Answers
The question is incomplete. The complete question is :
In your job as a mechanical engineer you are designing a flywheel and clutch-plate system. Disk A is made of a lighter material than disk B, and the moment of inertia of disk A about the shaft is one-third that of disk B. The moment of inertia of the shaft is negligible. With the clutch disconnected, A is brought up to an angular speed ?0; B is initially at rest. The accelerating torque is then removed from A, and A is coupled to B. (Ignore bearing friction.) The design specifications allow for a maximum of 2300 J of thermal energy to be developed when the connection is made. What can be the maximum value of the original kinetic energy of disk A so as not to exceed the maximum allowed value of the thermal energy?
Solution :
Let M.I. of disk A = [tex]$I_0$[/tex]
So, M.I. of disk B = [tex]$3I_0$[/tex]
Angular velocity of A = [tex]$\omega_0$[/tex]
So the kinetic energy of the disk A = [tex]$\frac{1}{2}I_0\omega^2$[/tex]
After coupling, the angular velocity of both the disks will be equal to ω.
Angular momentum will be conserved.
So,
[tex]$I_0\omega_0 = I_0 \omega + 3I_0 \omega$[/tex]
[tex]$I_0\omega_0 = 4I_0 \omega$[/tex]
[tex]$\omega = \frac{\omega_0}{4}$[/tex]
Now,
[tex]$K.E. = \frac{1}{2}I_0\omega^2+ \frac{1}{2}3I_0\omega^2$[/tex]
[tex]$K.E. = \frac{1}{2}I_0\frac{\omega_0^2}{16}+ \frac{1}{2}3I_0\frac{\omega_0^2}{16}$[/tex]
[tex]$K.E. = \frac{1}{2}I_0\omega_0^2 \left(\frac{1}{16}+\frac{3}{16}\right)$[/tex]
[tex]$K.E. = \frac{1}{2}I_0\omega_0^2\times \frac{1}{4}$[/tex]
[tex]$\Delta K = \frac{1}{2}I_0\omega_0^2 - \frac{1}{2}I_0\omega_0^2 \times \frac{1}{4} $[/tex]
[tex]$2300=\frac{3}{4}\left(\frac{1}{2}I_0\omega_0^2\right)$[/tex]
[tex]$\frac{1}{2}I_0\omega_0^2=2300 \times \frac{4}{3 } \ J $[/tex]
Therefore, the maximum initial K.E. = 3066.67 J
Related Questions
For an electrical project in a residence, the electrical engineer had resistors
resistances equal to 300 and 100 to assemble a circuit of an electrical appliance that must be connected 12
hours per day. In order to obtain a chain for optimal operation, he came to the conclusion that the best
configuration would be the one shown in the figure below (consider the middle thread as ideal). Knowing that
kWh value is $ 0.35, what is the amount that must be paid for energy consumption over 1 month (30 days)?
Answers
Answer:
$ 0.077
Explanation:
We'll begin by calculating the equivalent resistance of the three 300 Ω resistors connected in series. This can be obtained as follow:
Equivalent resistance of the three 300 Ω (R₃₀₀) = 300 + 300 + 300
= 900 Ω
Next, we shall determine the equivalent resistance of the two 100 Ω resistors connected in series. This can be obtained as follow:
Equivalent resistance of the two 100 Ω (R₁₀₀) = 100 + 100
= 200 Ω
Next, we shall determine the equivalent resistance in the circuit. This can be obtained as follow:
Equivalent resistance of the three 300 Ω (R₃₀₀) = 900 Ω
Equivalent resistance of the two 100 Ω (R₁₀₀) = 200 Ω
Equivalent Resistance (R) =?
R = R₃₀₀ × R₁₀₀ / R₃₀₀ + R₁₀₀ (since they are in parallel connections)
R = 900 × 200 / 900 + 200
R = 163.64 Ω
Next, we shall determine the energy in KWh. This can be obtained as follow:
Voltage (V) = 10 V
Resistance (R) = 163.64 Ω
Time (t) for 30 days = 12 × 30 = 360 h
Energy (E) =?
E = V²t / R
E = 10² × 360 / 163.64
E = 100 × 360 / 163.64
E = 36000 / 163.64
E = 220 Wh
Divide by 1000 to express in KWh
E = 220 Wh / 1000 = 0.22 KWh
Finally, we shall determine the amount paid for 1 month (30 days). This can be obtained as follow:
Cost per KWh = $ 0.35
Energy (E) = 0.22 KWh
Cost for 30 days =?
Cost for 30 days = Energy × Cost per KWh
Cost for 30 days = 0.22 × 0.35
Cost for 30 days = $ 0.077
Therefore, the amount that must be paid for 1 month is $ 0.077
A bird is standing on an electric transmission line carrying 3000 A of current. A wire like this has about 3.0 x 10-5 22 of resistance per meter. The bird's feet are 6 cm apart. The bird itself has a resistance of about 4 x 105 12. The bird experiences a potential difference of 0.0054 V. What current goes through the bird?
Answers
Answer:
13.5 x 10^-9 A
Explanation:
Yes
A sphere has a surface uniformly charged with 3.30 C. At what distance from its center is the potential 4.50 MV
Answers
Answer:
r = 6.6 x 10³ m = 6600 m
Explanation:
The potential at a distance from a charged sphere can be given as follows:
[tex]V = \frac{kq}{r}\\\\r = \frac{kq}{V}[/tex]
where,
r = distance = ?
k = Colomb Constant = 9 x 10⁹ Nm²/C²
q = charge on sphere = 3.3 C
V = potential = 4.5 MV = 4.5 x 10⁶ V
Therefore,
[tex]r = \frac{(9\ x\ 10^9\ Nm^2/C^2)(3.3\ C)}{4.5\ x\ 10^6\ V}[/tex]
r = 6.6 x 10³ m = 6600 m
what happen to the total energy of a moving object if all the applied forces are conserved
Answers
Answer:
As objects move around over time, the energy associated with them—e.g., kinetic, gravitational potential, heat—might change forms, but if energy is conserved, then the total will remain the same. Conservation of energy applies only to isolated systems.
thenks and pls mark me barinliestt :))
8. Which of Newton’s Laws would allow a passenger to fly right out of their seat if they do not have a seat belt on and a
car suddenly stops.
A) The First Law C) The Third Law
B) The Second Law D) The Fourth Law
Answers
The answer is A The first law
Which planet(s) in the solar system has/have retrograde orbits around the Sun?
A) Uranus
B) Venus and Uranus
C) Earth, Mars, and Saturn
D) Jupiter
Answers
All of the planets move in an eastward direction except Venus and Urunus
Answer:B
Explanation:
What is the electric field strength 7.50 x 10E-1 meters from a 2.8 x 10 E-3 C charged object?
Answers
Answer:hi
Explanation:
the process where water vapor into the atmosphere is changed back into liquid water
Answers
Answer:
Condensation is the process by which water vapor in the air is changed into liquid water. Condensation is crucial to the water cycle because it is responsible for the formation of clouds.
Explanation:
just is
Please help... I'm confused on what I represents in terms of solving the total current. Would variable would I be singling out?
Answers
Answer:
the researcher say hi for us the best pa the best of us are going out to eat that I can get my money toward a little bit but the best of luck to be at work by then and we will see what the status
Why do we never notice quantization?
a. because the fundamental quanta are so large
b. because the fundamental quanta are so small
C. because we are moving quickly relative to such objects
d because we are moving slowly relative to such objects
Answers
Answer:
B
Explanation:
quantization of energy is only seen in atoms
Two loudspeakers in a plane are 2.0 m apart and in phase with each other. Both emit 700 Hz sound waves into a room where the speed of sound is 341 m/s. A listener stands 5.0 m in front of the loudspeakers and 2.0 m to one side of the center line. Is the interference at this point completely constructive, completely destructive, or in between
Answers
Answer:
interference is between destructive and constructive
Explanation:
The interference of two sound waves periodicity in phase by the speakers is
Δr = [tex]\frac{\phi }{2\pi } \ \lambda[/tex]
in this case they indicate that the frequency is f = 700 Hz, the wave speed is
v =λ f
λ = v / f
λ = 341/700
λ = 0.487 m
Let's use the Pythagorean theorem to find the distance that each wave travels
r₁ = [tex]\sqrt{x^2 + y^2}[/tex]
let's measure the distance from speaker 1
r₁ = [tex]\sqrt{5^2 + 1^2}[/tex]
r₁ = 5,099 m
the distance from the second speaker
r₂ = \sqrt{x^2 + y^2}
r₂ = [tex]\sqrt{5^2 +3^2}[/tex]
r₂= 5.831 m
the difference in the way is
Δr = r₂ -r₁
Δr = 5,831 - 5,099
Δr = 0.732 m
[tex]\frac{ \phi }{2\pi }[/tex] = Δr /λ
\frac{ \phi }{2\pi } = 0.732 / 0.487
\frac{ \phi }{2\pi } = 1.50
this is the phase difference this phase difference is approximately
Ф= [tex]\frac{\pi }{2}[/tex] =1.57,
so the interference is between destructive ( Ф = π) and constructive (Ф=2π)
A planet moves in a circular orbit of radius 4.5x10^15 m with a period of 4
days. What is its velocity?
Answers
Answer:
2.6x10^{10}
Explanation:
please do follow me
A system has two possible energy states, E0 and E1 (with E1 > E0). If the difference between these energy states grows (E0 and E1 get further apart while the temperature stays constant), then the ratio of the number of particles in state E0 over the number of particles in state E1 will:__________
Answers
Answer:
The number of particles in state E0 over the number of particles in state E1 will reduce
Explanation:
E0 represents the ground level state when all the particles have same energy level.
E1 represents excited state in which only a few particle reaches
E0 and E1 get further apart means that the energy difference between the two level increases.
Thus, the number of particles in state E0 over the number of particles in state E1 will reduce.
Suppose you have a 6.0 V motorcycle battery that can move 3,000 C of charge. How much energy does it deliver
Answers
Answer:
1.8*10^4 Joules
Explanation:
Given data
Voltage= 6volts
Q= 3000 C
We know that the energy due to a point charge is
Pe= QV
substitute
Pe= 3000*6
Pe=18000
Pe= 18000Joules
Pe= 1.8*10^4 Joules
is burning trash a physical change or chemical change?
Answers
Consider a 30-cm-diameter hemispherical enclosure. The dome is maintained at 600 K, and heat is supplied from the dome at a rate of 65 W while the base surface with an emissivity of 0.55 is maintained at 400 K. Determine the emissivity of the dome.
Answers
Answer:
[tex]\epsilon_2=0.098[/tex]
Explanation:
Diameter [tex]d=30cm=0.3m[/tex]
Temperature [tex]T=600k[/tex]
Rate of supply [tex]r=65W[/tex]
Emissivity of base surface [tex]\in_b =0.55[/tex]
Temperature at base [tex]T_b=400k[/tex]
Generally the equation for Area of base surface is mathematically given by
[tex]A_b=\frac{\pi}{4}d^2[/tex]
[tex]A_b=\frac{\pi}{4}0.3^2[/tex]
[tex]A_b=0.0707m^2[/tex]
Generally the equation for Area of Hemispherical dome is mathematically given by
[tex]A_h=\frac{\pi}{2}d^2[/tex]
[tex]A_h=\frac{\pi}{2}0.3^2[/tex]
[tex]A_h=0.1414m^2[/tex]
Since base is a flat surface
[tex]F_{11}+F_{12}=1[/tex]
[tex]F_{11}=0[/tex]
Therefore
[tex]F_{12}=1[/tex]
[tex]A_b=0.0707m^2[/tex]
Generally the equation for Net rate of radiation heat transfer between two surfaces is mathematically given by
[tex]Q_{21}=-Q_{12}[/tex]
[tex]Q_{21}=\frac{\sigma(T_1^4-T_2^4)}{\frac{1-\epsilon}{A_b\epsilon_1} +\frac{1}{A_bF_{12}} +\frac{1-\epsilon_2}{A_h*\epsilon_2} }[/tex]
Where
[tex]\sigma=5.67*10^{-8}[/tex]
Therefore
[tex]65=\frac{(5.67*10^{-8}(400^4-600^4))}{\frac{1-0.55}{0.0707*0.55}+\frac{1}{0.0707}+\frac{1-\epsilon_2}{0.1414*\epsilon_2}}[/tex]
[tex]\epsilon_2=0.098[/tex]
[tex]\epsilon_2 \approx 0.1[/tex]
Therefore the emissivity of the dome is
[tex]\epsilon_2=0.098[/tex]
12)A black body is heated from 27°C to 127° C. The ratio of their energies of radiations emitted will be
a)3:4
c)27:64
b)9:16
d)81:256
Answers
Answer:
[tex]81:256[/tex].
Explanation:
Let [tex]T[/tex] denote the absolute temperature of this object.
Calculate the value of [tex]T[/tex] before and after heating:
[tex]T(\text{before}) = 27 + 273 = 300\; \rm K[/tex].
[tex]T(\text{after}) = 127 + 273 = 400\; \rm K[/tex].
By the Stefan-Boltzmann Law, the energy that this object emits (over all frequencies) would be proportional to [tex]T^4[/tex].
Ratio between the absolute temperature of this object before and after heating:
[tex]\displaystyle \frac{T(\text{before})}{T(\text{after})} = \frac{3}{4}[/tex].
Therefore, by the Stefan-Boltzmann Law, the ratio between the energy that this object emits before and after heating would be:
[tex]\displaystyle \left(\frac{T(\text{before})}{T(\text{after})}\right)^{4} = \left(\frac{3}{4}\right)^{4} = \frac{81}{256}[/tex].
A magnetic field of 0.27 T exists in the region enclosed by a solenoid that has 599 turns and a diameter of 9.29 cm. Within what period of time must the field be reduced to zero if the average magnitude of the induced emf within the coil during this time interval is to be 12.8 kV
Answers
Answer: [tex]8.54\times 10^{-5}\ s[/tex]
Explanation:
Given
The initial magnetic field is [tex]B=0.27\ T[/tex]
No of turns [tex]N=599\ \text{turns}[/tex]
Diameter of the solenoid [tex]d=9.29\ cm[/tex]
Induced EMF [tex]E=12.8\ kV[/tex]
Induced emf is the product of no of turns and rate of change of flux.
[tex]\Rightarrow E=-N\cdot \dfrac{\Delta \phi }{\Delta t}\\\\\Rightarrow E=-N\cdot \dfrac{\Delta (B\cdot A)}{\Delta t}\\\\\Rightarrow E=-NA\cdot \dfrac{\Delta B}{\Delta t}\\\\\text{Insert the values}\\\\\Rightarrow 12.8=-599\times \pi r^2\cdot \dfrac{(0-B)}{\Delta t}\\\\\Rightarrow \Delta t=\dfrac{599\times \pi \times (4.64\times 10^{-2})\times 0.27}{12.8\times 10^3} \\\\\Rightarrow \Delta t=854.71\times 10^{-7}\ s\\\\\text{Taking absolute value}\\\Rightarrow \Delta t=8.54\times 10^{-5}\ s[/tex]
PLS HELP!! Our eyes perceive colors because of differences in which of the following properties of light?
Amplitude
Brightness
Wavelength
Source
Answers
Answer:
Your answer is wavelength
1 point
4. When mass is in kilograms and velocity is in meters per second then
momentum is in kilograms-meters per second.
True
Ο Ο
False
Answers
Answer:
true
Explanation:
momentum = kg (m/s)
momentum = mass × velocity
The springs of a 1500 kg car compress 5.00 mm when its 68 kg driver gets into the driver's seat. Part A If the car goes over a bump, what will be the frequency of oscillations
Answers
Answer:
the frequency of the oscillation is 1.5 Hz
Explanation:
Given;
mass of the spring, m = 1500 kg
extention of the spring, x = 5 mm = 5 x 10⁻³ m
mass of the driver = 68 kg
The weight of the driver is calculated as;
F = mg
F = 68 x 9.8 = 666.4 N
The spring constant, k, is calculated as;
k = F/m
k = (666.4 N) / (5 x 10⁻³ m)
k = 133,280 N/m
The angular speed of the spring is calculated;
[tex]\omega = \sqrt{\frac{k}{m} } \\\\\omega = \sqrt{\frac{133280}{1500} } = 9.426 \ rad/s[/tex]
The frequency of the oscillation is calculated as;
ω = 2πf
f = ω / 2π
f = (9.426) / (2π)
f = 1.5 Hz
Therefore, the frequency of the oscillation is 1.5 Hz
7) The coefficient of performance (COP) of a refrigerator is defined as the ratio of A) the heat removed from the inside to the heat expelled (dismissed) to the outside. B) the heat expelled (dismissed) to the outside to the heat removed from the inside. C) the heat removed from the inside to the work done to remove the heat. D) the heat expelled (dismissed) to the outside to the work done to remove the heat
Answers
Answer:
C) the heat removed from the inside to the work done to remove the heat.
Explanation:
Refrigerator is a heat engine working in reverse direction . Heat from cold source is taken out , some work is done to remove them and total heat and work energy is thrown into outside surrounding .
If q heat is taken out and W is work done to get this heat out .
coefficient of performance ( COP ) = q / W .
Hence C ) is the right choice .
A boat that can travel at 4.60 km/h in still water crosses a river with a current of 1.80 km/h. At what angle must the boat be pointed upstream to travel straight across the river
Answers
Answer:
The angle the boat must be pointed upstream is 69⁰
Explanation:
Check the image uploaded for the diagram;
Given;
speed of the boat on still water, = 4.6 km/h
speed of the boat on a river with current, = 1.8 km/h
The angle the boat must be pointed upstream is calculated as follows
[tex]tan(\theta) = \frac{4.6}{1.8} \\\\tan(\theta) = 2.556\\\\\theta = tan^{-1}(2.556)\\\\\theta = 68.63^0\\\\\theta = 69^0[/tex]
1-The amount of heat required to raise the temperature
of 1 g of a substance by degree celsius is
one
Answers
Answer:
• specific heat
1 Answer. The specific heat is the amount of heat required to raise the temperature of 1 g of substance by one degree Celsius or one Kelvin
An electrical insulator is a material that:
A) contains no charge
B) does not allow electrons to flow
C) has more protons than electrons
D) must be a crystal
Answers
Answer:
Option B is appropriate for this question
A child moving at constant velocity carries a 2 N ice-cream cone 1 m across a level surface. What is the net work done on the ice-cream cone?
Answers
Answer:
2 Joule
Explanation:
Work=force *dISPLACMENT
2N*1M
2 JOUL
The diagram below shows a person swinging a hammer.
Which position has the least amount of kinetic energy?
A-1
B-2
C-3
D-4
Answers
After 60 days, 100g of a certain element has decayed to only 12.5g.
What is the half- life of this element?
А
30 days
B.
8 days
С
20 days
D
5 days
Answers
Answer:
8 days
Explanation:
True or False? To observe physical properties in matter, the matter must change into a new substance.
Answers
Explanation:
It just is trust me
True False: Marke each statement as true or false.
shift
1. Light intensity affects the rate of photosynthesis.
in
2. Energy is required by all organisms for life.
3. The ability of a plant to repair tissue depends on respiration.
4. The gas needed for photosynthesis is carbon dioxide (CO2).
5. Plants only carry on photosynthesis, not respiration.
6. Respiration can occur without photosynthesis.
Answers
Answer:
1) true 2) true 3) true 4) true 5) false 6) false
Explanation: