1) The final angular speed is 4.85 rad/s
2) The change in kinetic energy is 1746 J
Explanation:
1)
The problem can be solved by applying the law of conservation of angular momentum: in fact, the total angular momentum of the system must be conserved,
[tex]L_1 = L_2[/tex]
The initial angular momentum is given by:
[tex]L_1 = (I_d + I_m) \omega[/tex]
where
[tex]I_d = \frac{1}{2}MR^2[/tex] is the moment of inertia of the cylinder, with
M = 63 kg is its mass
R = 2.5 m is the radius
[tex]I_m = mr^2[/tex] is the moment of inertia of the man, with
m = 97 kg is the mass of the man
r = 2.5 m is the distance of the man fro mthe axis of rotation
[tex]\omega=0.19 rev/s \cdot 2 \pi = 1.19 rad/s[/tex] is the angular speed
The final angular momentum is given by
[tex]L_2 = I_d \omega'[/tex]
where [tex]\omega'[/tex] is the final angular speed, and where the angular momentum of the man is zero because he is at the axis of rotation.
Combining the two equations, we get:
[tex](\frac{1}{2}MR^2 + mr^2) \omega = \frac{1}{2}MR^2 \omega'\\\omega'=(1+2\frac{m}{M})\omega=(1+2\frac{97}{63})(1.19)=4.85 rad/s[/tex]
2)
The initial kinetic energy (which is rotational kinetic energy) of the system is given by
[tex]K_1 = \frac{1}{2}(I_d + I_m) \omega^2[/tex]
And substituting,
[tex]K_1 = \frac{1}{2}(\frac{1}{2}MR^2+mr^2)\omega^2=\frac{1}{2}(\frac{1}{2}(63)(2.5)^2+(97)(2.5)^2)(1.19)^2=568.6 J[/tex]
The final kinetic energy is given by
[tex]K_2 = \frac{1}{2}I_d \omega'^2[/tex]
And substituting,
[tex]K_2 = \frac{1}{2}(\frac{1}{2}MR^2)\omega'^2=\frac{1}{2}(\frac{1}{2}(63)(2.5)^2)(4.85)^2=2315 J[/tex]
So, the change in kinetic energy is
[tex]\Delta K = 2315 J - 568.6 J = 1746 J[/tex]
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The angular speed of the merry-go-round changes when the man moves closer to the center due to conservation of angular momentum, resulting in a new angular speed. The change in kinetic energy is calculated by comparing kinetic energy before and after the man's movement.
Explanation:Understanding Angular Speed Change in a Merry-Go-RoundWhen a 97 kg man on a merry-go-round moves closer to the center, the angular speed of the system changes due to the conservation of angular momentum. The merry-go-round is described as a solid cylinder, and the movement of the man towards the center means his radius of rotation decreases, which leads to an increase in angular velocity. Initially, the man is 2.5 m away from the axis, standing on a merry-go-round that rotates at 0.19 rev/s. Upon reaching the center (0 m from the center), the entire system's angular momentum is conserved but concentrated within a smaller radius.
To calculate the new angular speed, we'll use the concept of moment of inertia (I) and the relation I1 * ω₁ = I2 * ω₂, where ω denotes angular speed. Since the man is no longer contributing to the rotational inertia when he moves to the center, only the merry-go-round's moment of inertia comes into play. Additionally, we'll need to convert the angular speed from rev/s to rad/s using the conversion factor: 1 rev = 2π rad.
The second part concerns the change in kinetic energy (KE) due to the man's movement. The rotational KE of a system is given by (1/2) * I * ω². By finding the KE before and after the man moves to the center, we can determine the change in kinetic energy.
The weight of the mass added to the hanger is equal to the extra force on the gas, but what area should we use to calculate the added pressure from this mass?
With some of the experimental details out of the way, let's think a bit about what we expect to see in our data if the ideal gas law is a good model for our gas. We would like to verify the ideal gas law PV = nRT
Answer: according to the Avagadro's law, volume is directly propotional to no of moles: VXn
according to the Charles law, volume is directly propotional to temperatue: VXT
according to the Boyle's law, volume is inversely propotional to P: VX1/P
when we combine them we get:
VXnT1/P
V=knT/P
k= R(universal gas constant)
V=RnT/P
PV=nRT
If a scuba diver fills his lungs to full capacity of 5.7 L when 8.0 m below the surface, to what volume would his lungs expand if he quickly rose to the surface? Assume he dives in the sea, thus the water is salt. Express your answer using two significant figures
To calculate the pressure in the body we will use the definition of the hydrostatic pressure for which the pressure of a body at a certain distance submerged in a liquid is defined. After calculating this relationship we will apply the equations of the relationship between the volume and the pressure to calculate the volume in state 2,
[tex]P = P_{atm} + \rho gh[/tex]
Here,
[tex]\rho[/tex]= Density of the Fluid (Water)
g = Acceleration due to gravity
h = Height
[tex]P = P_{atm} + 10^3*9.8*8[/tex]
[tex]P = 1.01*10^{5} +10^3*9.8*8[/tex]
[tex]P = 179400Pa[/tex]
Applying the equations of relationship between volume and pressure we have
[tex]P_1V_1 = P_2 V_2[/tex]
[tex]179400*5.7 = 101000*V_2[/tex]
[tex]V_2 = 10.12L[/tex]
Therefore the volume that would his lungs expand if he quickly rose to the surface is 10.12L
If the length of the air column in the test tube is 14.0 cm, what is the frequency of this standing wave?
Answer:
f = 614.28 Hz
Explanation:
Given that, the length of the air column in the test tube is 14.0 cm. It can be assumed that the speed of sound in air is 344 m/s. The test tube is a kind of tube which has a closed end. The frequency in of standing wave in a closed end tube is given by :
[tex]f=\dfrac{nv}{4l}[/tex]
[tex]f=\dfrac{1\times 344}{4\times 0.14}[/tex]
f = 614.28 Hz
So, the frequency of the this standing wave is 614.28 Hz. Hence, this is the required solution.
3. An engine’s fuel is heated to 2,000 K and the surrounding air is 300 K. Calculate the ideal efficiency of the engine. Hint: The efficiency (e) of a Carnot engine is defined as the ratio of the work (W) done by the engine to the input heat QH : e=W/QH. W=QH – QC, where Qc is the output heat. That is, e=1-Qc/QH =1-Tc/TH, where Tc for a temperature of the cold reservoir and TH for a temperature of the hot reservoir. The unit of temperature must be in Kelvin.
Answer: E = 0.85
Therefore the efficiency is: E = 0.85 or 85%
Explanation:
The efficiency (e) of a Carnot engine is defined as the ratio of the work (W) done by the engine to the input heat QH
E = W/QH.
W=QH – QC,
Where Qc is the output heat.
That is,
E=1 - Qc/QH
E =1 - Tc/TH
where Tc for a temperature of the cold reservoir and TH for a temperature of the hot reservoir.
Note: The unit of temperature must be in Kelvin.
Tc = 300K
TH = 2000K
Substituting the values of E, we have;
E = 1 - 300K/2000K
E = 1 - 0.15
E = 0.85
Therefore the efficiency is: E = 0.85 or 85%
To calculate the ideal efficiency of an engine with specified temperatures, convert to Kelvin and use the Carnot efficiency formula.
Explanation:The Carnot Engine Efficiency Calculation:
First, convert the temperatures to Kelvin. TH = 2000 K, TC = 300 K.Calculate the efficiency using the formula: e = 1 - TC/TH = 1 - 300/2000 = 0.85.Learn more about Carnot Engine Efficiency Calculation here:https://brainly.com/question/36599883
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A rubber ball with a mass of 0.30 kg is dropped onto a steel plate. The ball's velocity just before impact is 4.5 m/s and just after impact is 4.2 m/s and just after impact is 4.2 m/s. What is the change in the ball's momentum?
Answer:
Change in momentum will be -2.61 kgm/sec
Explanation:
We have given mass of the rubber ball m = 0.30 kg
Velocity of the ball before the impact [tex]v_1=4.5m/sec[/tex]
Velocity of ball after impact [tex]v_2=-4.2m/sec[/tex] ( negative sign is due to opposite direction of motion )
Change in momentum is given by [tex]m(v_2-v_1)=0.3\times (-4.2-4.5)=0.3\times =0.3\times -8.7=-2.61kgm/sec[/tex] ( negative sign shows the direction of change in momentum )
Answer:
-0.09 kg m/s
Explanation:
You would like to know whether silicon will float in mercury and you know that can determine this based on their densities. Unfortunately, you have the density of mercury in units of kg.m^3 and the density of silicon in other units of 2.33 g.cm^3. You decide to convert the density of silicon into units of kg.m^3 to perform the comparison. By which combination of conversion factors will you multiply 2.33 g.cm^3 to perform the unit conversion?
Answer:
The conversion factor used here will be 1000 (kg/m^3)/(g/cm^3).
Which is a combination of two conversion factors:
1 kg = 1000 g
1 x 10^6 cm^3 = 1 m^3
Explanation:
We will use unitary method to convert g/cm^3 into kg/m^3. This is shown below:
Since, 1 kilogram is equivalent to 1000 gram and 1 meter is equivalent to 100 centimeter. Therefore:
1 g/cm^3 = (1 g/ cm^3)(1 kg/ 1000 g)(100 cm / 1 m)^3
1 g/cm^3 = 1000 kg/m^3
Hence, the conversion factor that will be multiplied is found to be 1000.
Using this in our case, we get:
Density of silicon = (2.33)(1000) kg/m^3
Density of Silicon = 2330 kg/m^3
Answer:
1000
Explanation:
Conversion from 'g' to 'kg': divide by 1000g/kg
Conversion from 'cm^3' to 'm^3': divide by 1000000cm^3/m^3
2.33g/cm^3 = [tex]\frac{2.33*1000000}{100}[/tex]
= 2330 kg/m^3
we simply multiply by 1000 to get the units converted to kg/m^3
How far is the center of mass of the Earth-Moon system from thecenter of the Earth? (Appendix C gives the masses of the Earth andthe Moon and the distance between the two.)
Answer:
[tex]\bar x=4679496.086\ m=4679.496086\ km[/tex] from the center of the earth.
Explanation:
We have a system of Earth & Moon:
we have the mass of earth, [tex]m_e=5.972\times 10^{24}\ kg[/tex]mass of the moon, [tex]m_m=7.348\times 10^{22}\ kg[/tex]distance between the center of the earth and the moon [tex]d=385000\ km[/tex]Now we assume the origin of the system to be at the center of the earth.
Now for the center of mass of this system:
[tex]\bar x=\frac{m_e.x_e+m_m.x_m}{m_e+m_m}[/tex]
here:
[tex]x_e\ \&\ x_m[/tex] are the distance of the centers (center of masses) of the Earth and the Moon from the origin of the system.
[tex]x_e=0[/tex] ∵ since we have taken the point as the origin of the system.
[tex]x_m=d[/tex]
now putting the values in the above equation:
[tex]\bar x=\frac{(5.972\times 10^{24}\times 0)+(7.348\times 10^{22}\times 385000\times 1000)}{5.972\times 10^{24}+7.348\times 10^{22}}[/tex]
[tex]\bar x=4679496.086\ m=4679.496086\ km[/tex] from the center of the earth.
momentum A proton interacts electrically with a neutral HCl molecule located at the origin. At a certain time t, the proton’s position is h1.6 × 10−9 , 0, 0i m and the proton’s velocity is h3200, 800, 0i m/s. The force exerted on the proton by the HCl molecule is h−1.12 × 10−11 , 0, 0i N. At a time t + (2 × 10−14 s), what is the approximate velocity of the proton? answer
Answer:
[tex]<3068.2352, 800, 0>\ m/s[/tex]
Explanation:
F = Force = [tex]<-1.12\times 10^{-11}, 0, 0>[/tex]
m = Mass of proton = [tex]1.7\times 10^{-27\ kg[/tex]
t = Time taken = [tex]2\times 10^{-14}\ s[/tex]
Acceleration is given by
[tex]a=\dfrac{F}{m}\\\Rightarrow a=\dfrac{<-1.12\times 10^{-11}, 0, 0>}{1.7\times 10^{-27}}\\\Rightarrow a=<-6.58824\times 10^{15}, 0, 0>\ m/s^2[/tex]
[tex]v=u+at\\\Rightarrow v=<3200, 800, 0>+<-6.58824\times 10^{15}, 0, 0>\times 2\times 10^{-14}\\\Rightarrow v=<3200, 800, 0>+<-6.58824\times 10^{15}, 0, 0>\times 2\times 10^{-14}\\\Rightarrow v=<3200, 800, 0>+<-131.7648, 0, 0>\\\Rightarrow v=<3068.2352, 800, 0>\ m/s[/tex]
The velocity of the proton is [tex]<3068.2352, 800, 0>\ m/s[/tex]
the density of gold is 19.3 g/cm3. suppose a certain gold wedding ring deplaced 0.55mL of liquid when dropped in a glass of sparkling cider. how much did this wedding ring cost
The question pertains to physics, specifically the concept of density. The mass of the gold in the ring is computed to be 10.615 g based on the provided volume displacement and density of gold. To determine the cost of the ring, additional information such as the current market price for gold and labor costs would be necessary.
The subject matter of this question relates to the physical property of density and its application in determining the mass of gold in a wedding ring. Given that the density of gold is 19.3 g/cm³ and the ring displaced 0.55 mL of liquid, one can calculate the mass of the ring using the rule that 1 mL equals 1 cm³. Hence, if the ring displaces 0.55 mL of the liquid, it means the volume of the ring is 0.55 cm³.
To find mass, we use Density = Mass/Volume, so Mass = Density * Volume. Therefore, the mass of the ring will be 19.3 g/cm³ * 0.55 cm³ = 10.615 g.
This calculation gives us the mass of the gold in the ring.
However, to determine the cost of the ring, we need more information such as the market price of gold per gram and the cost of workmanship and other potential elements in the ring, which are not provided in the question.
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During a tennis match, a player serves the ball at a speed s, with the center of the ball leaving the racquet at angle θ below the horizontal at a height y0. The net is a distance d away and has a height h. When the ball is directly over the net, what is the distance between them?
Answer: Maximum distance
= {s²/g} * sine(2*theta)unit
Explanation: This is a projectile motion problem. The horizontal distance between the tennis player and where the tennis reaches over the net is given by the horizontal Range.
Range = {s² * sine2*theta}/g
(s)is the initial speed of projection
Theta is the angle of projection
g is acceleration due to gravity 10m/s².
What region of the spectrum best corresponds to light with a wavelength equal to:_____ a. The diameter of a hydrogen atomb. The size of a virus.c. Your height?
We will make the comparison between each of the sizes against the known wavelengths.
In the case of the hydrogen atom, we know that this is equivalent to [tex]10^{-10}[/tex] m on average, which corresponds to the wavelength corresponding to X-rays.
In the case of the Virus we know that it is oscillating in a size of 30nm to 200 nm, so the size of the virus is equivalent to the range of the wavelength of an ultraviolet ray.
In the case of height, it fluctuates in a person around [tex]10 ^ 0[/tex] to [tex]10 ^ 1[/tex] m, which falls to the wavelength of a radio wave.
The region of the spectrum that best corresponds to light with a wavelength equal to the diameter of a hydrogen atom is the X-ray region. The visible light spectrum corresponds to objects around the same size as the wavelength. The size of a virus is much smaller than the wavelength of visible light
Explanation:The region of the spectrum that best corresponds to light with a wavelength equal to the diameter of a hydrogen atom is the X-ray region of the electromagnetic spectrum.
The wavelength of visible light corresponds to the size of objects that are around the same size as the wavelength. For example, if you want to use light to see a human, you would need to use a wavelength at or below 1 meter, since humans are about 1 meter in size.
The size of a virus is much smaller than the wavelength of visible light, so the wavelength is very small compared to the object's size.
In the Boyle’s law experiment, what was used to increase the pressure on the air (gas)?
Answer:
Volume.
Explanation:
Boyle’s law experiment :
This is also known as Mariotte's law or in the other words it is also known as Boyle–Mariotte law.
This law tell us about the variation of gas pressure when the volume of the gas changes at the constant temperature.According to this law the abslute pressure is inversely proportional to the volume .
We can say that
[tex]P\alpha \dfrac{1}{V}[/tex]
Where P=Pressure
V=Volume
PV = K
K=Constant
When volume decrease then the pressure of the gas will increase.
That is why the answer is "Volume".
A river barge, whose cross section is approximately rectangular, carries a load of grain. The barge is 28 ft wide and 93 ft long. When unloaded its draft (depth of submergence) is 6 ft, and with the load of grain the draft is 9 ft. Determine: (a) the unloaded weight of the barge, and (b) the weight of the grain.
Answer:
a) [tex] W_B = F_B = 62.4 \frac{lb}{ft^3} (6ft*28ft*93ft)= 974937.6 lb[/tex]
b) [tex] W_g= 62.4 \frac{lb}{ft^3} * (9ft*28ft*93ft) -974937.6 lb =487468.8 lb[/tex]
Explanation:
Part a
For this case we have the situation illustrated on Figure 1. We will have two forces involved in equilibrium the weight [tex] W_B[/tex] and the Bouyance force[tex] F_B[/tex], and since the system is on equilibrium we have:
[tex] \sum F_{vertical}=0[/tex]
So then we have:
[tex] W_B = F_B = \gamma_{w} V_s[/tex]
Where [tex] V_s[/tex] represent the submerged volume. [tex]\gamma_w[/tex] represent the specific weight for the fluid. So we can replace and we have:
[tex] W_B = F_B = 62.4 \frac{lb}{ft^3} (6ft*28ft*93ft)= 974937.6 lb[/tex]
Part b
As we can see on figure 2 attached we have the illustration for this case. We add the weight for the grain and now the depth is 9ft.
W can do the balance of forces in the vertical and we got again:
[tex] W_B +W_g = F_B[/tex]
Where [tex] W_g[/tex] represent the weight for the grain.
And if we solve for [tex] W_g[/tex] we got:
[tex] W_g = F_B -W_B[/tex]
[tex] W_g =\gamma_w V_S -W_B[/tex]
Where [tex] \gamma_w[/tex] represent the specific weight of rthe water and [tex] V_s[/tex] the submerged volume. If we replace we got:
[tex] W_g= 62.4 \frac{lb}{ft^3} * (9ft*28ft*93ft) -974937.6 lb =487468.8 lb[/tex]
The weight of the unloaded barge is 975,769.6 lbs, and the weight of the grain is 486,572.8 lbs. These calculations were made based on Archimedes' principle, which states that the buoyant force (the weight of water displaced) is equal to the weight of the object.
Explanation:This question is about calculating the weight of a river barge and its load based on the principles of fluid mechanics. Here, we are examining the fact that the weight of the water displaced by the barge equals the weight of the barge according to Archimedes' principle.
Firstly, we calculate the unloaded weight of the barge. The volume of water displaced by the barge when it is empty is the volume of a rectangular prism with dimensions 28ft x 93ft x 6ft, which gives us 15,624 cubic feet. Given that the density of water is 62.4 lbs/ft³, the weight of this water, which is equal to the weight of the empty barge, would be (Volume x Density) = 15,624ft³ x 62.4 lbs/ft³ = 975,769.6 lbs.
Secondly, let's calculate the weight of the grain. The volume of water displaced when the barge is loaded is the volume of a rectangular prism with dimensions 28ft x 93ft x 9ft, which equals 23,436 cubic feet. The weight of this water, which is equal to the weight of the loaded barge, is (Volume x Density) = 23,436ft³ x 62.4 lbs/ft³ = 1,462,342.4 lbs. Hence, the weight of the grain is the weight of the loaded barge minus the weight of the barge itself = 1,462,342.4 lbs - 975,769.6 lbs = 486,572.8 lbs.
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A particle has a charge of -4.25 nC.
Part A
Find the magnitude of the electric field due to this particle at a point 0.250 m directly above it.
Part B
Find the direction of the field
up, away from the particle
down, toward the particle
Part C
At what distance from this particle does its electric field have magnitude of 13.0 N/C?
Answer:
Explanation:
q = - 4.25 nC = - 4.5 x 10^-9 C
(A) d = 0.250 m
The formula for the electric field is given by
[tex]E = \frac{1}{4\pi \epsilon _{0}}\frac{q}{d^{2}}[/tex]
By substituting the values
[tex]E = \frac{9\times 10^{9}\times 4.5\times10^{-9}}{0.25\times 0.25}[/tex]
E = 648 N/C
(B) As the charge is negative in nature so the direction of electric field is towards the charge and downwards.
(a) The magnitude of the electric field is 612 N/C.
(b) The direction of the electric field will be up, away from the particle.
(c) The distance from the particle is 1.71 m.
Magnitude of the electric fieldThe magnitude of the electric field is calculated as follows;
E = (kq)/r²
where;
k is Coulomb's constant
q is the charge
r is distance
E = ( 9 x 10⁹ x 4.25 x 10⁻⁹)/(0.25 x 0.25)
E = 612 N/C
Direction of the fieldThe direction of the electric field is always opposite to the direction of the negative charge.
Thus, the direction of the electric field will be up, away from the particle.
Distance from the particleThe distance from the particle is determined using the following formula;
E = (kq)/r²
r² = kq/E
r² = (9 x 10⁹ x 4.25 x 10⁻⁹) / 13
r² = 2.94
r = √2.94
r = 1.71 m
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Perform the following unit conversions using units of length, mass, and time only to convert. Show your work, do not just use Google.
(a) 1 L to in.3
(b) 0.135 kW to ft.·lbf./s
(c) 304 kPa to psi
(d) 122 ft.3 to m3
(e) 100 hp to kW
(f) 1000 lbm. to kg
Answer:
[tex]\mathbf{1\ L=61.02384\ in^3}[/tex]
[tex]\mathbf{0.135\ kW=99.5709185406\ ft-lb/s}[/tex]
[tex]\mathbf{304\ kPa=44.091435811\ psi}[/tex]
[tex]\mathbf{122\ ft^3=3.45465495258\ m^3}[/tex]
[tex]\mathbf{100\ hp=74.6\ kW}[/tex]
[tex]\mathbf{1000\ lbm=453.592\ kg}[/tex]
Explanation:
[tex]1\ L=10^{-3}\ m^3[/tex]
[tex]1\ m=39.3701\ in[/tex]
[tex]10^{-3}\ m^3=10^{-3}\times 39.3701^3=61.02384\ in^3[/tex]
[tex]\mathbf{1\ L=61.02384\ in^3}[/tex]
[tex]0.135\ kW=135\ W[/tex]
[tex]135\ W=135\ Nm/s[/tex]
[tex]1\ N=0.224809\ lbf[/tex]
[tex]1\ m=3.28084\ ft[/tex]
[tex]135\times 0.224809\times 3.28084=99.5709185406\ ft-lb/s[/tex]
[tex]\mathbf{0.135\ kW=99.5709185406\ ft-lb/s}[/tex]
[tex]304\ kPa=304000\ N/m^2[/tex]
[tex]1\ m=39.3701\ in[/tex]
[tex]304000\ N/m^2=304000\times 0.224809\times \dfrac{1}{39.3701^2}=44.091435811\ psi[/tex]
[tex]\mathbf{304\ kPa=44.091435811\ psi}[/tex]
[tex]122\ ft^3=\dfrac{122}{3.28084^3}=3.45465495258\ m^3[/tex]
[tex]\mathbf{122\ ft^3=3.45465495258\ m^3}[/tex]
[tex]1\ hp=746\ W[/tex]
[tex]100\ hp=100\times 746\ W=74.6\ kW[/tex]
[tex]\mathbf{100\ hp=74.6\ kW}[/tex]
[tex]1\ lbm=0.224809\ kg[/tex]
[tex]1000\ lbm=1000\times 0.453592=453.592\ kg[/tex]
[tex]\mathbf{1000\ lbm=453.592\ kg}[/tex]
For each of the cases listed below, decide whether or not the motion described is an example of acceleration: (T/F)
1) a roller coaster as it starts to roll down the track
2) a ball tossed straight up, at the peak of its trajectory
3) a planet tracing out a circular orbit at a constant speed
4) a block sliding down a straight ramp at a constant speed
5) an airplane skidding to a stop on a runway
6) a dump truck carrying a load straight forward at a constant speed
Answer:
1. True
2. True
3. False
4. False
5. True
6. False
Explanation:
Acceleration: It refers to the change in velocity/speed of an object with respect to time. When the speed increases with time we call it acceleration and when its decreases it is called as deceleration. Let us analyze each instance individually:
1. When roller coaster starts to roll down the track its speed will increase with time. That means it is accelerating.
2. When the ball reaches at the peak of its trajectory, it comes to a stop for a fraction of a second that means it decelerates.
3. Since the velocity remains constant there is no acceleration.
4. Since the speed is no changing with time, there is no acceleration.
5. Since the moving plane comes to a stop, it is a case of deceleration.
6. Since the truck is moving at a constant speed so the acceleration is zero.
A roller coaster as it starts to roll down a track and an airplane skidding to a stop are examples of acceleration, while a ball tossed straight up, a planet tracing a circular orbit, a block sliding down a ramp, and a dump truck carrying a load at a constant speed are not examples of acceleration.
Explanation:1) True. When a roller coaster starts to roll down the track, it experiences a change in velocity, which means it is accelerating.
2) False. At the peak of its trajectory, a ball tossed straight up has zero velocity and is momentarily at rest, so it is not accelerating.
3) False. A planet tracing out a circular orbit at a constant speed is not experiencing a change in velocity, so it is not accelerating.
4) False. The block sliding down a ramp at a constant speed is not experiencing a change in velocity, so it is not accelerating.
5) True. An airplane skidding to a stop on a runway experiences a change in velocity, so it is accelerating.
6) False. A dump truck carrying a load straight forward at a constant speed is not experiencing a change in velocity, so it is not accelerating.
A 11.8-m-long steel [E = 206 GPa] pipe column has an outside diameter of 202 mm and a wall thickness of 5 mm. The column is supported only at its ends and it may buckle in any direction. Calculate the critical load Pcr for the following end conditions:
Answer:
A
Explanation:
i took the test pimp
A wheel accelerates from rest to 59 rad/s^2 at a uniform rate of 58 rad/s^2. Through what angle (in radians) did the wheel turn while accelerating?
A) 24 rad
B) 38 rad
C) 30 rad
D) 60 rad
To solve this problem we will apply the physical equations of the angular kinematic movement, for which it defines the square of the final angular velocity as the sum between the square of the initial angular velocity and the product between 2 times the angular acceleration and angular displacement. We will clear said angular displacement to find the correct response
Using,
[tex]\omega^2 = \omega_0^2 +2\alpha \theta[/tex]
Here,
[tex]\omega[/tex] = Final angular velocity
[tex]\omega_0[/tex] = Initial angular velocity
[tex]\alpha =[/tex] Angular acceleration
[tex]\theta =[/tex] Angular displacement
Replacing,
[tex]59^2 = 0+2*58\theta[/tex]
[tex]\theta = 30rad[/tex]
Therefore the correct answer is C.
The angle at which the wheel turns while accelerating is 30 radians and this can be determined by using the kinematics equation.
Given :
A wheel accelerates from rest to 59 rad/[tex]\rm s^2[/tex] at a uniform rate of 58 rad/[tex]\rm s^2[/tex].
The equation of kinematics is used in order to determine the angle at which the wheel turn while accelerating.
[tex]\omega^2 = \omega^2_0+2\alpha \theta[/tex]
where [tex]\omega[/tex] is the final angular velocity, [tex]\omega_0[/tex] is the initial angular velocity, [tex]\alpha[/tex] is the angular acceleration, and [tex]\theta[/tex] is the angular displacement.
Now, substitute the values of the known terms in the above formula.
[tex]59^2 =0+2\times 58 \times \theta[/tex]
Simplify the above expression.
[tex]\rm \theta = 30\; rad[/tex]
Therefore, the correct option is C).
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The blood flow rate through the aorta is measured to be 104.1 cm^3/s, and an adult is measured to have 4.93 L of blood. How long does it take for all of your blood to pass through the aorta?
If the adult's aorta has a diamter of 1.85 cm, what is the speed of blood as it flows through the aorta?
Answer:
a)time t = 47.4s
b)speed v = 38.7cm/s
Explanation:
Given:
Total volume of blood = 4.93L × 1000cm^3/L = 4930cm^3
Volumetric rate of flow = 104.1cm^3/s
a) Time taken for all the blood to pass through the aorta is:
Time t = total volume/ volumetric rate
t = 4930/104.1
t = 47.4s
b) Given that the diameter of the aorta is 1.85cm.
V = Av
Where V = Volumetric rate
A = area of aorta
v = speed of blood
v = V/A ...1
Area of a circular aorta = πr^2 = (πd^2)/4
d = 1.85cm
A = (π×1.85^2)/4
A = 2.69cm^2
From equation 1.
v = V/A = 104.1/2.69
v = 38.7 cm/s
Describe the difference between technology based effluent standards and water quality based effluent standards under the Clean Water Act. Also, indicate which of these two different standards is likely to be controlling on a small stream designated as a cold water fishery and why.
Explanation:
Technology-based:
1.As the name implies technology, no technology will be clarified about it. It only depends on the variables, which describes them.
2. That is based on a single facility's findings.
3. It takes into account the contaminants type and volume, and their equations to monitor them.
4. This is reserved for city or urban wastewater treatment plants only.
5. It takes into account the pH, need for oxygen and the suspended solids.
Water quality based on:
1.This is enforced if there is a need to apply stricter limits to pollutants that are not pleased with the limits of technology.
2. All basing on water quality was risk-based.
3. They placed some less importance on the technologies which is used in the technology based limit.
Water quality dependent restrictions are used as cool water fishery for streams.
The act on clean water will also include bodies of water belonging to wildlife, agriculture and others. The law also included that the physical chemical and biological variables of all the state water bodies must be controlled by these water quality based limits.
What is the ratio of the intensities and amplitudes of an earthquake P wave passing through the Earth and detected at two points 27 km and 13 km from the source?
(a) I 27 / 13 =__________
(b) A 27 / 13 =_____________-
For both cases we will use the proportional values of the distance referring to the amplitude and intensity. Theoretically we know that the intensity is inversely proportional to the square of the distance, while the amplitude is inversely proportional to the distance, therefore,
PART A ) Intensity is inversely proportional to the square of the distance
[tex]Intensity \propto \frac{1}{distance^2}[/tex]
Therefore the intensity of the two values would be
[tex]\frac{I_{27}}{I_{13}} = \frac{(13km)^2}{(27km)^2}[/tex]
[tex]\mathbf{\therefore \frac{I_{27}}{I_{13}} = 0.232 }[/tex]
PART B) Amplitude is inversely proportional to the distance
[tex]Amplitude \propto \frac{1}{distance}[/tex]
[tex]\frac{A_{27}}{A_{13}}= \frac{(13km)}{(27km)}[/tex]
[tex]\mathbf{\therefore\frac{A_{27}}{A_{13}}= 0.4815}[/tex]
The intensity ratio of an earthquake P wave passing through the Earth and detected at two points is equal to the square of the amplitude ratio.
Explanation:The ratio of the intensities of an earthquake P wave passing through the Earth and detected at two points is equal to the square of the ratio of their amplitudes.
Let's assume the amplitudes of the earthquake P wave at the two points are given by A27 and A13.
The intensity of a wave is given by the square of its amplitude. Therefore, the ratio of the intensities I27/I13 is equal to the square of the ratio of the amplitudes A27/A13.
So, the answer is:
(a) I27/I13 = (A27/A13)2
(b) A27/A13
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Verify that for values of n less than 8, the system goes to a stable equilibrium, but as n passes 8, the equilibrium point becomes unstable, and a stable oscillation is created.
Answer:
Biological system is one of the major causes of oscillation due to sensitive negative feedback loops. For instance, imagine a father teaching his son how to drive, the teen is trying to keep the car in the centre lane and his father tell him to go right or go left as the case may be. This is a example of a negative feedback loop of a biological system. If the father's sensitivity to the car's position on the road is reasonable, the car will travel in a fairly straight line down the centre of the road. On the other hand, what happens if the father raise his voice at the son "go right" or when the car drifts a bit to the left? The startled the son will over correct, taking the car too far to the right. The father will then starts yelling "go left" then the boy will over correct again and the car will definitely oscillate back and forth. A scenario that indicates the behavior of a car driver under a very steep feedback control mechanism. Since the driver over corrects in each direction. Therefore causes oscillations.
Explanation:
In physics, a system's equilibrium point is considered stable if the system returns to that point after being slightly disturbed. For an n value less than 8, the system remains in stable equilibrium; once n exceeds 8, stable oscillations indicate an unstable equilibrium. This concept can be visualized by the marble in a bowl analogy, where the bowl's orientation determines the stability of the marble's equilibrium.
Explanation:The stability of an equilibrium point is determined by the response of a system to a disturbance. If an object at a stable equilibrium point is slightly disturbed, it will oscillate around that point. The stable equilibrium point is characterized by forces that are directed toward it on either side. On the contrary, an unstable equilibrium point will not allow the object to return to its initial position after a slight disturbance, since the forces are directed away from that point. For values of n less than 8, the system finds a stable equilibrium. However, when n surpasses 8, the system exhibits unstable equilibrium, leading to stable oscillations.
As an example, consider a marble in a bowl. When the bowl is right-side up, the marble represents a stable equilibrium; when disturbed, it returns to the center. If the bowl were inverted, the marble on top would be at an unstable equilibrium point; any disturbance would cause it to roll off, as the forces on either side would be directed outwards. Extending this concept to potential energy, n in a potential energy function acts as an adjustable parameter. For n=<8, the system remains in stable equilibrium, as with NaCl, which has an n value close to 8. Beyond this value, the equilibrium becomes unstable, giving rise to oscillatory behavior.
Stability also depends on the nature of damping in the system. An overdamped system moves slowly towards equilibrium without oscillations, an underdamped system quickly returns but oscillates, and a critically damped system reaches equilibrium as quickly as possible without any oscillations.
Radiation from the Sun The intensity of the radiation from the Sun measured on Earth is 1360 W/m2 and frequency is f = 60 MHz. The distance between the Earth and the Sun is 1.5 x 1011 m.a) Assuming it radiates uniformly in all directions what is the total power output of the Sun?b) If the frequency increases by 1 MHz what would be the relative (percentage) change in the power output? c) For frequency in b) what is the intensity of the radiation from the Sun measured on Mars? Note that Mars is 60% farther from the Sun than the Earth is.
a) Total power output: [tex]3.845\cdot 10^{26} W[/tex]
b) The relative percentage change of power output is 1.67%
c) The intensity of the radiation on Mars is [tex]540 W/m^2[/tex]
Explanation:
a)
The intensity of electromagnetic radiation is given by
[tex]I=\frac{P}{A}[/tex]
where
P is the power output
A is the surface area considered
In this problem, we have
[tex]I=1360 W/m^2[/tex] is the intensity of the solar radiation at the Earth
The area to be considered is area of a sphere of radius
[tex]r=1.5\cdot 10^{11} m[/tex] (distance Earth-Sun)
Therefore
[tex]A=4\pi r^2 = 4 \pi (1.5\cdot 10^{11})^2=2.8\cdot 10^{23}m^2[/tex]
And now, using the first equation, we can find the total power output of the Sun:
[tex]P=IA=(1360)(2.8\cdot 10^{23})=3.845\cdot 10^{26} W[/tex]
b)
The energy of the solar radiation is directly proportional to its frequency, given the relationship
[tex]E=hf[/tex]
where E is the energy, h is the Planck's constant, f is the frequency.
Also, the power output of the Sun is directly proportional to the energy,
[tex]P=\frac{E}{t}[/tex]
where t is the time.
This means that the power output is proportional to the frequency:
[tex]P\propto f[/tex]
Here the frequency increases by 1 MHz: the original frequency was
[tex]f_0 = 60 MHz[/tex]
so the relative percentage change in frequency is
[tex]\frac{\Delta f}{f_0}\cdot 100 = \frac{1}{60}\cdot 100 =1.67\%[/tex]
And therefore, the power also increases by 1.67 %.
c)
In this second case, we have to calculate the new power output of the Sun:
[tex]P' = P + \frac{1.67}{100}P =1.167P=1.0167(3.845\cdot 10^{26})=3.910\cdot 10^{26} W[/tex]
Now we want to calculate the intensity of the radiation measured on Mars. Mars is 60% farther from the Sun than the Earth, so its distance from the Sun is
[tex]r'=(1+0.60)r=1.60r=1.60(1.5\cdot 10^{11})=2.4\cdot 10^{11}m[/tex]
Now we can find the radiation intensity with the equation
[tex]I=\frac{P}{A}[/tex]
Where the area is
[tex]A=4\pi r'^2 = 4\pi(2.4\cdot 10^{11})^2=7.24\cdot 10^{23} m^2[/tex]
And substituting,
[tex]I=\frac{3.910\cdot 10^{26}}{7.24\cdot 10^{23}}=540 W/m^2[/tex]
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The total power output of the Sun is 3.8 x 10^26 W and does not change with frequency variations. Therefore, increasing frequency by 1MHz won't change the power output. Using a distance that takes into account Mars being farther from the Sun, the radiation intensity at Mars can be calculated.
Explanation:The total power output of the sun can be calculated using the equation for the intensity of radiant power (P = I * 4πd^2). So, the total power output of the sun is P = 1360 W/m^2 * 4π * (1.5 x 10^11 m)^2 ≈ 3.8 x 10^26 W.
As for the relative change in power output with frequency change, it is important to note that the power output of the Sun is independent of frequency. Therefore, an increase in frequency by 1 MHz would not result in any relative change in power output. The power output remains 3.8 x 10^26 W regardless of frequency.
Lastly, to find the intensity at Mars which is 60% farther from the Sun than Earth, we use the same intensity equation (I = P / 4πd²) but adjust the distance accordingly. If r is the distance to Earth, then the distance to Mars is 1.6r. Substituting these values, we get I = 3.8 x 10^26 W / 4π * (1.6 * 1.5 x 10^11 m)². From this, you can calculate the radiation intensity at Mars.
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The error in the measurement of the radius of a sphere is 2%. What will be the error in the calculation of its volume?
To solve this problem we will apply the geometric concepts of the Volume based on the consideration made of the radius measurement. The Volume must be written in differential terms of the radius and from the formula of the margin of error the respective response will be obtained.
The error in radius of sphere is not exceeding 2%
[tex]\frac{dr}{r} = \pm 0.02[/tex]
The objective is to find the percentage error in the volume.
The volume can be defined as
[tex]V = \frac{4}{3} \pi r^3[/tex]
Differentiate with respect the radius we have,
[tex]\frac{dV}{dr} = 4\pi r^2[/tex]
[tex]dV = 4\pi r^2 \times dr[/tex]
[tex]dV = 4\pi r^2 (\pm 0.02r)[/tex]
[tex]dV = \pm 4\times 0.02 \times \pi r^3[/tex]
The percentage change in the volume is as follows
[tex]\% change = \frac{dV}{V} \times 100[/tex]
[tex]\% change = \frac{\pm 4 \times 0.02 \times \pi r^3 \times 3}{4\pi r^3}\times 100[/tex]
[tex]\% change = \pm 6\%[/tex]
Therefore the percentage change in volume is [tex]\pm 6\%[/tex]
A stretched string is fixed at both ends which are 160 cm apart. If the density of the string is 0.038 g/cm, and its tension is 600 N, what is the wavelength of the 6th harmonic?
Final answer:
The wavelength of the 6th harmonic of a stretched string fixed at both ends with a length of 160 cm is 53.33 cm.
Explanation:
To calculate the wavelength of the 6th harmonic of a stretched string fixed at both ends, we need to use the formula for the wavelength of standing waves on a string. The formula for the nth harmonic on a string of length L is given by:
\[\lambda = \frac{2L}{n}\]
In this case, the length L is 160 cm, and the harmonic number n is 6.
So, the wavelength for the 6th harmonic is:
\[\lambda_6 = \frac{2 \times 160}{6}\]
\[\lambda_6 = \frac{320}{6}\]
\[\lambda_6 = 53.33 \text{ cm}\]
Therefore, the wavelength of the 6th harmonic is 53.33 cm.
Find the change in internal energy of a system which receives 70 J of heat from its environment and does 20 J of work.
Select one:
a. 90 J
b. 50 J
c. Zero
d. -70 J
Answer:
option B
Explanation:
given,
Q = energy input = 70 J
U = increase in internal energy
W is the work done = 20 J
using first law of thermodynamics
The change in internal energy of a system is equal to the heat added to the system minus the work done.
U = Q - W
U = 70 - 20
U = 50 J
The change in internal energy is equal to 50 J
Hence, the correct answer is option B
A van traveling at a speed of 36.0 mi/h needs a minimum of 50.0 ft to stop. If the same van is traveling 69.0 mi/h, determine its minimum stopping distance (in ft), assuming the same rate of acceleration.
Answer:
Van will stop after a distance of 183.216 ft
Explanation:
We have given initial speed of the van = 36 mi/hr
As the van finally stops so final velocity v = 0 mi/hr
Distance after which van stop = 50 ft
As 1 ft = 0.000189 mi
So 50 ft [tex]=50\times 0.000189=0.00945mi[/tex]
From third equation of motion [tex]v^2=u^2+2as[/tex]
[tex]0^2=36^2+2\times a\times 0.00945[/tex]
[tex]a=-68571.42mi/hr^2[/tex]
In second case u = 69 mi/hr
And acceleration is same
So [tex]0^2=69^2-2\times 68571.42\times s[/tex]
[tex]s=0.03471mi[/tex]
As 1 mi = 5280 ft
So [tex]0.0347mi=0.0347\times 5280=183.216ft[/tex]
The string is fixed at two ends with distance 1.5 m. Its mass is 5 g and the tension in the string is 50N and it vibrates on its third harmonic.
a) What is the wavelength of waves of the string.
b) What is the frequency of the waves.
c) The vibrations produce the sound with the same frequency. What is the wavelength of the sound emitted by the string?
Answer:
a) [tex]\lambda=1\ m[/tex]
b) [tex]f=122.47\ Hz[/tex]
c) [tex]\lambda_s=2.8\ m[/tex]
Explanation:
Given:
distance between the fixed end of strings, [tex]l=1.5\ m[/tex]
mass of string, [tex]m=5\ g=0.005\ kg[/tex]
tension in the string, [tex]F_T=50\ N[/tex]
a)
Since the wave vibrating in the string is in third harmonic:
Therefore wavelength λ of the string:
[tex]l=1.5\lambda[/tex]
[tex]\lambda=\frac{1.5}{1.5}[/tex]
[tex]\lambda=1\ m[/tex]
b)
We know that the velocity of the wave in this case is given by:
[tex]v=\sqrt{\frac{F_T}{\mu} }[/tex]
where:
[tex]\mu=[/tex] linear mass density
[tex]v=\sqrt{\frac{50}{(\frac{m}{l}) } }[/tex]
[tex]v=\sqrt{\frac{50}{(\frac{0.005}{1.5}) } }[/tex]
[tex]v=122.47\ m.s^{-1}[/tex]
Now, frequency:
[tex]f=\frac{v}{\lambda}[/tex]
[tex]f=\frac{122.47}{1}[/tex]
[tex]f=122.47\ Hz[/tex]
c)
When the vibrations produce the sound of the same frequency:
[tex]f_s=122.47\ Hz[/tex]
Velocity of sound in air:
[tex]v_s=343\ m.s^{-1}[/tex]
Wavelength of the sound waves in air:
[tex]\lambda_s=\frac{v_s}{f_s}[/tex]
[tex]\lambda_s=2.8\ m[/tex]
An astronomer looks at the Andromeda galaxy (the other large galaxy in the Local Group) through her telescope. How long ago did that light leave Andromeda?
Answer:
[tex]2.537\times 10^{6}\ years[/tex]
Explanation:
Distance to Andromeda galaxy
[tex]2.537\times 10^{6}\ ly=2.537\times 10^{6}\times c\times y[/tex]
Speed of light is
[tex]c=3\times 10^8[/tex]
Time is given by
[tex]t=\dfrac{Distance}{Speed}\\\Rightarrow t=\dfrac{2.537\times 10^{6}\times c\times y}{c}\\\Rightarrow t=2.537\times 10^{6}\ y[/tex]
Hence, the light from Andromeda left [tex]2.537\times 10^{6}\ years[/tex] ago
The light observed from the Andromeda galaxy by the astronomer left Andromeda around 2 million years ago, showcasing the vast distances in space and providing insights into the universe's evolution.
The light from Andromeda galaxy that the astronomer observes left Andromeda approximately 2 million years ago. This is because the distance in light years is the same as the time it takes for the light to reach us.
This phenomenon is due to the vast distances in space. The Andromeda galaxy is the closest large galaxy to the Milky Way, located 2 million light years away from us.
Understanding the age of the light we observe helps us gain insights into the history of distant galaxies and the evolution of the universe.
Light from the star Betelgeuse takes 640 years to reach Earth. How far away is Betelgeuse in units of light-years? Name any historical event that was occurring on Earth at about the time the light left Betelgeuse. Is the distance to Betelgeuse unusual compared with other stars?
Answer:
The distance is 641.8207 light years, and the star Betelgeuse is further away when compared to other stars
Historical event: Benedict XI succeeds Boniface VIII as pope (1302)
Explanation:
the solution is in the attached Word file