Hi there!
a.
We can use the initial conditions to solve for w₀.
It is given that:
[tex]\frac{d\theta}{dt} = w_0e^{-\sigma t}[/tex]
We are given that at t = 0, ω = 3.7 rad/sec. We can plug this into the equation:
[tex]\omega(0)= \omega_0e^{-\sigma (0)}\\\\3.7 = \omega_0 (1)\\\\\omega_0 = \boxed{3.7 rad/sec}[/tex]
Now, we can solve for sigma using the other given condition:
[tex]2 = 3.7e^{-\sigma (8.6)}\\\\.541 = e^{-\sigma (8.6)}\\\\ln(.541) = -\sigma (8.6)\\\\\sigma = \frac{ln(.541)}{-8.6} = \boxed{0.0714s^{-1}}[/tex]
b.
The angular acceleration is the DERIVATIVE of the angular velocity function, so:
[tex]\alpha(t) = \frac{d\omega}{dt} = -\sigma\omega_0e^{-\sigma t}\\\\\alpha(t) = -(0.0714)(3.7)e^{-(0.0714) (3)}\\\\\alpha(t) = \boxed{-0.213 rad\sec^2}[/tex]
c.
The angular displacement is the INTEGRAL of the angular velocity function.
[tex]\theta (t) = \int\limits^{t_2}_{t_1} {\omega(t)} \, dt\\\\\theta(t) = \int\limits^{2.5}_{0} {\omega_0e^{-\sigma t}dt\\\\[/tex]
[tex]\theta(t) = -\frac{\omega_0}{\sigma}e^{-\sigma t}\left \| {{t_2=2.5} \atop {t_1=0}} \right.[/tex]
[tex]\theta = -\frac{3.7}{0.0714}e^{-0.0714 t}\left \| {{t_2=2.5} \atop {t_1=0}} \right. \\\\\theta= -\frac{3.7}{0.0714}e^{-0.0714 (2.5)} + \frac{3.7}{0.0714}e^{-0.0714 (0)}[/tex]
[tex]\theta = 8.471 rad[/tex]
Convert this to rev:
[tex]8.471 rad * \frac{1 rev}{2\pi rad} = \boxed{1.348 rev}[/tex]
d.
We can begin by solving for the time necessary for the angular speed to reach 0 rad/sec.
[tex]0 = 3.7e^{-0.0714t}\\\\t = \infty[/tex]
Evaluate the improper integral:
[tex]\theta = \int\limits^{\infty}_{0} {\omega_0e^{-\sigma t}dt\\\\[/tex]
[tex]\lim_{a \to \infty} \theta = -\frac{\omega_0}{\sigma}e^{-\sigma t}\left \| {{t_2=a} \atop {t_1=0}} \right.[/tex]
[tex]\lim_{a \to \infty} \theta = -\frac{3.7}{0.0714}e^{-0.0714a} + \frac{3.7}{0.0714}e^{-0.0714(0)}\\\\ \lim_{a \to \infty} \theta = \frac{3.7}{0.0714}(1) = 51.82 rad[/tex]
Convert to rev:
[tex]51.82 rad * \frac{1rev}{2\pi rad} = \boxed{8.25 rev}[/tex]
A 0.050 kg metal bolt is heated to an unknown initial temperature. It is then dropped into calorimeter containing 0.15 kg of water with an initial temperature of 21.0°C. The bolt and the water then reach a final temperature of 25.0°C. If the metal has a specific heat capacity of 899 J/kg•°C, find the initial temperature of the metal.
The initial temperature of the metal bolt is 80.8 °C
We'll begin by calculating the heat absorbed by the water.
Mass of water (M) = 0.15 Kg Initial temperature (T₁) = 21 °CFinal temperature (T₂) = 25 °CChange in temperature (ΔT) = T₂ – T₁ = 25 – 21 = 4 °CSpecific heat capacity of water (C) = 4184 J/KgºCHeat absorbed (Q) =?Q = MCΔT
Q = 0.15 × 4184 × 4
Q = 2510.4 J
Finally, we shall determine the initial temperature of the metal bolt.
Heat absorbed by water = 2510.4 JHeat released by metal (Q) = –2510.4 JMass of metal (M) = 0.050 Kg Final temperature (T₂) = 25 °CSpecific heat capacity of metal (C) = 899 J/Kg°CInitial temperature (T₁) =?Q = MC(T₂ – T₁)
–2510.4 = 0.050 × 899 (25 – T₁)
–2510.4 = 44.95 (25 – T₁)
Clear bracket
–2510.4 = 1123.75 – 44.95T₁
Collect like terms
–2510.4 – 1123.75 = –44.95T₁
–3634.15 = –44.95T₁
Divide both side by –44.95
T₁ = –3634.15 / –44.95
T₁ = 80.8 °C
Thus, the initial temperature of the metal is 80.8 °C.
