Answer:
1) The amplitude of the motion is approximately 0.274 meters.
2) The total energy of the object at any point of its motion is 16.892 joules.
Explanation:
1) An object under simple harmonic motion is conservative, since there is no dissipative forces acting during motion (i.e. friction, air viscosity). The amplitude of the motion can be found easily by Principle of Energy Conservation by the fact that maximum elastic potential energy ([tex]U_{e}[/tex]), in joules, is equal to maximum translational kinetic energy ([tex]K[/tex]), in joules:
[tex]U_{e} = K[/tex]
[tex]\frac{1}{2}\cdot k \cdot A^{2} = \frac{1}{2}\cdot m \cdot v^{2}[/tex] (1)
Where:
[tex]k[/tex] - Spring constant, in newtons per meter.
[tex]A[/tex] - Amplitude, in meters.
[tex]m[/tex] - Object mass, in kilograms.
[tex]v[/tex] - Speed of the object at equilibrium, in meters per second.
If we know that [tex]k = 450\,\frac{N}{m}[/tex], [tex]m = 0.25\,kg[/tex] and [tex]v = 0.3\,\frac{m}{s}[/tex], then the amplitude of the motion is:
[tex]\frac{1}{2}\cdot k \cdot A^{2} = \frac{1}{2}\cdot m \cdot v^{2}[/tex]
[tex]k\cdot A^{2} = m\cdot v^{2}[/tex]
[tex]A = v\cdot \sqrt{\frac{m}{k} }[/tex]
[tex]A = \left(0.3\,\frac{m}{s} \right)\cdot \sqrt{\frac{0.25\,kg}{0.3\,\frac{m}{s} } }[/tex]
[tex]A \approx 0.274\,m[/tex]
The amplitude of the motion is approximately 0.274 meters.
2) The total energy of the object ([tex]E[/tex]), in joules, is found either by maximum elastic potential energy or by maximum translational kinetic energy, that is: ([tex]k = 450\,\frac{N}{m}[/tex], [tex]A \approx 0.274\,m[/tex])
[tex]E = U_{e}[/tex]
[tex]E = \frac{1}{2}\cdot k\cdot A^{2}[/tex]
[tex]E = \frac{1}{2}\cdot \left(450\,\frac{N}{m} \right) \cdot (0.274\,m)^{2}[/tex]
[tex]E = 16.892\,J[/tex]
The total energy of the object at any point of its motion is 16.892 joules.
1. 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 person
B. The person and the Earth
C. The Earth
2. Based on your answer to Question 1, why doesn’t the total energy of the Earth-person system change when the person goes up to a new height, gaining potential energy?
Answer:
1. B. The person and the Earth
2. This is because the energy gained by the person equals the energy lost by the earth,
Explanation:
1.
B. The person and the Earth
This is because the person and the earth both represent a system. A system consists of more than one item. A system consists of two or more items interacting with each other.
2. This is because, the energy of an isolated system is conserved according to the second law of thermodynamics which states that in an isolated system, energy can neither be created nor destroyed. So, there is an exchange of energy between the person and the Earth. So, the energy gained by the person at the new height equals the energy lost by the earth. And thus, the total energy of the system remains constant.
What is the solubility of KNO3 at 50°C?
45 grams
63 grams
70 grams
83 grams
Answer:
The solubility of KNO3 at 50 degrees C is 83 g/100 g water.
Explanation:
when u see the graph and by using graph reading techniques then u find the solubility.
Unpolarized light with intensity 370 W/m2 passes first through a polarizing filter with its axis vertical, then through a second polarizing filter. It emerges from the second filter with intensity 132 W/m2 . You may want to review (Pages 897 - 898) . Part A What is the angle from vertical of the axis of the second polarizing filter
Answer:
θ = 32.4º
Explanation:
For this exercise let's use Malus's law
I = Io cos² θ
in this case it indicates that the incident intensity is 370 W/m², when the first polarization passes, only the radiation with the same polarization of the polarizer emerges, that is, vertical
I₀ = 370/2 = 185 W / m²
this is the radiation that affects the second polarizer, let's apply the expression of Maluz
θ = cos⁻¹ ([tex]\sqrt{\frac{I}{I_o} }[/tex])
θ = cos⁻¹ ([tex]\sqrt{132/185}[/tex])
θ = cos⁻¹ (0.844697)
θ = 32.4º
can someone please take there time and answer this for me :)
Answer:
number 1
Explanation:
they have common ancestors
Electric Charge and Current Quiz CP ( fill in blank)
Answer:
1. Positive
2. Negative
3. induction
4. Insulator
5. Voltage
6. Static energy
7. Positive, Negative
8. Resistance
9. Increase
Would appreciate if you mark me as brainliest answer
1. Protons have positive electric charge and electrons have negative electric charge.
2. Opposite charges attract and like charges repel.
3. Charging by induction is the rearrangement of electrons on a neutral object caused by a nearby charged object.
4. Insulator are materials that do not allow electric current to pass through easily.
5. Voltage is the accumulation of electrical charges on on object.
6.Current is usually the flow of static electricity.
7. Charges flow from positive voltage to negative voltage.
8. The tendency of material to oppose the flow of electron is called resistance.
9. Making wires thinner, longer or hotter Increase the resistance.
What is current?The current is the stream of charges which flow from positive to negative terminal of voltage source.
Voltage is the collection or storage of charges. Resistance of the circuit is the opposition to the flow of current.
Charging a neutral object is done by induction. Like charges repel each other and unlike charges attract each other. The electron are positive charged and proton are positive charged.
Learn more about current.
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what kind of charge does an object have if it has extra positive charges
When 16.35 moles of SI reacts with 11.26 moles of N2, how many moles of SI3N4 are formed
Answer:
5.45 moles
Explanation:
The chemical balanced equation of this reaction is;
3Si + 2N2 → Si3N4
From the balanced equation, we can see that that 3 moles of Si reacts with 2 moles of N2 to produce 1 mole of Si3N4.
Thus imies that the molar ration of Si to N2 is 3:2.
Now, we are told that 16.35 moles of Si reacts with 11.26 moles of N2.
16.35
Thus, using the ratio 3:2, we can say that moles of 16.35 miles of Si will react completely with (16.35 × ⅔) = 10.9 moles of N2.
Remaining N2 = 11.26 - 10.9 = 0.36 will be the excess.
From our balanced chemical equation, we saw that;
3 moles of Si produced 1 mole of Si3N4.
Thus; 16.35 moles of Si will produce;
no. of moles of Si3N4 produced = (1 × 16.35)/(3.0) = 5.45 moles
During transpiration, water goes from a _____ to a _____.
Answer:
WATER TO A VAPOR
Explanation:
Explanation:
During transpiration, water goes from a root to a stomata.
What is the animal behavior where organisms imitate another organism or environment in some way?
Mimicry. This is when oraganisms imitate another oraganism whether it be physical or behavoioral.
A nuclear power plant generates a total of 3 GW of power at an efficiency of 33%. The nuclear reactor has a recoverable energy per fission of 210 MeV. Approximately 65% of the plant's power comes from fissions in 235U, the remainder from fissions in plutonium, 239Pu. calculate: (a) the net electric power output, (b) the rate of fission events (per second) in the reactor core, (c) the mass of 235U used up in one year (hint: every fission event consumes one 235U nucleus and in the reactor core about 1.0 (1020) nuclei of U 235 are consumed every second. (d) If the plant were operated at full power for 1 year, how many
Answer:
Explanation:
From the question we are told that:
Plant Generates [tex]P=3GW[/tex]
Efficiency [tex]\eta =33\%[/tex]
Recoverable energy per fission [tex]\mu=210MeV \approx 336.42*18^{-7}J[/tex]
Fission Power [tex]F_p=235U[/tex] [tex](65\% of Plant\ power)[/tex]
Fission in plutonium [tex]F_{pl}=239Pu[/tex]
a)
Generally the equation for net electric power output [tex]P_o[/tex] is mathematically given by
[tex]P_o=P*\frac{1}{\eta}[/tex]
[tex]P_o=3*\frac{100}{3}[/tex]
[tex]P_o=9.0GW[/tex]
b)
Generally the equation for Rate of Fission [tex]F_{rate}[/tex] is mathematically given by
[tex]F_{rate}=\frac{P_o}{\mu}}[/tex]
[tex]F_{rate}=\frac{9*10^{9}}{336.42*18^{-7}}}[/tex]
[tex]F_{rate}=27.02*10^{13}[/tex]
c)
Generally the equation for Mass of [tex]^{235} U[/tex] used in a yr [tex]M_{U/yr}[/tex] is mathematically given by
[tex]M_{U/yr}=P_o*\frac{65}{100}[/tex]
[tex]M_{U/yr}=5.91GW[/tex]
how can we know that atmosphere exert pressure explain with figure
compute the distance and displacment of the puppy using visual analysis of the diagram?
Answer:
Distance A:11km
B:10km
Explanation:
Displacement A and B is 9km
The speed of surface waves in water decreases as the water becomes shallower. Suppose waves travel across the surface of a lake withn a speed of 2m/s and a wavelength of 1.5m. When these waves move into a shallower part of the lake, their speed decreases to 1.6m/s, though their frequency remains the same. Find the wavelength of the wave in the shallower water.
Answer:
The correct solution is "1.2 m".
Explanation:
The given values are:
Wavelength of waves,
λ = 1.5 m
Speed of waves on surface,
V = 2 m/sec
Speed of waves in water,
V₁ = 1.6 m/sec
As we know,
⇒ [tex]V=f\times \lambda[/tex]
or,
⇒ [tex]f=\frac{V}{\lambda}[/tex]
On substituting the values, we get
⇒ [tex]=\frac{2}{1.5}[/tex]
⇒ [tex]=1.33 \ Hz[/tex]
hence,
⇒ [tex]\lambda_1=\frac{V_1}{f}[/tex]
On substituting the values, we get
⇒ [tex]=\frac{1.6}{1.33}[/tex]
⇒ [tex]=1.2 \ m[/tex]
Why would the kinetic energy at the bottom of the track be less than the potential energy at the top of the track?
Answer:
This is because of friction and heat lost.
Explanation:
A negative point charge - is at the center of a hollow insulating spherical shell, which has an inner radius R1 and an outer radius R2. There is a total charge of +7Q spread uniformly throughout the volume of the insulating shell, not just on its surface. Determine the electric field for the following. (Use any variable or symbol stated above along with the following as necessary: r and E
(a) r < R1
(b) R1
(c) R2
You are riding in the passenger seat of a car as it goes around a tight turn. You slide across the seat to the passenger side door. Which statement below properly describes what happens? a. You are exerting a centripetal force on the car door. b. The door is exerting a centripetal force on you that balances the centrifugal force of the turn. c. The car seat is exerting a centripetal force on you, but not enough to keep you in place. d. The turn exerts a centrifugal force on you that throws you out toward the door. 2. An object is moving in a circle at a constant speed. From this you can be certain that a. There is at least one force acting on the object. b. There is no net force acting on the object. c. There are at least two forces acting on the object, which balance each other. d. There are at least two forces acting on the object, which do not balance each other. e. There must be more than two forces acting on the object.
Answer:
1. b. The door is exerting a centripetal force on you that balances the centrifugal force of the turn.
2. b. There is no net force acting on the object.
Explanation:
1. This is because as you move to the right due to the centrifugal force of the turn, a corresponding centripetal force acts on you due to the door which does not allow you fall out of the car since, the door is exerting a centripetal force on you that balances the centrifugal force of the turn.
So, the answer is b
2. This is because, since the object moves at a constant speed and thus does not accelerate, no net force can act on it since, a net force would imply that the object accelerates. Note that a constant speed does not imply that no force acts on it. It only shows that the resultant or net force is zero since the object does not accelerate.
So, there is no net force acting on the object.
So, b is the answer.
A microphone is attached to a spring that is suspended from the ceiling, as the drawing indicates. Directly below on the floor is a stationary 440-Hz source of sound. The microphone vibrates up and down in simple harmonic motion with a period of 2.0 s. The difference between the maximum and minimum sound frequencies detected by the microphone is 2.1 Hz. Ignoring any reflections of sound in the room and using 343 m /s for the speed of sound, determine the amplitude of the simple harmonic motion.
Answer:
[tex]0.261\ \text{m}[/tex]
Explanation:
[tex]\Delta f[/tex] = Change in frequency = 2.1 Hz
[tex]f[/tex] = Frequency of source of sound = 440 Hz
[tex]v_m[/tex]= Maximum of the microphone
[tex]v[/tex] = Speed of sound = 343 m/s
[tex]T[/tex] = Time period = 2 s
We have the relation
[tex]\Delta f=2f\dfrac{v_m}{v}\\\Rightarrow v_m=\dfrac{\Delta fv}{2f}\\\Rightarrow v_m=\dfrac{2.1\times 343}{2\times 440}\\\Rightarrow v_m=0.8185\ \text{m/s}[/tex]
Amplitude is given by
[tex]A=\dfrac{v_m T}{2\pi}\\\Rightarrow A=\dfrac{0.8185\times 2}{2\pi}\\\Rightarrow A=0.261\ \text{m}[/tex]
The amplitude of the simple harmonic motion is [tex]0.261\ \text{m}[/tex].
Question 2 of 20 :
Select the best answer for the question.
2. Which of the following is considered to be a vector?
A. Velocity
B. Time
C. Temperature
D. Mass
Mark for review (Will be highlighted on the review page)
The answer is A. velocity .
Velocity is a vector quantity because it need magnitude as well as direction to be defined.
A car advertisement states that a certain car can accelerate from rest to
27m/s in 4.9 seconds at a temperature of 75F. What is the acceleration of
the car?
Answer:
Acceleration of the car = 5.51 m/s²
Explanation:
Given:
Initial speed of car = 0 m/s
Final speed of car = 27 m/s
Time taken by car = 4.9 seconds
Find:
Acceleration of the car
Computation:
Using first equation of motion
v = u + at
Where
v = Final velocity
u = Initial velocity
t = Time taken
a = Acceleration
So,
v = u + at
27 = 0 + a(4.9)
a(4.9) = 27
a = 5.51 m/s²
Acceleration of the car = 5.51 m/s²
Which type of wires are ferromagnetic metals?
cooper
aluminum
string
why are the nuclei of the heavier elements radioactive and not the lighter elements of nuclei?
Answer:
becouse most of nuclear elements are heave
Explanation:
A
ring
made
up of equal semicircular section
of cast Iron and cast steel with two air gaps
of o-imm and 0.25mm respectively has a cross
soctional area of 400 cm and a mean diameter
of 5m. The ring is uniformly wound with a coil
of 1200 furns. if the relative permeability
of cast iron and cast steel are 2800 and
900 respectively, determine the current
required to produce
a flux of lomwb in
Explanation:
I couldn't have information on this question.
10 POINTS! SPACE QUESTION!!
If a set of Bluetooth headphones has a resistance of 4.5 ohms and has a current of 1.5 amps, what is the voltage of the headphones?
Answer:
6.75 v
Explanation:
A negative charge of 4.0 x 10 C and a positive charge of 7.0 x 10 C are separated by 0.15 m. What is the force between the two charges?
Why are some tsunamis described as local?
Answer:
A local tsunami is one that originates from within about 100 km or less than 1 hour tsunami travel time from the impacted coastline. Local tsunamis can result in a significant number of casualties since authorities have little time to warn/evacuate the population.
Explanation:
Hope this helps
Which best labels the chart?
Title 1 is “Longitudinal Waves,” and Title 2 is “Transverse Waves.”
Title 1 is “Transverse Waves,” and Title 2 is “Longitudinal Waves.”
Title 1 is “Electromagnetic Waves,” and Title 2 is “Mechanical Waves.”
Title 1 is “Mechanical Waves,” and Title 2 is “Electromagnetic Waves.”
Answer:
the answer is b!!!!
Explanation:
just took the test
The best labeling for the chart would be Title 1 is "Transverse Waves," and Title 2 is "Longitudinal Waves." Therefore, the correct option is B.
The two types of waves that are the subject of the chart under consideration are transverse waves and longitudinal waves. While longitudinal waves have vibrations parallel to the path of wave travel, transverse waves have vibrations perpendicular to the direction of wave propagation.
The graphic distinguishes between these wave types by designating title 1 as "transverse wave" and title 2 as "longitudinal wave". Using this labeling, viewers can understand and differentiate the two wave ranges based on their unique characteristics.
So, the correct option is B.
Learn more about longitudinal wave, here:
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4. Speedy leaves the ground with an initial vertical velocity of 53 m/s and a horizontal velocity of 42 m/s.
How much time does he spend in the air?
How far (horizontally) does he travel during this time?
5. The Angry Bird is fired at an angle of 35 above the horizontal at a speed of 72 m/s.
Draw the initial velocity vector
Determine the initial horizontal velocity
Determine the initial vertical velocity
How much time does it spend in the air?
What horizontal distance does it go?
g A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 39.0kg and diameter 78.0cm. The power is off for 34.0s, and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 170 complete revolutions.At what rate is the flywheel spinning when the power comes back on?
Answer:
[tex]10.54\ \text{rad/s}[/tex]
Explanation:
[tex]\omega_i[/tex] = Initial angular velocity = 500 rpm = [tex]500\times \dfrac{2\pi}{60}\ \text{rad/s}[/tex]
[tex]\omega_f[/tex] = Final angular velocity
t = Time = 34 s
[tex]\theta[/tex] = Angular displacement = 170 revs = [tex]170\times 2\pi\ \text{rad}[/tex]
[tex]\alpha[/tex] = Angulr acceleration
From the kinematic equations of angular motion we have
[tex]\theta=\omega_it+\dfrac{1}{2}\alpha t^2\\\Rightarrow \alpha=\dfrac{\theta-\omega_it}{\dfrac{1}{2}t^2}\\\Rightarrow \alpha=\dfrac{170\times 2\pi-500\times \dfrac{2\pi}{60}\times 34}{\dfrac{1}{2}\times 34^2}\\\Rightarrow \alpha=-1.23\ \text{rad/s}^2[/tex]
[tex]\omega_f=\omega_i+\alpha t\\\Rightarrow \omega_f=500\times \dfrac{2\pi}{60}+(-1.23)\times 34\\\Rightarrow \omega_f=10.54\ \text{rad/s}[/tex]
The rate at which the wheel is spinning when the power comes back on is [tex]10.54\ \text{rad/s}[/tex].
ou are making a clock out of a solid disk with a radius of 0.2m and mass of 0.1 kg that will be attached at its center of mass to the end of a uniform thin rod with a mass of 0.3 kg. Calculate The length of the rod such that the period of the system is 1 second.The distance from the pivot to theCOM of the system must be expressed in terms of L. The parallel axis theorem must be used for both therod and the solid disk in terms of L as well. There will be a quadratic equation to be solved
Answer:
the correct result is L = 0.319 m
Explanation:
This system is a physical pendulum whose angular velocity is
w² = [tex]\frac{M \ g \ d}{I}[/tex]
where d is the distance from the center of mass to the point of rotation and I is the moment of inertia of the system
The Moment of Inertia is a scalar, therefore an additive quantity
I = I_bar + I_disk
the moment of inertia of each element with respect to the pivot point can be found with the parallel axes theorem
let's use M for the mass of the bar and m for the mass of the disk
Bar
I_bar = I_{cm} + Md²
the moment of inertia of the center of mass is
I_{cm} = [tex]\frac{1}{12}[/tex] M L²
the distance from the center of mass
d = L / 2
we substitute
I_bar = [tex]\frac{1}{12}[/tex] M L² + M ([tex]\frac{L^2}{4}[/tex])
Disk
I_disk = I_{cm} + m d²
moment of inertia of the center of mass
I_{cm} = ½ m R²
the distance d is
d = L
we substitute
I_disk = 1/2 m R² + m L²
the total moment of inertia is
I = [tex]\frac{1}{12}[/tex] M L² +[tex]\frac{1}{4}[/tex] M L² + [tex]\frac{1}{2}[/tex] m r² + m L²
I = [tex]\frac{1}{4}[/tex] M L² + m L² + ½ m r²
I = L² (m + [tex]\frac{1}{4}[/tex] M) + ½ m r²
The position of the center of mass of the system can be found with the expressions
d_{cm} = [tex]\frac{1}{M} \sum r_i m_i[/tex]
d_{cm} = [tex]\frac{1}{m+M} \ ( M \frac{L}{2} + m L)[/tex]
d_{cm} = [tex]L \frac{m + M/2}{m +M }[/tex]
now we can substitute in the expression for the angular velocity
w² = (m + M) g L [tex]\frac{m + \frac{M}{2} }{m+M}[/tex] [tex]\frac{1}{L^2 (m+ \frac{M}{4} ) + \frac{1}{2} m r^2 }[/tex]
w² = g (m + [tex]\frac{1}{2}[/tex] M) [tex]\frac{L}{ L^2 ( m +\frac{1}{4} M ) + \frac{1}{2} m r^2}[/tex]
angular velocity and period are related
w = 2π/T
sustitute
4π²/T² = g (m + [tex]\frac{1}{2}[/tex] M) [tex]\frac{L}{ L^2 ( m +\frac{1}{4} M ) + \frac{1}{2} m r^2}[/tex]
L² (m + [tex]\frac{1}{4}[/tex] M) + ½ m r² = [tex]\frac{T^2}{4 \pi ^2 } \ g ( m + \frac{1}{2} M ) \ \ L[/tex]
we substitute the values and solve the second grade equation
L² (0.1 + [tex]\frac{1}{4}[/tex] 0.3) - [[tex]\frac{1^2}{4\pi ^2}[/tex] 9.8 (0.1 + 0.3/2) ] L + ½ 0.1 0.2² = 0
L² 0.175 - 0.06206 L + 0.002 = 0
the equation remains after simplifying
L² - 0.3546 La + 0.01143 = 0
solve us
L = [tex]\frac{0.3546 \ \pm \sqrt{ 0.3546^2 - 4 \ 0.01143 }}{2}[/tex]
L = [tex]\frac{0.3546 \ \pm \ 0.28288 }{2}[/tex]
L₁ = 0.319 m
L₂ = 0.036m
the correct result must have a value greater than the radius of the disk. The correct result is L = 0.319 m