
I1
I2
= The answer to this one is 64.
(b) Determine the additive amount by which the sound level intensity decreases as you go from the first to the second site. (Assume the sound level intensities at the first and second sites are ?1 and ?2, respectively.) How is sound intensity level related to sound intensity? Recall that
log10(ab) = log10(a) + log10(b).
?1 ? ?2 = dB
a) The multiplicative factor by which the sound intensity decreases as you go from the first to the second site is 64.
b) The additive amount by which the sound level intensity decreases as you go from the first to the second site is -15.56 dB.
a) The intensity of the sound is measured in decibels and the sound intensity level with the intensity I is calculated by the expression,
β(dB) = 10 log(I/I₀)
where,
β/dB is the intensity level
I is sound intensity
The intensity is given by the relation,
Intensity = Power/Area
I = (P/πr²)
Intensity is inversely related to the square of radius.
I₁/I₂ = (r₂/r₁)² = (8/1)² = 64
I₁ = 64 I₂
So, the multiplicative factor is 64.
b) The formula for the intensity level is given by,
β(dB) = 10 log(I/I₀)
β₁ = 10 dB log(I₁/I₀)
β₂ = 10 dB log(I₂/I₀)
β₂ - β₁ = 10 dB[log(I₂/I₀) - log(I₁/I₀)]
β₂ - β₁ = 10 dB log(I₂/I₁)
β₂ - β₁ = 10 dB log(1/36) = -15.56 dB
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Continuing the preparation of the proposal for the Eau Gaullie treatment plant (Problem 6-38), design the flocculation tank by providing the follow- ing for the first two compartments only: 1. Water power input in kW 2. Tank dimensions in m 3. Diameter of the impeller in m 4. Rotational speed of impeller in rpm Use the following assumptions: 1. Number of tanks = two 2. Tapered G in three compartments: 90, 60, and 30 s 3. GO= 120,000 4. Compartment length = width = depth 5. Impeller type: axial-flow impeller, three blades, Np = 0.31 6. Available impeller diameters: 1.0, 1.5, and 2.0 m 1 7. Assume B = 1/3 H Answers for first compartment only: P = 295.31, or 295 W or 0.295 kW L=W=D = 3.3 m Impeller diameter = 1.5 m Rotational speed = 30 rpm
Eau Gaullie treatment a) expected flow rate is 1852 gpm. b) Tank diameter is 41.7 ft. c) input power is 21.1 hP
From flow in tank coefficient equation C_Q = Q/(W×D³)
Q ∝ d³
Qd₁/Qd₂ = d₁³/d₂³
where Eau Gaullie treatment Qd₁ and Qd₂ are different discharges with respect to different diameter, (Qd₁ = 3200 gpm) and d₁ is diameter one ( 12 in) while d₂ is diameter 2 ( 10 in),
now we substitute
Qd₂ = Qd₁(d₂³/d₁³)
Qd₂ = 3200( 10/12)³
Qd₂ = 1852 gpm
∴ expected flow rate is 1852 gpm
next we calculate the head
h ∝ d²
hd₁/hd₂ = d₁²/d₂²
where hd₁ and hd₂ are different heads with respect to different diameter, (hd₁ = 60 ft) and d₁ is diameter one ( 12 in) while d₂ is diameter 2 ( 10 in),
now we substitute
hd₂ = hd₁(d₂²/d₁²)
hd₂ = 60 ( 10/12 )²
hd₂ = 41.7 ft
∴ head is 41.7 ft
Now calculate the input power
W ∝ d⁵
Wd₁/Wd₂ = d₁⁵/d₂⁵
where Wd₁ and Wd₂ are different power with respect to different diameter, (Wd₁ = 60 hp) and d₁ is diameter one ( 12 in) while d₂ is diameter 2 ( 10 in),
now we substitute
Wd₂ = Wd₁(d₂⁵/d₁⁵)
Wd₂ = 60 ( 10/12 )⁵
Wd₂ = 21.1 hP
∴ input power is 21.1 hP
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The position of a particle moving in the x-y plane at any time t is given by : x=(3t^3−6t) metres; y=(t^2−2t) metres. Select the correct statement.
a. acceleration is zero at t=0
b. Valocity is zero at t=0
c. Valocity is zero at t=ts
d. Valocity and acceleration of the particle are never zero
The required velocity and acceleration of this particle when position of the particle is given are never zero. Correct option is D.
The position of the particle is given as x = 3t³ - 6t, y = t² - 2t
The particle's velocity is determined by,
v = dx/dt i + dy/dt j = (9t² - 6) i + (2t - 2) j
The velocity at the point t = 0 is,
v = (9t² - 6) i + (2t - 2) j = - 6 i - 2 j
The velocity at the point t = 1 is,
v = (9t² - 6) i + (2t - 2) j = 3 i
The acceleration of the particle is,
a = d²x/dt² i + d²y/dt² j = 18t i + 2 j
The particle's acceleration at time zero is,
a = 2 j
Thus, the velocity and acceleration of this particle are never zero.
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Question
What is the angular speed of the second hand of a clock? If the second hand is 10cm long, then find the linear speed of its tip. (in rad/s and m/s)
A
0.1047,0.01047
B
1047,0.01047
C
0.1047,1047
D
0.0047,0.01047
Easy
The correct answer of the angular speed and linear speed respectively is option A) 0.1047,0.01047
To find the angular speed of the second hand of a clock, we use the formula:
Angular speed = 2π / time
Since the second hand of a clock completes one full rotation every 60 seconds, the time is 60 seconds. Therefore:
Angular speed = 2π / 60
Angular speed = 0.1047 rad/s
To find the linear speed of the tip of the second hand, we use the formula:
Linear speed = angular speed x radius (v = ωr)
Since the radius of the second hand is 10cm or 0.1m, we can plug in the values:
Linear speed = 0.1047 x 0.1
Linear speed = 0.01047 m/s
Therefore, the angular speed of the second hand of a clock is 0.1047 rad/s and the linear speed of its tip is 0.01047 m/s.
The correct answer to the angular speed and linear speed is therefore option A) 0.1047, 0.01047.
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An object that can move in either direction along a horizontal line ( the positive axis). Assume that friction is so small that it can be neglected. Sketch the shape of the graph of the force applied to the object that would produce the motion described.
A) The object moves away from the origin with a constant velocity.
B)The object moves toward the origin with a constant velocity.
C) The object moves away from the origin with a steadily increasing velocity (a constant acceleration)
A) and B): No force whenever, F(t) = 0, ∀t. C): A constant force,
F(t) = F0,∀t.
Newton's Laws
In the year 1687, Isaac Newton distributed his fundamental work "Philosophiae Naturalis Principia Mathematica", in which he included three essential standards of movement. These standards are referred to now as Newton's maxims or Newton's laws.
A) and B): No force whenever,
F(t) = 0, ∀t.
As indicated by Newton's most memorable regulation, an article moves with constant velocity when no net force is following up on it.
C): A constant force,
F(t) = F0,∀t.
As indicated by Newton's subsequent regulation, the speed increase is corresponding to the acting force. Assuming that the speed increase is constant, the force is constant.
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a car comes to a bridge during a storm and finds the bridge washed out. the driver must get to the other side, so he decides to try leaping it with his car. the side the car is on is 18.1 m above the river, whereas the opposite side is a mere 2.0 m above the river. the river itself is a raging torrent 68.0 m wide. for help with math skills, you may want to review: vector magnitudes for general problem-solving tips and strategies for this topic, you may want to view a video tutor solution of different initial and final heights.
Equation to solve for v:v = sqrt(u² + 2as)Substituting the given values, we get:v = sqrt((25.7 m/s)² + 2(-9.8 m/s²)(16.1 m))v = 14.9 m/s
What is speed?It is a scalar quantity that represents the speed at which an item moves or changes position with respect to time.
A) To determine the initial velocity required to clear the river and land safely on the other side, we need to use the following equation d = vt + (1/2)at²
Where d is the distance the car needs to travel horizontally, which is the width of the river (68 m).v is the initial velocity of the car. An is the acceleration due to gravity (-9.8 m/s²).
T is the time the car spends in the air. We can rearrange this equation to solve for v:v = (d – (1/2)at²) / substituting the given values, we get:v = (68 m – (1/2)(-9.8 m/s²)(18.1 m)²) / (2(18.1 m)/v)v = 25.7 m/s
B) To determine the speed of the car just before it lands on the other side, we can use the following equation: where:u is the initial velocity of the car. An is the acceleration due to gravity (-9.8 m/s²).s [tex]v^² = u^² + 2as[/tex]is the vertical distance the car travels from the cliff to the other side (18.1 m – 2 m = 16.1 m).
Therefore, (A) To clear the river and safely land on the other side, the car must be moving at a speed of 25.7 m/s (or approximately 92.5 km/h) immediately as it exits the cliff.
(B) The car is travelling at a speed of 14.9 m/s, or approximately 53.6 km/h, shortly before it safely falls on the opposite side.
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A car comes to a bridge during a storm and finds the bridge washed out. The driver must get to the other side, so he decides to try leaping it with his car. The side the car is on is 18.1 m above the river, whereas the opposite side is a mere 2 m above the river. The river itself is a raging torrent 68 m wide.A) How fast should the car be travelling just as it leaves the cliff in order to just clear the river and land safely on the opposite side? B) What is the speed of the car just before it lands safely on the other side?
A solid nonconducting sphere is inside a solid nonconducting spherical shell, as shown in the figure. A total charge +Q is evenly distributed throughout the sphere and is also evenly distributed throughout the shell. Which of the following statements is a correct claim about the electric field at point X between the sphere and shell and has a valid supporting statement?
(A). The electric field points to the left, because the electric field from sphere is zero and the electric field from the shell is directed to the left (B). The electric field points to the left, because a Gaussian sphere concentric with the sphere X on its surface only encloses the charge on the inner sphere. (c). The electric field points to the right, because the electric field from the shell has a larger magnitude that the electric field from the sphere (d). The electric field is zero, because a Gaussian sphere concentric with the sphere with X on its surface encloses zero net charge.
(E). The electric field is zero, because point X is inside a nonconducting shell.
The correct claim about the electric field at point X between the sphere and shell is option (d). The electric field is zero, because a Gaussian sphere concentric with the sphere with X on its surface encloses zero net charge.
According to Gauss's law, the electric field at a point in space is proportional to the net charge enclosed by a Gaussian surface around that point. In this case, a Gaussian sphere concentric with the sphere with point X on its surface will enclose the charges on both the inner sphere and the outer shell. However, since the total charge on both objects is equal and opposite, the net charge enclosed by the Gaussian surface is zero, and therefore, the electric field at point X is zero. The fact that point X is inside a non-conducting shell (as stated in option E) is not relevant to the electric field at that point. Option A is incorrect because the electric field from the shell is directed outward, away from the center, not to the left. Option B is also incorrect because the Gaussian surface will enclose the charges on both the inner sphere and the outer shell, not just the charges on the inner sphere. Option C is incorrect because the magnitudes of the electric fields from the sphere and shell do not determine the direction of the electric field at point X.
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For each of the regions, use the midpoint method to identify whether the supply of this good is elastic or inelastic.Region Elastic or InelasticBetween Y and Z Between W and X
(a). Elasticity of supply between W and X is elastic.
(a)-1.The supply elasticity relationship Y and Z becomes inelastic.
b. The assertion is accurate.
What kind of products are elastic?Like a dishwasher or a car, these are infrequently acquired things that can be put off if the price increases. Elasticity is a crucial economic metric because it shows how much of an item or service consumers consumes when the price varies, which is especially essential for businesses that sell goods or services. That whenever a commodity is elastic, a price fluctuation prompts a shift in demand for it rapidly.
What three forms of elasticity are there?Economists use elasticity to determine how different factors interact. Pricing, cross-price quantity demanded, and quantity demanded are the three main types of elasticity. Goods' elasticity gauges how sensitive they are to price changes.
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True or False: The longer a pendulum is, the longer it takes to swing. Therefore, when the pendulum of a clock is lengthened, the clock slows down.
Yes, it is true, the longer a pendulum is, the longer it takes to swing. Therefore, when the pendulum of a clock is lengthened, the clock slows down.
The length of a pendulum influences the time it takes to complete one swing, which is referred to as the period. The pendulum swings more slowly and has a longer period as it gets longer. A clock slows down when the pendulum is stretched because it takes longer for each swing to be completed. Similar to how the clock speeds up when the pendulum is shorter, it swings quicker as well. The operation of pendulum clocks and other timekeeping instruments that employ pendulums to measure time is based on this idea.
A pendulum's period, or how long it takes to complete one full swing back and forth, can be used to define how it moves. The length, gravitational acceleration, and angle of displacement are some of the variables that affect a pendulum's period. However, the length of a particular pendulum is what essentially determines its period.
The period of a basic pendulum is described mathematically as
T = 2(L/g), where T is the period, L is the length of the pendulum, and g is the gravitational acceleration.
As you can see, the square root of the length and the period are precisely proportional. This implies that the period likewise grows as the pendulum's length does.
The pendulum offers a means of controlling the clock's timekeeping mechanism. The clock's hands are moved by a gear train that is moved back and forth by the pendulum. The pendulum's length can be changed by the clockmaker to alter the clock's rate of movement. The pendulum can be shortened to make it swing more quickly and speed up the clock if it is running quickly. The pendulum can be stretched to make it swing more slowly and slow down the clock if it is operating slowly.
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A velocity vector 39∘ above the positive x -axis has a y -component of 10m/s .What is the value of its x -component?
The y component of the velocity vector is 10 m/s. Then the v is 12.86 m/s. Now the x component of this velocity is v sin θ.That is , x component is 8 m/s.
What is velocity ?Velocity of an object is the measure of its distance travelled per unit time. Velocity is a vector quantity thus having both magnitude and acceleration. The magnitude is called speed.
For a velocity vector there are three translation components possible for three different axes.
here, x component = v sinθ
y component = v cos θ
Given that v cos θ = 10 m/s
θ = 39
Vy = v cos 39 = 10 m/s
then v = 12.8 m/s
Now, the x component is calculated as:
vx = 12.8 m/s sin 39 = 8 m/s.
Therefore, the x component of velocity here is 8 m/s.
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Sally was removing her nail polish to get ready for a dance. She was also drinking a bottle of water. The doorbell rang and she rushed to answer it, leaving the open bottle of nail polish remover (acetone) and the bottle of water open. Sally forgot about them until the next morning and when she checked, the nail polish remover (acetone) was empty and the water looked untouched.
Sally believes the particles in water stick together more. In terms of your knowledge of the strength of electrical forces and the structure of substances, explain Sally's statement.
Sally's observation that the water bottle appeared untouched while the acetone bottle was empty can be explained by the stronger cohesive forces between the water molecules compared to the acetone molecules. The water molecules stick together more tightly, preventing them from evaporating as quickly as the acetone molecules
Explaining Sally's statementSally's statement that particles in water stick together more is partially correct. The cohesive forces between the particles in water, also known as hydrogen bonds, are indeed stronger than the intermolecular forces between the particles in acetone, which are dipole-dipole interactions.
The strength of the intermolecular forces between particles is determined by the type of chemical bonding and the molecular structure of the substance. In the case of water, the oxygen atom in each molecule attracts electrons more strongly than the two hydrogen atoms, giving rise to partial negative charges around the oxygen and partial positive charges around the hydrogen. This creates an electrostatic attraction between neighboring water molecules, resulting in hydrogen bonding.
On the other hand, acetone molecules have a polar covalent bond between the carbon and oxygen atoms, resulting in partial positive and negative charges. The intermolecular forces between acetone molecules are weaker than those between water molecules, because the dipole moments in acetone are not as large as the dipole moments in water.
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If a car is pushed with a force of 18N for 8m, how much work has been done?
According to the question, the work done by a car is calculated as 144Nm.
What is force?Force may be defined as a process of pushing or pulling on an object that significantly produces acceleration in the body on which it acts. It is an external agent capable of changing a body's state of rest or motion. It has a magnitude and a direction.
According to the question,
The force applied on a car = 18 N
The displacement made by a car = 8m.
Now, the work done is calculated with the help of the given formula:
Work done = Force × Displacement.= 18 N × 8m = 144Nm.
Therefore, the work done by a car is calculated as 144Nm.
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A scale of 1:900,000 is _____________ a scale of 1:24,000:
A - equal to
B - smaller than
C - twice as much as
D - larger than
The stated statement indicates that Scales less than 1:24,000 are 1:900,000 and 1:24,000, respectively.
The correct option is B.
In what sense is a scale defined?a graded object, particularly when used as a rule or measure: a set of markings or points spaced apart at defined intervals used to measure distances, such as: a relationship between the distances shown on a map and their corresponding actual distances (such as the height of the mercury in a thermometer)
What other names do scales go by?To visually depict the scale of a map, maritime chart, engineering design, or architectural drawing, use a linear scale, also known as a bar scale, scale bar, or graphic scale.
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4) Collision in which K.E and momentum of system remain same is called__________
(*)Elastic Collision
(*) Inelastic collision
(*) Conserved collision
(*) Linear collision
A collision that is elastic occurs when there is no net loss of kinetic energy in the system as a result of the collision. Kinetic energy and momentum are both conserved in elastic collisions.
Give an example of an elastic collision.When two balls collide at a pool table, that is an instance of an elastic collision. When you throw a ball on the ground and it bounces back into your hand, there is no net change in the kinetic energy, making it an elastic collision.
Give an illustration of what an elastic collision is.Two balls colliding at a pool table is an example of an elastic collision. When a ball is tossed to the ground and subsequently returns to your hand, there is no net change in the kinetic energy, making it an elastic collision.
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what a geologist sees. a geology student sits beside an outcrop on mont royal, the namesake of montreal. this exposure shows the intrusion of molten basalt into preexisting limestone.
The geologist sees depositional contact. Therefore, option A is correct.
What is depositional contact?A sedimentary or volcanic rock is said to have been deposited on an older rock at a depositional contact (of any type). Where volcanic rocks encroach on older rock, this is known as an intrusive contact (of any type).
The ten different types of contacts are as follows: (1) bedding planes, (2) diastems, (3) angular irregularities, (4) disconformities, (5) para-conformities, (6) nonconformities, (7) pedologic contacts, (8) faults, 9) intrusive contacts, and 10) extrusive contacts.
Hence, option A is correct.
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your question is incomplete, most probably the full question is this:
what a geologist sees. a geology student sits beside an outcrop on mont royal, the namesake of montreal. this exposure shows the intrusion of molten basalt into preexisting limestone.
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The true statement about the motion of the helicopter is " the helicopter travels at a greater speed between D and E than it did between A and B.
option D.
What is motion?
Motion is the process of an object changing its position with respect to a reference point over time. It involves the movement of an object from one point in space to another.
Motion can be described in terms of its speed, direction, and acceleration. Speed refers to the rate at which an object is moving, while direction refers to the path that the object is following. Acceleration refers to the rate at which an object's speed or direction changes.
v = Δx / Δt
where;
Δx is change in positionΔt is change in timeThe change in position of the helicopter between A and B = 0
because, A = 100 m and B = 100 m
so the speed of the helicopter between A and B = 0 m/s.
Thus, the last statement is the only correct option,
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