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A 4.0-mF capacitor initially charged to 50 V and 6.0-mF capacitor charged to 30 V are connected to each other with the positive plate of each connected to the negative plate of the other. what is the final charge of the 6.0-mF capacitor?
a. 20 mC
b. 8.0 mC
c. 10 mC
d. 12 mC
e. 230 mC
[tex]\huge\color{pink}\boxed{\colorbox{black}{Answer ☘}}[/tex]
12 mC
Explanation:We are given that...
[tex]C_{1} = 4mF \\ V_{1} = 50v \\ C_{2} = 6mF \\ V_{2} = 30v \\ \\ we've \: to \: find \: the \: final \: charge \: on \: the \: 6mF \\capacitor \:- \\ \\ we \: know \: that ,\: \\ Q = CV \\ \\ using \: the \: formula \: \\ Q_{1} = 4 \times 50 = 200mC \\ Q_{2} = 6 \times 30 = 180mC \\ \\ total \: charge , \: Q_{1} - Q_{2} = 200 - 180 = 20mC \\ \\ let \: V \: be \: the \: final \: potential \: \\ 4V + 6V = 20mC\\ 10V = 20mC \\ V = \frac{20}{10} = 2V \\ final \: charge \: Q = CV = 6 \times 2 = 12mC[/tex]
therefore,
✯ σptíσn ( d ) íѕ cσrrєct!hope helpful~
~Be Brainly!A wire that is 1.0 m long with a mass of 90 g is under a tension of 710 N. When a transverse wave travels on the wire, its wavelength is 0.10 m. What is the frequency of this wave?
Answer:
890 HzI hope you liked my answer. Thank You!
Two Blocks are connected by a massless rope over a massless,
frictionless pulley, as shown in the figure. The mass of block 2
is m2 = 10.1 kg, and the coefficient of kinetic friction
between block 2 and the incline is Mk = 0.200. The angle 0 of
the incline is 27.5º. If block 2 is moving up the incline at
constant speed, what is the mass mi of block 1?
The mass of block 1 will be 1.99 kg.The tension force is applied along the whole length of the wire, pulling energy equally on both ends.
What is tension force?The tension force is described as the force transferred through a rope, string, or wire as it is pulled by opposing forces.
Given that,
Mass of block 1=? kg
The coefficient of the kinetic friction,μ=0.200
Now consider the weight component in the uphill direction.The weight is found as;
[tex]\rm W=m_1gsin \theta[/tex]
The force is balanced in the vertical direction as;
[tex]\rm T=F_f-W[/tex]
When the force of friction is;
[tex]\rm F_F=\mu_k N[/tex]
[tex]\rm F_f=(m_1 gcos \theta)[/tex]
Substitute the value in the vertical balanced equation;
[tex]\rm T=m_1gsin(27.5)^0-\mu_kmgcos27.5^0[/tex]
[tex]\rm T-m_2g=0\\\\T=m_2g[/tex]
[tex]\rm (10.1) g=m_1g(0.699-0.2 \times(-0.714) ) \\\\ (10.1) g=m_1g (0.699+0.1428) \\\\\ (10.1) g= m_1 \times 0.8418 \\\\ m_1 =11.99 \ kg[/tex]
Hence the mass of block 1 will be 1.99 kg.
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In three to five sentences, identify the acid, base, conjugate acid, and conjugate base. Use patterns in the periodic table to explain why the substances you identified acted as the acid and the base in this reaction.
A conjugate acid is formed from the base by accepting a proton from the acid .
A conjugate base is obtained from the Brownstead - Lowry acid when it looses a proton while the conjugate acid is obtained from the Brownstead - Lowry base when it accepts a proton. In the Brownstead - Lowry sense, acid base reaction involves the loss or gain of a proton.
Consider the hypothetical reaction; AH + :B ⇄ BH + :A. The specie BH is the conjugate acid while the specie :B is the Brownstead - Lowry base . The specie :A is the conjugate base while the specie AH is the Brownstead - Lowry acid.
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A first order reaction is 25% completed in 1h minutes. Calculate the time required for its 50% completion.
How many valence electrons do most stable atoms have?
A) one
B) two
C) four
D) eight
Answer:
D) 8
Explanation:
Due to the octet rule the most stable atoms will have 8 valence electrons.
