Answer:
The third force = [tex]-(26.0 \, N \, \hat{i} + 12.00 \, N \, \hat{j})[/tex]
Explanation:
Here we note that, the formula for the resultant force is as follows;
[tex]\Sigma F = \Sigma F_x + \Sigma F_y[/tex]
Also
∑F = m×a
Where:
[tex]F_x[/tex] = Force components in the x direction
[tex]F_y[/tex] = Force components in the y direction
∑F = Resultant force vector
m = Mass of the object
a = Acceleration vector ob the object =
[tex]a = 8.00 \, m/s^2 \, \hat{i} + 6.00 \, m/s^2 \, \hat{j}[/tex]
[tex]F_1 = 30.0 \, N \, \hat{i} + 16.0 \, N \, \hat{j}[/tex]
[tex]F_2 = 12.0 \, N \, \hat{i} + 8.00 \, N \, \hat{j}[/tex]
Therefore, since ∑F = m×a, we have;
[tex]\Sigma F = 2 kg \times (8.00 \, m/s^2 \, \hat{i} + 6.00 \, m/s^2 \, \hat{j})[/tex]
[tex]\Sigma F = (16.00 \, m/s^2 \, \hat{i} + 12.00 \, m/s^2 \, \hat{j})[/tex]
Hence from [tex]\Sigma F = \Sigma F_x + \Sigma F_y[/tex], we have;
[tex]F_{x1} + F_{x2} + F_{x3} = 16[/tex]
That is 30 + 12 + [tex]F_{x3}[/tex] = 16
∴ [tex]F_{x3}[/tex] = 16 - (30 + 12) = -26
Similarly,
[tex]F_{y1} + F_{y2} + F_{y3} = 12[/tex]
Therefore, [tex]F_{y3}[/tex] = 12 - (16 + 8) = -12
Hence, [tex]F_3 = -26.0 \, N \, \hat{i} - 12.00 \, N \, \hat{j} = -(26.0 \, N \, \hat{i} + 12.00 \, N \, \hat{j})[/tex]
The third force, [tex]F_3, = -(26.0 \, N \, \hat{i} + 12.00 \, N \, \hat{j})[/tex]
The third force applied on the object calculated using Newton's second law provides a magnitude of (-26.00 N î - 12.00 N ĵ).
Explanation:The subject of this problem is Newton's second law (F=ma), where F is the total force, m is the mass of the object, and a is acceleration. Each of these elements (i, j) represent a vector quantity with both a magnitude and a direction, and in this case, they represent different directions in two-dimensional space. The total acceleration of the object is a vector sum of these accelerations, as is the total force. Therefore, you can calculate the third force by subtracting the first two forces from the total force (which is found by multiplying mass and acceleration).
Total Force (F) = m*a = (2 kg)*(8.00m/s² î + 6.00m/s² ĵ) = 16.00 N î + 12.00 N ĵ.
We know two forces, F1 = 30.00 N î + 16.00 N ĵ and F2 = 12.00 N î + 8.00 N ĵ. Adding them, we get F1 + F2 = 42.00 N î + 24.00 N ĵ.
The third Force (F3) is the total force (F) subtracted from (F1 + F2), thus, F3 = F - (F1 + F2) = (-26.00 N î - 12.00 N ĵ).
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Every chemical element goes through natural exponential decay, which means that over time its atoms fall apart. The speed of each element's decay is described by its half-life, which is the amount of time it takes for the number of radioactive atoms of this element to be reduced by half.
The half-life of the isotope beryllium-11 is 14 seconds. A sample of beryllium-11 was first measured to have 800 atoms. After t seconds, there were only 50 atoms of this isotope remaining, Write an equation in terms of t that models the situation.
The equation modeling the exponential decay of the Beryllium-11 isotope is 50 = 800(1/2)^(t/14). This lets you find out the time that has passed since there were initially 800 atoms.
Explanation:The situation described is an example of exponential decay, modeled by the formula N = N0(1/2)^(t/h). In this case, N0 is the original number of atoms (800), N is the remaining number of atoms (50), t is the time that has passed, and h is the half-life of the isotope (14 seconds for Beryllium-11).
So the equation modelling this scenario is 50 = 800(1/2)^(t/14). This equation will let you solve for the time t (in seconds) that has passed since the sample initially contained 800 atoms of Beryllium-11.
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The hydraulic oil in a car lift has a density of 8.53 x 102 kg/m3. The weight of the input piston is negligible. The radii of the input piston and output plunger are 5.43 x 10-3 m and 0.135 m, respectively. What input force F is needed to support the 22600-N combined weight of a car and the output plunger, when (a) the bottom surfaces of the piston and plunger are at the same level, and (b) the bottom surface of the output plunger is 1.20 m above that of the input plunger
Answer:
(a) the input force is 36.56 N
(b) the input force is 37.49 N
Explanation:
Given;
density of hydraulic oil, ρ = 8.53 x 10² kg/m³
radius of plunger, r₁ = 0.135 m
radius of piston, r₂ = 5.43 x 10⁻³ m
Part (a) The input force needed to support 22600-N weight, when the bottom surfaces of the piston and plunger are at the same level;
[tex]P =\frac{F}{A}[/tex]
Where;
P is pressure
F is force
A is circular area = πr²
[tex]\frac{F_1}{A_1} =\frac{F_2}{A_2} \\\\F_2 = \frac{F_1*A_2}{A_1} =\frac{F_1* \pi r_2^2}{\pi r_1^2} = \frac{F_1* r_2^2}{ r_1^2} \\\\F_2 = \frac{22600*(5.43*10^{-3})^2 }{(0.135)^2}\\\\F_2 = 36.56 \ N[/tex]
Part (b) The input force needed to support 22600-N weight, when the bottom surface of the output plunger is 1.20 m above that of the input plunger
[tex]P_2 = P_1 + \rho gh[/tex]
But, F = PA and A = πr²
[tex]F_2 = F_1(\frac{A_2}{A_1} ) + \rho gh*A_2\\\\F_2 = F_1(\frac{r_2^2}{r_1^2} )+\rho gh(\pi r_2^2)\\\\F_2 = 22600(\frac{5.43*10^{-3}}{0.135})^2 \ + 853*9.8*1.2*\pi (5.43*10^{-3})^2\\\\F_2=36.56 + 0.93\\\\F_2 = 37.49 \ N[/tex]
The solution of this problem involves the use of Pascal's principle and a concept known as hydrostatic pressure.
First, let's identify the given parameters:
- The density (ρ) of the hydraulic oil is 8.53 x 10ˆ2 kg/m³
- The radius of the input piston is 5.43 x 10ˆ-3 m
- The radius of the output plunger is 0.135 m
- The total weight (W) being lifted is 22600 N
- The acceleration due to gravity (g) is approximately 9.81 m/s²
- The height difference (Δh) between the pistons is 1.2 m
We will use these in our calculations.
We begin by determining the areas of the input piston and the output plunger using the formula for the area of a circle A = πr². We denote the area of the input piston as Ain and the area of the output plunger as Aout.
Let's now focus on when the pistons are at the same level.
Part (a) requires us to find the input force (F) needed to support the weight of the car and output plunger. This is governed by Pascal's principle, which states that for an incompressible, non-viscous fluid in a hydraulic system, pressure is transmitted undiminished throughout the fluid and acts with equal force on all areas. Using Pascal's principle, the force required on the input piston is equal to the weight divided by the ratio of the areas. F = W * (Ain / Aout). After performing the calculation, we find that F equivales to approximately 36.562893827160494 N.
Next, let's turn to when the bottom surface of the output plunger is 1.2 m above the input piston.
Part (b) of the problem asks us to calculate the input force needed in this scenario. We must consider not only Pascal's principle but the additional hydrostatic pressure due to the height difference between the pistons. Firstly, we calculate the hydrostatic pressure difference (ΔP): ΔP = ρ * g * Δh. We then add this pressure difference to the force required when pistons were at the same level. Remember that pressure is force divided by area, thus when we add pressure we need to multiply it by the area of the input piston to maintain the units consistent. F = F_same_level + ΔP * Ain. The result of this calculation yields an input force of approximately 37.49208673165364 N.
In conclusion, the input force required to support the specified weight when the bottom surfaces of the pistons are at the same level is about 36.56 N. This force increases to roughly 37.49 N when the output plunger is pushed 1.2 m above the input piston due to the added hydrostatic pressure.
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If a system is isolated the total energy within that system is constant. Consider the case of a hot cup of coffee: when it cools down, the energy goes into the surrounding air, causing the air to warm. If the coffee and the air are placed in an isolated chamber, the total energy of the system (coffee + air) is constant because the energy lost by the coffee is exactly equal to the energy gained by the air. The only way for the total energy of a system to change is when it is not isolated, meaning that external forces or sources of energy interact with the system. If we want to define a system where the total energy is conserved, which one of the choices below would be the best system to consider?A. The personB. The person and the EarthC. The Earth
Answer:b-The person and the earth
Explanation:
The best system will be the person and earth as a system
It is so because whatever the energy required by the person is derived from earth resource and thus by depleting the earth resource person is getting is required form of energy .
for example person want thermal energy , for this he need coal which is earth resource and thus all the energy is derived from earth and is being converted into some other form of energy.
What factors does the kinetic energy of a body depend
on?
Ans
Answer:
Kinetic energy depends on the mass of a body and the velocity it is travelling at
Explanation:
Referring to the equation of Kinetic Energy
EK = 0.5 m [tex]v^{2}[/tex]
We can see that Kinetic energy depends on the mass of a body and the velocity it is travelling at
Answer:
The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) that an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object.
A biker can ride at 12 m/s on a level road when there is no wind and at 7.5 m/s on a level road when there is a head wind of 5 m/s. Assume that fluid drag and resistance due to friction are the only forces acting on the biker. The friction force is given by the product of rolling resistance and bike velocity. The density of ambient air is 1.2 kg/m3 If the biker delivers 10.2500 W of power while riding the bike, determine the value of LaTeX: C_D A
Answer:
The answer is "[tex]1.94 \ m^2[/tex]".
Explanation:
Formula:
[tex]F= \frac{1}{2} \times C_D \times density \times area \times velocity^2\\\\Power (P) = F \times velocity \\\\P = \frac{C_D}{2} \times density \times area \times velocity^3\\[/tex]
Given value:
[tex]\ P = 10.25 \ W \\\\\ density = 1.2 \ kg/m^3 \\\\\ velocity= 2.5 \\\\[/tex]
[tex]10.25 = \frac{C_D A}{2} \times 1.2 \times 2.5^3\\\\C_D A= \frac{10.25 \times 2 }{1.2 \times 2.5^3}\\\\C_D A = 1.94 m^2\\[/tex]
A 50-kilogram student is running and has 225 joules of kinetic energy.What is the students speed in meters per second
Answer:3m/s
Explanation:
mass(m)=50kg
Kinetic energy =225 joules
Kinetic energy=(m x (velocity)^2)/2
225=(50 x (velocity)^2)/2
Cross multiplying we get
225x2=50x(velocity)^2
450=50x(velocity)^2
Divide both sides by 50
450/50=(50x(velocity)^2)/50
9=(velocity)^2
Taking the square root of both sides we get
√9=velocity
3=velocity
Velocity=3m/s
An oil tanker has collided with a smaller vessel, resulting in an oil spill in a large, calm-water bay of the ocean. You are investigating the environmental effects of the accident and need to know the area of the spill. The tanker captain informs you that 18000 liters of oil have escaped and that the oil has an index of refraction of n = 1.1. The index of refraction of the ocean water is 1.33. From the deck of your ship you note that in the sunlight the oil slick appears to be blue. A spectroscope confirms that the dominant wavelength from the surface of the spill is 485 nm. Assuming a uniform thickness, what is the largest total area o
Complete Question
An oil tanker has collided with a smaller vessel, resulting in an oil spill in a large, calm-water bay of the ocean. You are investigating the environmental effects of the accident and need to know the area of the spill. The tanker captain informs you that 18000 liters of oil have escaped and that the oil has an index of refraction of n = 1.1. The index of refraction of the ocean water is 1.33. From the deck of your ship you note that in the sunlight the oil slick appears to be blue. A spectroscope confirms that the dominant wavelength from the surface of the spill is 485 nm. Assuming a uniform thickness, what is the largest total area oil slick
Answer:
The largest total area of the oil slick [tex]A = 8.257 *10^{9} \ m^2[/tex]
Explanation:
From the question we are told that
The volume of oil the escaped is [tex]V = 18000 \ L[/tex]
The refractive index of oil is [tex]n_o = 1.1[/tex]
The refractive index of water is [tex]n_w = 1.33[/tex]
The wavelength of the light is [tex]\lambda = 485 \ nm = 485 * 10^{-9} \ m[/tex]
Generally the thickness of the oil for condition of constructive interference between the oil and the water is mathematically represented as
[tex]d = m *\frac{\lambda}{2n_w}[/tex]
Where is the order of interference of the light and it value ranges from 1, 2, 3,...n
It is usually take as 1 unless stated otherwise by the question
substituting value
[tex]d = 1 * \frac{485 *10^{-9}}{2 * 1.1}[/tex]
[tex]d = 218 nm[/tex]
The are can be mathematically evaluated as
[tex]A = \frac{V}{d}[/tex]
Substituting values
[tex]A = \frac{18000}{218*10^{-8}}[/tex]
[tex]A = 8.257 *10^{9} \ m^2[/tex]
Which plants are usually the first to live in soil?
The plants that are typically the first to live in soil are known as pioneer plants or pioneer species.
What are the first plants?Pioneer plants or pioneer species are the plants that are often the first to live in soil. These plants are distinguished by their propensity to colonize bare or disturbed soil, such as on newly formed land or in the wake of a natural disaster.
The process of primary succession, which is the gradual formation of plant and animal communities in a region devoid of soil or organic matter, depends critically on pioneer plants.
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wyatt is designing a hollow cylindrical metal can with volume 1000 cm3.the materialused to make the circular top and bottom of the can costs twice as much as the material used tomake the side of the can. what dimensions should wyatt choose in order to minimize the cost ofthe can?show all your work, round off the numerical part of your final answer to four (4) decimal places,and express your final answer in the form of a complete sentence, using the correct units.
Answer:
Explanation:
Let r be the radius of circular top and h be the height of the cylinder
Given
π r² h = 1000
Let cost of making side of can be p per unit area , the cost of making top and bottom will be 2p per unit area.
total cost
C = 2 x π r² x 2p + 2πrh x p
= 2(1000 / h) x 2p + 2π x (1000 / π) x [tex]\frac{1}{\sqrt{h} }[/tex] x h x p
= 2(1000 / h) x 2p + 2π x (1000 / π) x √h x p
differenciating
dC / dh = 2(- 1000 / h²) x 2p + 2π x (1000 / π) x [tex]\frac{1}{2\sqrt{h} }[/tex] x p = 0 for minimum cost
- 4 / h² + 1 / √h = 0
h³ = 16
h = 2.519 cm .
π r² h = 1000
π r² x 2.519 = 1000
r = 11.24 cm
The cylinder will have height of 2.519 cm and radius of 11.24 cm.
Wyatt should design the can with a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm to minimize cost. This considers the volume constraint of 1000 cm³ and the different material costs for the top/bottom and side. Detailed steps involve deriving these dimensions mathematically.
Let's denote the radius of the base of the cylinder by r and the height by h. The volume V of the cylinder is given by V = πr²h. Given that the volume is 1000 cm³, we have:
Step 1: V = πr²h = 1000 cm³
Therefore, h = 1000 / (πr²).
Step 2: Next, we need to express the cost of the material. The cost for the top and bottom parts is double the cost of the side. The surface area A of the can is:
Area of the top and bottom (each): [tex]A_t[/tex] = πr²
Area of the side: [tex]A_s[/tex] = 2πrh
Total area A:
A = 2πr² + 2πrh
Considering the cost factor, the effective cost area C is:
C = 2(2πr²) + 2πrh
C = 4πr² + 2πrh
Step 3: Substitute h from the volume equation:
C = 4πr² + 2πr(1000 / (πr²))
C = 4πr² + 2000 / r
Step 4: To minimize the cost, take the derivative of C with respect to r and set it to zero:
[tex]\frac{dC}{dr}[/tex] = 8πr - 2000 / r² = 0
8πr = 2000 / r²
8πr³ = 2000
r³ = 250 / π
r ≈ 3.4198 cm
Step 5: Calculate the height h:
h = 1000 / (πr²)
h ≈ 1000 / (π * (3.4198)²)
h ≈ 27.2837 cm
In summary, Wyatt should design the can with a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm to minimize the cost.
Wyatt should choose a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm for the metal can to minimize the cost, given the volume constraint of 1000 cm³.
Two electrical motors, one with a power output of 250 watts and one with a power output of 500 watts are both connected to a standard home outlet. Which motor draws greater current?
Answer:
The 500 watts motor
Explanation:
Power is the workdone per unit time, it can be expressed as;
P = VI
P = I^2 × R
Where;
P = power
V = potential difference
I = current
R = resistance
Making current the subject of formula;
I = P/V
I^2 = P/R
Since they are both connected to the same standard home outlet. The potential difference across them is thesame( V is constant). Therefore the higher the power the higher the current.
I ∝ P
So the electrical motors with higher power 500 watts draws greater current.
A certain sound is recorded by a microphone. The same microphone then detects a second sound, which is identical to the first one except that the amplitude of the pressure fluctuations is larger. In addition to the larger amplitude, what distinguishes the second sound from the first one? View Available Hint(s) A certain sound is recorded by a microphone. The same microphone then detects a second sound, which is identical to the first one except that the amplitude of the pressure fluctuations is larger. In addition to the larger amplitude, what distinguishes the second sound from the first one? It is perceived as higher in pitch. It is perceived as louder. It has a higher frequency. It has a longer wavelength.
Answer:
It is perceived as louder.
Explanation:
Amplitude affects the loudness of sound.
Frequency and wavelength affect the pitch of the sound.
A steel drill making 180 rpm is used to drill a hole in a block of steel. The mass of the steel block and the drill is 180 g. If the entire mechanical work is used up in producing heat and the rate of rise in temperature of the block and the drill is 0.5 °C/sec. Find (a) the rate of working of the drill in Watts and (b) torque required to drive the drill. Given: specific heat capacity of steel = 420 J/(kgK)
Answer:
a) 37.8 W
b) 2 Nm
Explanation:
180 g = 0.18 kg
We can also convert 180 revolution per minute to standard angular velocity unit knowing that each revolution is 2π and 1 minute equals to 60 seconds
180 rpm = 180*2π/60 = 18.85 rad/s
We can use the heat specific equation to find the rate of heat exchange of the steel drill and block:
[tex]\dot{E} = mc\Delta \dot{t} = 0.18*420*0.5 = 37.8 J/s[/tex]
Since the entire mechanical work is used up in producing heat, we can conclude that the rate of work is also 37.8 J/s, or 37.8 W
The torque T required to drill can be calculated using the work equation
[tex]E = T\theta[/tex]
[tex]\dot{E} = T\dot{\theta} = T\omega[/tex]
[tex]T = \frac{\dot{E}}{\omega} = \frac{37.8}{18.85} = 2 Nm[/tex]
Calculating the rate of working of a drill involves using the specific heat capacity, mass of the block, and rate of temperature increase to find the power. The torque can be derived from this power and the angular velocity of the drill.
The question involves calculating the rate of working of the drill in Watts and the torque required to drive the drill based on the information that all mechanical work is converted to heat that raises the temperature of the steel block and drill at 0.5 0C/s. Given the mass of the steel block and drill is 180 g and the specific heat capacity of steel is 420 J/(kgK), we can use the formula power (P) = mcigtriangleup T/igtriangleup t, where m is the mass, c is the specific heat capacity, is the temperature change, and is the change in time. To find the torque, we can use the power-torque relationship P = au imes w, where P is power in watts, au is the torque in Newton-meters, and w is the angular velocity in radians per second. As the drill makes 180 revolutions per minute (rpm), we'll convert that to radians per second to use in the power-torque equation.
The binding energies of K-shell and L-shell electrons in a certain metal are EK and EL, respectively, If a Kαx ray from this metal is incident on a crystal and gives a first-order Bragg reflection at an angle θ measured relative to parallel planes of atoms, what is the spacing between these parallel planes? State your answer in terms of the given variables, using h and c when needed.
Answer:
The separation distance between the parallel planes of an atom is hc/2sinθ(EK - EL)
Explanation:
The relationship between energy and wavelength is expressed below:
E = hc/λ
λ = hc/EK - EL
Considering the condition of Bragg's law:
2dsinθ = mλ
For the first order Bragg's law of reflection:
2dsinθ = (1)λ
2dsinθ = hc/EK - EL
d = hc/2sinθ(EK - EL)
Where 'd' is the separation distance between the parallel planes of an atom, 'h' is the Planck's constant, 'c' is the velocity of light, θ is the angle of reflection, 'EK' is the energy of the K shell and 'EL' is the energy of the K shell.
Therefore, the separation distance between the parallel planes of an atom is hc/2sinθ(EK - EL)
(Laminar flow) A fluid flows through two horizontal pipes of equal length which are connected together to form a pipe of length 2l. The flow is laminar and fully developed. The pressure drop for the first pipe is 1.44 times greater than it is for the second pipe. If the diameter of the first pipe is D, determine the diameter of the second pipe.
Answer:
The diameter of the second pipe is [tex]D_2 = 1.095 D[/tex]
Explanation:
From the question we are told that
The length of the connected pipe is [tex]d = 2L[/tex]
The pressure drop for the first pipe is [tex]\Delta p __{1}} = 1.44* \Delta p__{2}}[/tex]
The diameter of the pipe is [tex]D[/tex]
The rate at which the fluid flows for laminar flow is mathematically represented as
[tex]\r m = \frac{\pi D^4 \Delta p}{128 \mu L}[/tex]
Where L is the length of the pipe
[tex]\mu[/tex] is the dynamic viscosity
[tex]\Delta p[/tex] is the difference in pressure
[tex]\r m[/tex] is the flow rate of the fluid
From the equation of continuity
[tex]\r m_ 1 = \r m_2[/tex]
Where [tex]\r m_1[/tex] is the flow rate in pipe one
[tex]\r m_2[/tex] is the flow rate in pipe two
So
[tex]\frac{\pi D^4 \Delta p_1}{128 \mu L} = \frac{\pi D^4_2 \Delta p}{128 \mu L}[/tex]
Where [tex]D_2[/tex] is the diameter of the second pipe
=> [tex]\frac{\pi D^4 (1.44 \Delta p_2)}{128 \mu L} = \frac{\pi D^4_2 \Delta p}{128 \mu L}[/tex]
=> [tex]1.44 D^4 = D_2 ^4[/tex]
[tex]D_2 =\sqrt[4]{ \frac{D ^4 }{1.44 } }[/tex]
[tex]D_2 = 1.095 D[/tex]
A water tower is a familiar sight in many towns. The purpose of such a tower is to provide storage capacity and to provide sufficient pressure in the pipes that deliver the water to customers. The drawing shows a spherical reservoir that contains 7.41 x 105 kg of water when full. The reservoir is vented to the atmosphere at the top. For a full reservoir, find the gauge pressure that the water has at the faucet in (a) house A and (b) house B. Ignore the diameter of the delivery pipes.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The gauge pressure that water has at the House A [tex]P_A = 257020.68 Pa[/tex]
The gauge pressure that water has at the House B [tex]P_B = 188454 \ Pa[/tex]
Explanation:
From the question we are told that
The mass of water when full is [tex]m_f = 7.41* 10^{5} kg[/tex]
Generally the volume of water in this tank is mathematically represented as
[tex]V = \frac{m }{\rho}[/tex]
Where [tex]\rho[/tex] is the density of water with a value of with a value of [tex]\rho = 1000 kg /m^3[/tex]
substituting values
[tex]V = \frac{7.41 *10^5}{10^3}[/tex]
[tex]V = 741 m^3[/tex]
This volume is the volume of a sphere since the tank is spherical so
[tex]V = \frac{4 \pi ^3}{3}[/tex]
making r the subject of the formula
[tex]r =\sqrt[3]{ \frac{741 *3 }{4\pi} }[/tex]
[tex]r = 5.6134 m[/tex]
Now we can use this parameter to obtain the diameter
So
[tex]d = 2 * r[/tex]
substituting values
[tex]d = 2 * 5.6134[/tex]
[tex]d = 11.23m[/tex]
The pressure the water has at faucet in House A is mathematically evaluated as
[tex]P_A = \rho g h_A[/tex]
This height is obtained as follows
[tex]h_A = d+ 15[/tex]
The value 15 is gotten from the diagram
so
[tex]h_A = 15 + 11.23[/tex]
[tex]h_A = 26.22 m[/tex]
Now substituting values
[tex]P_A = 26.23 * 9.8 * 1000[/tex]
[tex]P_A = 257020.68 Pa[/tex]
The pressure the water has at faucet in House B is mathematically evaluated as
[tex]P_B = \rho g h_B[/tex]
This height is obtained as follows
[tex]h_B = d+ 15[/tex]
The value 15 is gotten from the diagram
so
[tex]h_B = d + 15 -h[/tex]
substituting values
[tex]h_B =11.23 + 15 -7[/tex]
[tex]h_A = 19.23 m[/tex]
Now substituting values
[tex]P_B = 19.23 * 9.8 * 1000[/tex]
[tex]P_B = 188454 \ Pa[/tex]
g A coil formed by wrapping 50 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to the plane of the coil makes an angle of 30.0° with the direction of the field. When the magnetic field is increased from 250 µT to 700 µT in 0.300 s, an emf of magnitude 60.0 mV is induced in the coil. What is the total length of wire in the coil?
Answer:
L = 182.4 m
Explanation:
Given:-
- The number of turns of the coil, N = 50
- The shape of the coil = square
- The angle between the coil and magnetic field, θ = 30°
- The change in magnetic field, ΔB = ( 700 - 250 ) μT
- The time duration in which magnetic field changes, Δt = 0.3 s
- The induced emf, E = 60.0 mV
Solution:-
- The problem at hand is an application of Faraday's law. The law states that the induced emf ( E ) is proportional to the negative rate of change of magnetic flux ( ΔФ / Δt ) and number of turns of the coil ( N ).
- The Faraday's law is mathematically expressed as:
E = - N* ( ΔФ / Δt )
Where,
- The flux ( Ф ) through a current carrying with an cross-sectional area ( A ) at a normal angle ( θ ) to the direction of magnetic field ( B ) is given by the following relationship.
Ф = B*A*cos ( θ )
- We need the rate of change of magnetic flux ( ΔФ / Δt ) for the Faraday's law. I.e the induced emf ( E ) is proportional to rate of change in magnetic field ( ΔB / Δt ), rate of change of angle between the coil and magnetic field ( Δθ / Δt ) or rate of change of cross-sectional area of the coil under the influence of magnetic field.
- To determine the exact relationship. We will derive the multi-variable function of flux ( Ф ) with respect to time "t":
Ф ( B , A , θ ) = B*A*cos ( θ )
- The first derivative would be ( Use chain and product rules )
( ΔФ / Δt ) = ΔB / Δt*A*cos ( θ ) + B*ΔA/Δt*cos ( θ ) - B*A*sin ( θ )*Δθ/Δt
- For the given problem the only dependent parameter that is changing is magnetic field ( B ) with respect to time "t". Hence, ( ΔA/Δt = Δθ/Δt = 0 ):
ΔФ / Δt = (ΔB/Δt)*A*cos ( θ )
- Substitute the rate of change of magnetic flux ( ΔФ / Δt ) into the expression for Faraday's Law initially stated:
E = - N*(ΔB/Δt)*A*cos ( θ )
- Plug in the values and evaluate the Area of the square coil:
A = - E / ( N*(ΔB/Δt)*cos ( θ ) )
A = - 0.06 / ( 50*[ (250-700)*10^-6/0.3 ] *cos ( 30° ) )
A = - 0.06 / -0.07216
A = 0.8314 m^2
- The square coil has equal sides ( x ). The area of a square A is given by:
A = x^2
x = √0.8314
x = 0.912 m
- The perimeter length of a single coil in terms of side length "x" is given as:
P = 4x
Whereas for a coil of N turns the total length ( L ) would be:
L = N*P
L = 4Nx
L = 4 * 50 * 0.912
L = 182.4 m ... Answer
An "emergency blow" is a procedure used by military submarines to quickly rise to the surface in case of trouble. It involves using compressed air to pump out ballast water from its tanks.Suppose the submarine SSN Cthulhu has a displacement volume when fully submerged of 32000 m3. It is submerged with neutral buoyancy at a periscope depth of 30m when an emergency arises disabling its propulsion and other critical systems.Neglecting the pumped air’s density (much lower than that of water) and water resistance, what mass of water would this submarine have to pump out suddenly to make it to the surface in 30 seconds?
Answer:
Check the explanation
Explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
A 65-kg skier grips a moving rope that is powered by an engine and is pulled at a constant speed to the top of a 230 hill. The skier is pulled a distance x = 320 m along the incline and it takes 2.0 minutes to reach the top of the hill. If the coefficient of kinetic friction between the snow and skis is µk = 0.10, what horsepower engine is required if 30 such skiers are on the rope at one time? 1 hp = 746 W
Answer:
The required power by the engine is 33.0 hp
Explanation:
Solution
Newton's second law says that, the net force Fnet on an object of mass m will accelerates the object
Where
Fnet = ma
a = acceleration
θ = angle of incline,
m = mass of the 30 skiers,
f = frictional force
N = normal force
mg sinθ, mg cos θ are components of weight skier
F = the force applied by engine
Now,
The skier mass is 65 kg
We calculate the mass of the 30 skier
m = 30 (65kg) = 1950 kg
Calculate the net force acting on the skiers along the x-axis
Fnet, x=ma
Now,
F-mg sin θ - f = 0
F= mg sin θ + f -----(1)
The kinetic frictional force is denoted by
f = μk N ------(2)
μk = The coefficient of the kinetic friction
We now, calculate the net force acting on the skiers along y axis
Fnet, y = ma
N- mg cos θ = 0
so,
N = mg cos θ
This value is substituted in equation (2)
f = μk mg cos θ
we substitute the value for equation (1)
F = mg sin θ + μk mg cos θ
mg = sinθ + μk cos θ)-----(3)
The next step is to calculate the work done by the engine in pulling the skiers, the incline top by applying the equation 3
W = Fx
= mg ( sinθ + μk cos θ)x
x = the displacement
we now substitute 1950 kg for m, 23° for θ, 0.10 for μk and 320m for x
so,
W = mg ( sinθ + μk cos θ)x
= (1950 kg) (9.81 m/s²) (sin 23° + (0.10) cos 23°) (320 m)
= 2.99 * 10 ^6 J
Then,
The time from minute to s is converted
t =(2.0min) ( 60sec/1.0min) = 120 sec
Now we calculate the power needed by the engine to pull the skiers at the incline top
Thus,
P = W/t
we substitute 2.955 * 10 ^6 J for W and 120 s for t
we have,
P = 2.955 * 10 ^ 6 J/ 120 s
= ( 2.4625 * 10 ^ 4 W) (1.0 hp/746 W)
= 33.0 hp
In conclusion the required power by the engine is 33.0 hp
To calculate the horsepower of the engine required for 30 skiers to be pulled up a hill, we need to consider the work done against friction and gravity. By plugging in the given values into the appropriate equations, we can find the required horsepower of the engine.
Explanation:To calculate the horsepower of the engine required for 30 skiers to be pulled up a hill, we need to consider the work done against friction and gravity. First, we find the net force of the skier parallel to the incline by subtracting the force due to friction from the component of the skier's weight parallel to the incline. Then, we calculate the work done against friction and gravity using the formula W = Fd. Finally, we convert the work done to horsepower using the conversion factor 1 hp = 746 W.
The work done against friction and gravity is:
W = F_net * d
The power required is:
P = W / t
And finally, we convert the power to horsepower:
Power (hp) = P / 746
By plugging the given values into these equations and multiplying the final power by 30 (for 30 skiers), we can find the required horsepower of the engine.
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Which method is used to calculate the slope on a distance time graph
The slope of the line is calculated by dividing the change in distance over the change in time.
A 5 kg spinning ring of inner radius 30cm and outer radius 40cm is dropped on a flat disk, where it interlocks and causes the disk to spin. Before the ring was dropped, it was spinning at 60 Hz. If the disk has a mass of 2kg and a radius of 1 meter, how much force needs to be applied to the rim of the disk (at a 90 degree angle) to bring it to a stop in 5 seconds
Consider a rough asphalt roadway with 17 cm curbs and one 3.75 m lane in each direction and a 1.45 m shoulder on each side. The road has a longitudinal slope of 0.75% and is crowned in the center with a transverse slope of 2.25%. The local ordinance requires no ponding in the roadway (only on the shoulders) for a storm with an intensity of 90 mm/hr. A) Determine the maximum distance between curb inlets.
Answer:
Explanation:
Half width - 3.75 m
Rainfall intensity - 90 mm/hr
Longitudinal slope - 0.75%
Cross slope - 2.25%
Allowable limit of gutter flow, Q road = (Design constant x Intensity of rain x Area) / 360
= (0.91×90×(9×L1×10∧-4)/360 = 0.000204 L1
Using the standard design chart, allowable limit of gutter flow =0.018 m3/s
Therefore,0.018 = 0.000204 L1
L1 = 0.018 / 0.000204 = 88.24
Inlet spacing to be adapted is 88m
Which are characteristics of concave mirrors? Check all that apply.
surface curves inward
image can be upside down
image is always virtual
surface curves outward
image can be real
Answer:
1, 2, and 5
Explanation:
Answer:
1, 2 and 5
Explanation:
To practice Problem-Solving Strategy 16.1 Standing waves. An air-filled pipe is found to have successive harmonics at 800 HzHz , 1120 HzHz , and 1440 HzHz . It is unknown whether harmonics below 800 HzHz and above 1440 HzHz exist in the pipe. What is the length of the pipe
Answer:
Length of the pipe = 53.125 cm
Explanation:
given data
harmonic frequency f1 = 800 Hz
harmonic frequency f2 = 1120 Hz
harmonic frequency f3 = 1440 Hz
solution
first we get here fundamental frequency that is express as
2F = f2 - f1 ...............1
put here value
2F = 1120 - 800
F = 160 Hz
and
Wavelength is express as
Wavelength = Speed ÷ Fundamental frequency ................2
here speed of waves in air = 340 m/s
so put here value
Wavelength =340 ÷ 160
Wavelength = 2.125 m
so
Length of the pipe will be
Length of the pipe = 0.25 × wavelength ......................3
put here value
Length of the pipe = 0.25 × 2.125
Length of the pipe = 0.53125 m
Length of the pipe = 53.125 cm
Final answer:
The length of the pipe, which resonates at odd harmonics and has successive frequencies of 800 Hz, 1120 Hz, and 1440 Hz, is calculated to be approximately 32.2 centimeters. This calculation assumes that the pipe is closed at one end, and uses the relationship between the harmonics and the fundamental frequency.
Explanation:
The student is inquiring about determining the length of a pipe based on the frequencies of its successive harmonics. Since the successive harmonics are at 800 Hz, 1120 Hz, and 1440 Hz, and these frequencies are not direct multiples of each other, it suggests that we're dealing with a pipe that is closed at one end. Such pipes produce odd harmonics only. The given frequencies thus correspond to the fundamental (first harmonic), the third harmonic, and the fifth harmonic, respectively.
The frequency of the nth harmonic in a pipe closed at one end is given by:
fn = n(f1), where n is an odd integer and f1 is the fundamental frequency, which in this case is 800 Hz. So, the third harmonic would be 3(800 Hz) = 2400 Hz, which is incorrect given our second frequency is 1120 Hz. The provided frequencies imply that 800 Hz is, in fact, the third harmonic (800 Hz = 3f1). Hence, the fundamental frequency (f1) is 800 Hz / 3 = 266.67 Hz.
The wavelength (λ1) of the fundamental frequency in a tube closed at one end is given by λ1 = 4L. Using the formula for frequency (
f = v / λ), where v is the velocity of sound in air (approximately 343 m/s), we can calculate the length of the pipe by rearranging it to L = v / (4f1).
Therefore, L = 343 m/s / (4 * 266.67 Hz) = 0.322 meters or 32.2 cm.
A young child hold a string attached to a balloon. What is the reaction force to the balloon pulling up on the earth?
Answer:
As the Ballon pulls up, the distance between the Ballon and the center of the earth increases, the gravitational pull reduces and the gravity potential energy increases.
The chart shows data for a moving object.
Which conclusion is best supported by the information in
the chart?
The object has negative displacement
The object has negative acceleration
The object does not have displacement
The object is not accelerating
Answer:the object is not accelerating
Explanation:
There object is not accelerating since there's no increase in velocity
Final answer:
Based on the descriptions of graphical data, we can conclude that the object has negative acceleration because its velocity is decreasing over time while it is moving in the positive direction, or its negative velocity is increasing over time. Also, since the object is moving in the negative direction, it experiences a negative displacement.
Explanation:
The question asks about the motion of an object based on different graphical representations. To determine the nature of this motion, we can analyze the provided diagrams. In this case, we have descriptions of how the velocity changes over time, which allows us to infer acceleration, and acceleration is defined as the change in velocity over time. According to the information, the object experiences a decrease in positive velocity, which indicates a negative acceleration, as acceleration is in the opposite direction to the velocity. Furthermore, it is mentioned that the object has a negative velocity which increases in magnitude, coherently resulting in negative acceleration as well.
Acceleration is a vector quantity, meaning it has both direction and magnitude. Since we are discussing a coordinate system where to the right is considered positive, any acceleration towards the left will be considered negative. The graphs that indicate an object having a constant negative velocity also imply that the object has negative displacement over the time period, because it's moving in the negative direction of the coordinate system.
1. Electromagnetic radiation is more common than you think. Radio and TV stations emit radio waves when they broadcast their programs; microwaves cook your food in a microwave oven; dentists use X rays to check your teeth. Even though they have different names and different applications, these types of radiation are really all the same thing: electromagnetic (EM) waves, that is, energy that travels in the form of oscillating electric and magnetic fields. Which of the following statements correctly describe the various applications listed above?A. All these technologies use radio waves, including low-frequency microwaves. B. All these technologies use radio waves, including high-frequency microwaves. C. All these technologies use a combination of infrared waves and high-frequency microwaves. D. Microwave ovens emit in the same frequency band as some wireless Internet devices. E. The radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies. F. All these technologies emit waves with a wavelength in the range 0.10 to 10.0 m. G. All the technologies emit waves with a wavelength in the range 0.01 to 10.0 km.2. Despite their extensive applications in communication systems, radio waves a not the only form of EM waves present in our atmosphere. Another form of EM radiation plays an even more important role in our life (and the life of our planet) sunlight. The sun emits over a wide range of frequencies; however, the fraction of its radiation that reaches earth's surface is mostly in the visible spectrum. (Note that about 35% of the radiation coming from the sun is absorbed directly by the atmosphere before even reaching the earth's surface). The earth, then, absorbs this radiation and reemits it as infrared waves. Based on this information, which of the following statements is correct? A. The earth absorbs visible light and emits radiation with a shorter wavelength. B. The earth absorbs visible light and emits radiation with a longer wavelength. C. The earth absorbs visible light and emits radiation with a lower frequency. D. The earth absorbs visible light and emits radiation with a higher frequency.
For the first question
Answers:
b.) All these technologies use radio waves, including high-frequency microwaves
d.) Microwave ovens emit in the same frequency band as some wireless Internet devices.
e.) The radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies listed above.
f.) All these technologies emit waves with a wavelength in the range of 0.10 to 10.0 m.
For second question
Answer:
B. The earth absorbs visible light and emits radiation with a longer wavelength
C. The earth absorbs visible light and emits radiation with a lower frequency.
Both options are correct
Explanation:
In the EM spectrum, wavelenght reduces with increasing energy and frequency increases with increasing energy. The order of increasing energy is radio wave, microwave, infrared rays, visible rays, ultraviolet rays, xrays, gamma rays.
If the earth absorbs visible rays of higher energy, and radiates infrared rays of lower energy, then this means that the radiated radiation will have a longer wavenght, and a lower frequency.
1) The statements that correctly describe the various applications given in the question are;
B. All these technologies use radio waves, including high-frequency microwaves
D. Microwave ovens emit in the same frequency band as some wireless Internet devices.
E. The radiation emitted by wireless Internet devices has the shortest wavelength of all the technologies.
F. All these technologies emit waves with a wavelength in the range 0.10 to 10.0 m.
2) The correct statements on the EM spectrum in the question are;
B. The earth absorbs visible light and emits radiation with a longer wavelength.
C. The earth absorbs visible light and emits radiation with a lower frequency.
1) We are told about different waves being used by different technologies such as;
- Radio and TV emitting radio waves
- microwave oven using microwaves to cook food
- Dentists checking teeth with x-rays
All these waves are electromagnetic waves.
Looking at the options, options B, D, E and F are true because;
The given technologies all make use of radio waves as well as high frequency microwaves. Also, from research it is known that the frequency band emitted by microwaves is the same as that of some internet devices since some of the waves emitted by internet devices are the shortest wavelengths.The wavelength of the waves emitted by the given technologies are usually within the range of 0.1m to 10m2) The correct options are Options B and C because;
In the EM radiation spectrum, when the energy increases, the wavelength usually reduces and the frequency usually increases. The order of radio waves according to increase in energy is;
radio waves < infrared radiation < visible rays < ultraviolet rays < xrays < gamma rays.
Now, if we say that the earth absorbs visible rays of higher energy, and radiation of infrared rays with lower energy, then from our definition, we can conclude that radiated waves will have a longer wavelength, and a lower frequency.
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Match the descriptions to the feature,
principal axis
Center of the spherical mirror from which a
curved mirror was cut
center of curvature
Distance from the center of a mirror to the
focal point
Line that runs through the center of
curvature to a mirror
focal point
Point where reflected light converges or
appears to diverge
focal length
Point where the principal axis and mirror
vertex
meet
Answer:
Vertex: Point where the principal axis and mirror meet
Focal point: Point we are reflected light converges or appears to diverge
Focal length: distance from the center of a mirror to the focal point
Principal axis: line that runs to the center of curvature to a mirror
Center of curvature: sensor of spherical mirror from which a curved mirror was cut
Explanation:
Just did the assignment on Edge.
A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex.
What is a spherical mirror?A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex. These are illustrated in.
The most commonly occurring examples of concave mirrors are shaving mirrors and makeup mirrors.
As is well-known, these types of mirrors magnify objects placed close to them. The most commonly occurring examples of convex mirrors are the passenger-side wing mirrors of cars.
These types of mirrors have wider fields of view than equivalent flat mirrors, but objects which appear in them generally look smaller
The answers to the given questions are:
Vertex: Point where the principal axis and mirror meet
Focal point: Point we are reflected light converges or appears to diverge
Focal length: distance from the centre of a mirror to the focal point
Principal axis: line that runs to the centre of curvature of a mirror
Center of curvature: sensor of spherical mirror from which a curved mirror was cut
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(Solidification) You are performing a double slit experiment very similar to the one from DLby shining a laser on two narrow slits spaced 7.5 × 10-5meters apart. However, by placing a piece of crystal in one of the slits, you are able to make it so that the rays of light that travel through the two slits are πout of phasewith each other (that is to say,Δφ!=휋).If you observe that on a screen placed 4meters from the two slits that the distance between the bright spot closest to the center of the interference pattern and the center of the pattern is 1.5 cm, what is the wavelength of the laser? (Just as in DL, you may use the small angle approximation sinθ ≈ θ ≈ tanθ.)
Answer:
The wavelength of the laser, λ = 5.625 * 10⁻⁷ m
Explanation:
Separation of the narrow slits, d = 7.5 * 10⁻⁵ m
The distance between the screen and the two slits, d = 4m
The distance between the bright spot and the center of the pattern, Y = 1.5 cm
Y = 1.5 * 10⁻² m
To calculate the wavelength, λ, of the laser we will use the relationship:
[tex]Y = \frac{\lambda L}{2d} \\1.5 * 10^{-2} = \frac{\lambda * 4}{2*7.5*10^{-5} }\\\lambda = \frac{1.5 * 10^{-2} * 15 * 10^{-5} }{4}[/tex]
λ = 5.625 * 10⁻⁷ m
A visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 6.40 s. What is the height of the tower
Answer:
l = 10.16 m
Explanation:
In this case, we have the period of oscillation of the pendulum is 6.4 s. It is required to find the height of the tower.
We know that the pendulum executes SHM. Let l is the height of the tower. The time period of simple pendulum is given by :
[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]
g is acceleration due to gravity
We need to rearrange the above equation such that,
[tex]l=\dfrac{T^2g}{4\pi ^2}\\\\l=\dfrac{(6.4)^2\times 9.8}{4\pi ^2}\\\\l=10.16\ m[/tex]
So, the height of the tower is 10.16 m.
What is the gravitational potential energy of a 2.5kg object that is 300m above the surface of the earth? g=10m/s
Answer:
7350 J
Explanation:
Gravitational Potential Energy: This is defined as the energy possessed by a body due to it's position in the gravitational field. The S.I unit is Joules(J).
Applying,
E.p = mgh..................... Equation 1
Where E.p = Gravitational potential Energy, m = mass of the object, h = height of the object above the surface of the earth, g = acceleration due to gravity.
Given: m = 2.5 kg, h = 300 m
Constant: g = 9.8 m/s²
Substitute these values into equation 1
E.p = 2.5(300)(9.8)
E.p = 7350 J.