Which phrase describes the energy transformation that happens in a
generator?
A. Electrical energy into chemical energy
ООО
B. Electrical energy into mechanical energy
C. Chemical energy into electrical energy
O
D. Mechanical energy into electrical energy
SI
Answer:
Mechanical energy into electrical energy
Explanation:
Answer:
ExplanMechanical energy into electrical energy
SIation:
How is the çhocolate shell on the outside of the bar different from the ice cream on the inside?
Answer:
Cake Crunch (Enriched Wheat Flour [Bleached Flour, Niacin, Reduced Iron, Thiamine Mononitrate, Riboflavin, Folic Acid]), Sugar, Vegetable Shortening [Partially Hydrogenated Soybean and Cottonseed Oil], Salt, Sodium Bicarbonate, Artificial Flavor, Soy Lecithin, Soybean Oil, Coconut Oil, Sugar, Chocolate Liquor, ...
If a force of 50 Newton's was applied to an object with a mass of 5 kilograms, what will the object's acceleration be?
A force of 50 N was applied to an object with a mass of 5 kg, then the acceleration of the object will be 10 m/s².
What is Acceleration?The rate of change in an object's velocity with respect to time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.
Since acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is a vector quantity as well. The definition of acceleration is the change in velocity vector over a time interval divided by the time interval.
There are several types of acceleration :
Uniform AccelerationNon-Uniform AccelerationAverage AccelerationAccording to the question, the given values are :
Force, F = 50 N
Mass, m = 5 kg
Force = m × a
a = 50 / 5
a = 10 m/s².
Hence, the acceleration of the object will be 10 m/s².
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A physics professor leaves her house and walk along the sidewalk toward campus. After 5 min it starts to rain and she returns home. Her distance from her house as a function of time shown in figure: 1. At which of the labelled point is her velocity (a) zero? (b) Constant and positive? (c) constant and negative ? (d) Increasing in magnitude? (e) Decreasing in magnitude?
Answer: I think its zero-
I dont really know about this...
A swimmer who can swim in still water at a speed of 4km/h is swimming in a river. the river flows at a speed of 3km/h. calculate the speed of the swimmer relative to the river bank when she swims:- 1. downstream 2.upstream
Explanation:
Downstream: you just sum the magnitude of the velocity vectors:
3km/h + 4km/h = 7km/h
Upstream: difference of the magnitudes of the velocity vectors, in absolute value:
|3km/h - 4km/h| = 1km/h
An ammeter has azero offset error This fault will affect
Answer:
An ammeter has a zero offset error. This fault will affect. neither the precision nor the accuracy of the readings. only the precision of the readings.
The accuracy of the present measurement will be impacted by an ammeter's zero offset inaccuracy, but the precision of the measurement will not change.
What is resistance?Resistance is the obstruction of electrons in an electrically conducting material.
voltage = current ×resistance
How accurate measurement or reading is may be determined by its accuracy. The measurements will be off because of zero inaccuracy.
Thus, The precision of the measurement would not alter if an ammeter made a mistake with its zero offsets, but the accuracy of the current measurement would be decreased.
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2. What is the oxidation number of oxygen in most compounds?
A. 6
B.-2
C. 8
D.O
Answer:i am pro
kExplanation:
Someone please help with this question. From my knowledge the answer I believe to be correct is 4Em but I’m still not so sure. Please explain!
Answer choices:
1/2 Em
Em
2Em
4Em
Answer:
Explanation:
For an ideal spring over a frictionless horizontal surface, stored energy is only a function of the spring constant k and the distance of compression. The mass of the block doing the compressing is irrelevant
Energy stored in the first example is
Em = ½kd²
Energy stored in the second example is
E₂m = ½k(2d)² = 4(½kd²) = 4Em
So the second situation has four times as much stored spring potential energy as the first situation
4 Em is correct
Good job!
how big is earth
today
Answer:
3,958.8 mi
Explanation:
The force as a function of displacement of a moving object is presented by the graph. How much work is done when the object moves from 5 m to 8 m? *
Answer:
Explanation:
Work is the area under the curve between the limits
W = ½(5)(8 - 5) = 7.5 J
The work done when an object moves from 5 m to 8 m is 7.5 J.
Work done
The work done in moving an object from one point to another is equal to the product of force and displacement of the object.
W = Fs
Area under a curveThe work done on an object is equal to area under the curve
The area between point 5 m and 8 m = ¹/₂ x (8 - 5) x 5 = 7.5 J
Thus, the work done when an object moves from 5 m to 8 m is 7.5 J.
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6. A man with a mass of 75 kg standing on a skateboard is holding a medicine ball that has
a mass of 20 kg. If the man throws the ball to the left with a speed of 10 m/s,
a) What happens to the man on the skateboard?
b) What is the man's speed after throwing the ball?
Answer:
Explanation:
Conservation of momentum
a) the man and skateboard move to the right.
b) His speed depends on the reference frame of the ball speed.
If the speed of the ball is 10 m/s relative to ground and the man's final speed is v, then.
(75 + 20)(0) = 20(10) + 75(v)
v = -200/75 = -2.6666...
|v| = 2.7 m/s relative to the ground
This is the likely answer they are seeking.
If the ball is thrown with a speed of 10 m/s relative to the man
(70 + 20)(0) = 20(v + 10) + 75v
20v + 200 = - 75v
200 = - 95v
v = -2.105... m/s velocity or a speed of
|v| = 2.1 m/s relative to ground
and the ball has a velocity of 10 - 2.1 = 7.9 m/s relative to ground.
The graph below shows the variation with distance r from the nucleus of the square of the wave function, Ψ^2, of a hydrogen atom according to Schrödinger theory.
A. is most likely to be near a.
B. is always a.
C. is always less than a.
D. is always greater than a.
The region a represents the distance of the electron from the nucleus.
According to the wave mechanical model of the atom, the probability of finding an electron within a given volume element (representing the atom) is the square of the wave function psi.
Since a is the region in space where there is the greatest probability of finding the electron in the atom, it follows that distance of the electron form the atom is always a.
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a hairdryer is used for 600 seconds to dry hair. it has a 750 watt rating. how much work did the hairdryer do
The amount of work done by the hairdryer is equal to 450 Kilojoules.
Given the following data:
Time = 600 secondsPower = 750 wattTo determine the amount of work done by the hairdryer:
Mathematically, the work done by an object with respect to power and time is given by the formula:
[tex]Work\;done = power \times time[/tex]
Substituting the given parameters into the formula, we have;
[tex]Work\;done = 750 \times 600[/tex]
Work done = 450,000 Joules
Note: 1000 Joules = 1 Kilojoules.
Work done = 450 Kilojoules.
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SOMEONE PLEASE HELP MEEEEEEE
Answer:
The movement of Tectonic plates.
Explanation:
if the force acting on a body of mass 40 k.g is doubled by how much will the acceleration change
Answer:
Explanation:
Ignoring friction, the acceleration will double
F = ma
2F = m(2a)
the driver of a 2.0 × 10³ kg red car traveling on the highway at 45m/s slams on his brakes to avoid striking a second yellow car in front of him, which had come to of because locking ahead.After the brakes are applied a constant friction force of 7.5 × 10³ N acts on the car ignore air resistance.
a₎ Determine the least distance should the brakes be applied to avoid a collision with the other vehicle?
Answer:
Explanation:
a = F/m = 7500/2000 = 3.75 m/s²
v² = u² + 2as
s = (v² - u²) / 2a
s = (0² - 45²) / (2(-3.75))
s = 270 m
A block slides on a rough 45 degree incline. The coefficient of friction is µk what is the ratio of acceleration when the block accelerates down the incline to the acceleration when the block is projected up the incline
Answer:
[tex]\frac{a_{d}}{a_{i}} = \frac{(1 -mu)}{mu}[/tex]
= (1 - μ)/μ
Explanation:
Always draw a diagram!
Up the incline:
[tex]Fr_{max}[/tex] = maximum friction
[tex]Fr_{max}[/tex] = μk
k = R = mg.cos(45) = mg.sin(45)
Resolution of forces parallel to the slope:
F (Fp in the diagram) = force of propulsion
g = gravity
[tex]F - Fr_{max} = ma_{i}[/tex]
[tex]F -[/tex] μ.mg.cos(45) [tex]= ma_{i}[/tex]
Down the decline:
Resolution of forces:
[tex]mg.sin(45) - Fr_{max} = ma_{d}[/tex]
[tex]mg.sin(45) -[/tex] μ.mg.cos(45) [tex]= ma_{d}[/tex]
Then, find the ratio:
[tex]\frac{ma_{d}}{ma_{i}} = \frac{mg.sin(45) - mu.mg.cos(45)}{-F + mu.mg.cos(45)} \\\\ \frac{a_{d}}{a_{i}} = \frac{k - k.mu}{-F + k.mu} \\\\ = \frac{k(1 -mu)}{-F + k.mu}[/tex]
Potentially, there is no need to consider F in this situation, in which case:
[tex]\frac{a_{d}}{a_{i}} = \frac{k(1 -mu)}{k.mu} \\\\ = \frac{(1 -mu)}{mu}[/tex]
= (1 - μ)/μ
7. Which of the following explains how radiometric dating is used to estimate absolute
age.
a. By comparing how deep in the curst the radioactive material in a sample of rock
is, scientists can calculate the length of time since the rock formed.
b. By comparing the amount of organic material in a sample of rock, to the known
rate of decay of the parent rock, scientists can calculate the length of time since
the rock formed.
C. By comparing the amount of radioactive material in a sample of rock, to the
surrounding rocks, scientists can calculate the length of time since the rock
formed.
d. By comparing the amount of a radioactive material in a sample of rock, to the
know rate of decay of the parent rock, scientists can calculate the length of time
since the rock formed.
Answer:
d.
Explanation:
Radiometric dating is a method of dating geological/ archaeological specimens by determining the relative proportions of particular radioactive isotopes present in a sample. Carbon dating is a form of radiometric dating, but, in choice b, you're not comparing the carbon to the rock. One would compare ¹⁴C levels within the organic compound, just as one would compare radioactive isotope levels in a rock.
True or False. Father of a multitude" obeyed God's command to kill His son because the Ten Commandments had not yet been given.
Answer:
Explanation:
The father of the Multitude was Abraham. And he did precede the 10 commandments. But the story really has nothing to do with the 10 commandments.
He obeyed God's Command because it was God who issued it. Abraham had complete faith in God's ability to make things come out right. The sacrifice of Isaac was a test of faith.
I would advise you to answer true, but whoever wrote the question employed a twisted kind of logic. The sacrifice of Isaac had nothing to do with the 10 commandments. Thou Shalt not murder is not really covered by this circumstance.
So true might not be the correct answer. The question is very complex and does not lend itself to a simple True/ False answer.
This is physics and it says collision and elastic/inelastic i need help
The initial velocity of the 3250 Kg mass is 2.1 m/s. The distance covered by the larger mass in 5s is 4.7 cm.
In this problem, we have to apply the law of conservation of linear momentum. Note that;
Momentum before collision = Momentum after collision
m1u1 + m2u2 = m1v1 + m2v2
(2150 × 10) + (3250u1) = (2150 + 3250)5.22
21500 + 3250u1 = 5400 × 5.22
3250u1 = 28188 - 21500
u1 = 28188 - 21500/3250
u1 = 2.1 m/s
2) Again from the principle of conservation of linear momentum;
(0.40 × 3.5) + (0.60 × 0) = (0.40 × 0.70) + (0.60 × v2)
1.4 = 0.28 + 0.60v2
1.4 - 0.28 = 0.60v2
v2 = 1.87 cm/s
Using;
s = 1/2 ( u + v)t
s = 1/2(0 + 1.87) × 5
s = 4.7 cm
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What is the average momentum of Cart 1 during the entire time shown before
kg-m
the collision, in units .?
$
Note that the collision appears to take place somewhere between 0.5 s and 0.6
s (perhaps at 0.6 s exactly, but we cannot be sure), so we can safely say that
data up to and including 0.5 s is "before the collision."
The average momentum of Cart 1 during the entire time shown before the collision is 0.24 kgm/s.
The given parameters:
Mass of the cart 1 = 500 g = 0.5 kgThe average velocity of the cart 1 before collision is calculated as follows;
[tex]v = \frac{\Delta x}{\Delta t} \\\\v = \frac{0.55 - 0.31}{0.5 - 0} \\\\v = 0.48 \ m/s\\\\[/tex]
The average momentum of Cart 1 during the entire time shown before the collision is calculated as follows;
[tex]P = mv\\\\P = 0.5 \times 0.48\\\\P = 0.24 \ kgm/s[/tex]
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Make a generalization about Earth's magnetic field and its properties. In not more than 10 sentences.
Answer:
Earth's magnetic field (and the surface magnetic field) is approximately a magnetic dipole, with the magnetic field S pole near the Earth's geographic north pole (see Magnetic North Pole) and the other magnetic field N pole near the Earth's geographic south pole (see Magnetic South Pole). This makes the compass usable for navigation. The cause of the field can be explained by dynamo theory. A magnetic field extends infinitely, though it weakens with distance from its source. The Earth's magnetic field, also called the geomagnetic field, which effectively extends several tens of thousands of kilometres into space, forms the Earth's magnetosphere. A paleomagnetic study of Australian red dacite and pillow basalt has estimated the magnetic field to be at least 3.5 billion years old
3. Particles carrying no charge ____________
Answer:
Neutrons
Explanation: