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]
Velocity v (m/s)
11/A stone is dropped from the top of a 45 m high building, How
fast will it be moving when it reaches the ground? And what
lits velocity be?
Explanation:
given solution
h=45m v^2=u^2+2gh
g=10m/s^2 v^2=0^2+2×10m/s^2×45m
vi=0 v^2=900m^2/s^2
v=30A block of mass m=10 kg at rest slides down a rough incline plane of θ=30° and length l=5 m. The coefficient of kinetic friction between the block and the incline is μ_k=0.1. At the bottom of the plane the block continues to slide on a frictionless surface and hits a spring with spring constant k=100 N/m.
The speed of the block at point B = 6.36 m/s
Given data :
Mass ( m ) = 10 kg
Angle of inclination ( θ ) = 30°
Length of incline = 5 m
Determine the speed of the block at a point B on the incline
First step : Calculate the work done by frictional force
given that there is no friction on the horizontal plane. Vinclined = Vhorizontal
∴ Work done by frictional force ( Wf ) = F * L cos 180
= - ( μ_k * N ) L
= - (0.1 * 84.86 ) * 5 = - 42.4 Joule
where N = mg cos 30°
= 10 * 9.8 * 0.866 = 84.86
Next step : Calculate the speed of the block at point B
applying work energy theorem
Wf = ΔK.E + ΔP.E
= ( 1/2 mv² - 0 ) + ( 0 - mgh )
∴ - 42.48 = 1/2 mv² - mgh
1/2 mv² = mgh - 42.48
= 10 * 9.8 * 5 sin 30° - 42.4
v² = 40.52
V ( speed of the block at point B ) = 6.36 m/s
Hence we can conclude that the speed of the block at point B = 6.36 m/s
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Attached below is the complete question related to your question
Water pumps use electrical energy to create mechanical energy needed to move water.
A 1875 W water pump is plugged into a 110 V electrical outlet.
Answer:
n/a
Explanation:
this question is not feasible
A student connects a 21.0 V battery to a capacitor of unknown capacitance. The result is that 52.8 µC of charge is stored on the capacitor. How much energy (in J) is stored in the capacitor?
Answer:
1.108 × [tex]10^{-3}[/tex]J
Explanation:
v=21.0v
Q=52.8× [tex]10^{-6}[/tex]
E=?
V=E/Q
E=v ×Q
=21 ×52.8 ×[tex]10^{-6}[/tex]
=1108.8 ×[tex]10^{-6}[/tex]
E= 1.108 × [tex]10^{-3}[/tex]J
When a 1 is on the input of an inverter, what is the output?
Answer:
When the input to an inverter is high (1) the output is low (0); and when the input is low, the output is high.
At liftoff, the space shuttle Discovery has a constant acceleration of 16.4 ft/s/s with an initial velocity of 1,341 ft/s due to the rotation of the Earth. How long does it take to travel 100,000 ft?
From orbital speed formula which is the ratio of the circumference of the earth and the period of time, it will take 6097.6 seconds to travel 100,000 ft
Given that the space shuttle Discovery has a constant acceleration of 16.4 ft/s with an initial velocity of 1,341 ft/s due to the rotation of the Earth.
The period of time T it will require to travel round the a distance 100,000 ft can be calculated by using the formula below.
V = 2πr / T
Where 2πr = 100,000 ft
V = 16.4 ft/s
Substitute both in the formula above.
16.4 = 100000 / T
T = 100000 / 16.4
T = 6097.6 seconds
Therefore, it will take 6097.6 seconds to travel 100,000 ft
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7. Cellular respiration that uses oxygen is called
Answer:
Cellular respiration that uses oxygen is called Cellular respiration
Explanation:
Without oxygen, it's call fermentation.
How do you find the capacitance in this?
Answer:
Explanation:
parallel capacitances add directly
Series capacitances add by reciprocal of sum of reciprocals.
Ceq = [ C ] + [1 / (1/C + 1/C)] + [1 / (1/C + 1/C + 1/C)]
Ceq = [ C ] + [C / 2] + [C / 3]
Ceq = [ 6C/6 ] + [3C / 6] + [2C / 6]
Ceq = 11C/6
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)
If a force of 20kn acts on a circular rod of a diameter 10mm, calculate the stress of the rod
σ = F/A = F/ (πD²/4) = 20000 / (π0.10²/4) = 2.55 MN/m²
hey if you talk to me i will mark you as a brainliest and if you answer all my question
huh huh huh
Answer:
what will happen if i will answer ur questions?
Explanation:
is there gonna be a bad thing or a good thing
The intensity of a sound wave increases as the wave spreads out from the source of the sound. True or false
Answer:False
Explanation:
the intensity of the sound wave decreases with increasing distance from the source.
A 30.0 kg child, initially at rest, slides down a 2.0 m tall slide. The child reaches the bottom of the slide with a speed of 6 m/s. There is friction between the child and the slide. Write a Law of Conservation of Energy equation to represent the transfer of energy from the top of the slide to the bottom. a. b. Use the equation from part (b) to calculate the energy dissipated by friction between the slide and the child? (g = 9.81 m/s) = 13
Answer:
Explanation:
Total energy is constant
E = mgh + ½mv² + Fd
At the top of the slide, all energy is potential
E = mgh + 0 + 0
At the bottom of the slide, all potential energy has converted to kinetic and work of friction.
mgh = ½mv² + W
W = mgh - ½mv²
W = 30.0[(9.81)(2.0) - ½6²]
W = 48.6 J
13) What property of matter would be measured with this piece of equipment?
A) The mass of an apple
hing
)
By the temperature of a room
The volume of water in a glass.
D) The length of a piece of string.
Answer:
a
Explanation:
i took the test 100%
How do you measure a English saddle to fit your horses?
Answer:
measure the area in which the rider will sit on, then take those measurements to a person who crafts saddles, tell them the exact measurements. then you wait a while until he/she is done then put the saddle on the horse.
Explanation:
Answer:
Explanation:
The shape of the horse's withers is also a determining factor in choosing a saddle. An adjustable hoop saddle allows you to choose with finesse the opening of the tree at the height of the withers, in order to best adapt to each horse. It is the size of the arch that determines the opening of the saddle.
English saddles are the main riding saddles used in equestrian disciplines around the world: Show jumping, endurance, require specific designs to meet specific needs. For example, dressage saddles are designed to bring the rider closer to the horse, allowing him to communicate very precisely with his horse.
a ball of mass 0.15 kg is attached to one end of a string 1.10 m long. the ball moves in a horizontal circle with a speed of 12 m/s. determine the magnitude of the tension in the string
Answer:
[tex]19.64N[/tex]
Explanation:
Let's remember that if a mass describes a circle of radius [tex]l[/tex] with a constant speed of [tex]v[/tex], it has an angular velocity [tex]\omega=\frac vl[/tex]. in our case, our angular velocity will be of [tex]12/1.1= 10.91 rad/s[/tex].
Now that same mass will be subject of a centripetal acceleration [tex]a_c[/tex], caused of the tension of the string, equal to [tex]a_c=\omega^2l[/tex], which, in our situation, will be [tex](10.91)^2\times1.1=130.91 m/s^2[/tex]
We're almost done. We got mass, we got acceleration, the tension has to be their product: [tex]T= ma=130.91\times0.15=19.64N[/tex]
Assume each trial ( roll of cubes) represents 1000 years. Imagine that you found a rock sample was 25% Lokium and 75% DOL, how would the rock sample be given the half-life you figured out? Show your work
Assuming each trial represents 1000years, and rock samples were found, the rock sample will be given half-life of
The rock sample will be [tex]2000years[/tex] oldIsotopeWe know that the parent Isotope remaining is given by the expression
[tex]\frac{1}{2}^n[/tex]
where,
n = number of half lives passed
lokium IsotopeFrom the question, the parent Isotope remaining is [tex]25\%[/tex] lokium
[tex]0.25 = \frac{1}{4} = \frac{1}{2^2} = \frac{1}{2}^2[/tex]
Therefore,
[tex]\frac{1}{2}^2[/tex] means 2 half lives have passed.
If from the question,
1 half life = 1000years
Rock ageTherefore,
The rock sample's age = [tex]2*1000 = 2000years[/tex]
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2- What is the kinetic energy in (N.m) and Joules of a 4Kg bowling ball rolling down a
bowling lane at 10 m/s? compare this energy with that of a 250g baseball traveling 50
m/s. which object would hurt more if it hit you (i.e., which object has the greater kinetic
energy)?
Happy Holidays!
Recall the equation for kinetic energy:
[tex]\large\boxed{KE = \frac{1}{2}mv^2 (J)}}[/tex]
m = mass (Kg)
v = velocity (m/s)
KE = kinetic energy (Nm or J)
We can find the kinetic energy for both the bowling ball and baseball:
Bowling ball:
[tex]\large\boxed{KE = \frac{1}{2}(4)(10^2) = 200 J}[/tex]
Baseball:
[tex]\large\boxed{KE = \frac{1}{2}(.25)(50^2) = 312.5 J}[/tex]
Since 312.5 J > 200 J, the BASEBALL has the greater kinetic energy. Thus, it would exert a greater impact force than the bowling ball, so it would hurt more.
An astronaut uses a pendulum with a mass of 0.200 kg to measure the acceleration due to gravity on Planet X. He lifts the pendulum's mass a vertical height of 0.500 m and is able to determine that it gains 15.0 J of gravitational potential energy as it is lifted. Using this information, calculate the acceleration due to gravity (g) on Planet X
Answer:
Explanation:
PE = mgh
g = PE/mh
g = 15.0 / (0.200(0.500))
g = 150 m/s²
This is one strong astronaut if he can work in an environment where gravity is more than 15 times stronger than on earth.
What are the characteristics of high energy wave?
A. Low frequencies and short wavelengths.
B. High frequencies and long wavelengths.
C. Low frequencies and long wavelengths.
D. High frequencies and short wavelengths
Answer:
D. High frequency and short wavelengths.
Explanation:
If a wave is high in energy it will have a higher frequency.
High frequency = short wavelengths
How should an artistic statement be written?
ОА.
from your own perspective
OB.
in a non-factual, persuasive manner
O C.
as a lengthy and overly extensive essay
OD. by the artist alone with no outside critique
An artistic statement should be written from your own perspective.
What is an artistic statement ?An artist's statement, also known as an artist statement, is a written summary of their creative output. The brief essay serves as an explanation of and a defense of their own work for the spectator. As a result, it is didactic, descriptive, or reflective in nature and seeks to inform, connect with an artistic environment, and reveal the inspiration behind the work.
The writing created by the artist aims to contextualize, justify, extend, and/or explain their body of work. It situates—or tries to situate—the piece in relation to art history, art theory, the contemporary art scene, and the times. The statement also demonstrates that the artist is aware of their aims, their practice, its place within the parameters of art, and the debate that surrounds it.
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the distance between student home and school is 1.5 km what is the distance traveld bythe students in a week
Answer:
10.5k
Explanation:
1.5x7=10.5
A ball rolling down a hill with a speed of 8 m/s has 139 J of kinetic energy. What is it's mass in kg?
Explanation:
Velocity of ball (v) = 8 m/sKinetic Energy (K.E) = 139 JMass (m) = ?We know that,
• K.E = ½mv²→ 139 = ½ × m × (8)²
→ 139 = ½ × m × 64
→ 139 = 1 × m × 32
→ 139 ÷ 32 = m
→ 4.34 kg = m
Therefore, mass in kg is 4.34 kg.
A teacher took two latex balloons and blew them up with helium gas to the same size. She took one and labeled it Balloon A and placed it in a -15o C freezer. The second one she labeled BALLOON B, and she took it outside and tied it to the railing in the sun on a 30o C day. After a half hour, she had the students measure the circumference of each balloon. Which TWO outcomes do you predict the students will find and why?
Answer:
n
Explanation:
TWO outcomes can be predicted the students will find:
The size of balloon A becomes smaller.The size of balloon B becomes larger.What is the relation between temperature and volume of the gases?When a constant mass of gas is cooled, its volume falls, and when the temperature is raised, its volume grows. The volume of the gas rises by 1/273 of its initial volume at 0 °C for every degree of temperature rise.
In layman's words, the volume of a fixed mass of gas is exactly proportional to temperature at constant pressure.
The teacher took two latex balloons and blew them up with helium gas to the same size. As she placed Balloon A in a -15° C freezer, its temperature decreases and that's why, the size of balloon A becomes smaller. Again she placed Balloon B in the sun on 30° C day, its temperature increases and that's why, the size of balloon B becomes larger.
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The range of a Cannon ball fired horizontally from a laboratory table equals to 8/ 3 times the height of the table . what is the direction of the velocity of the projectile as it strikes the ground?
A,450 from the horizontal
B,600 from the horizontal
C,530 from the horizontal
D,370 from the horizontal
Theprojectile launch allows to find the correct answer for the question about the direction of the ball when it hits the ground is:
D) θ = 37º measured clockwise from the x-axis.
projectile launch is an application of kinematics where there is no acceleration on the horizontal axis and the acceleration on the vertical axis is the gravity acceleration.
The horizontal distance traveled until it reaches the ground is
x = v₀ₓ t
The height of the bullet is
y = y₀ + [tex]v_o_y[/tex] t - ½ g t²
The initial vertical velocity is zero and when it reaches the ground its height is zero.
0 = y₀ - ½ g t²
t = [tex]\sqrt{\frac{2y_o}{g} }[/tex]
We substitute
[tex]x = v_{ox} \ \sqrt{\frac{2y_o}{g} }[/tex]
They indicate that the distance is:
x = [tex]\frac{8}{3} \ y_o[/tex]
We substitute
[tex]\frac{8}{3} y_o = v_{ox} \sqrt{\frac{2y_o}{g} }[/tex]
[tex]v_{ox} = \frac{8}{3} \sqrt{\frac{y_o g}{2} }[/tex]
The vertical speed when reaching the ground is:
[tex]v_y = v_{oy} - g t \\v_y = - g t \\v_y = - g \sqrt{\frac{2y_o}{g} }[/tex]
Let's use trigonometry for the direction at the point of hitting the ground.
tan θ = [tex]\frac{v_y}{v_x}[/tex]
θ = tan⁻¹ ( [tex]- \frac{3}{8} \ \frac{\sqrt{2y_o/g}}{\sqrt{y_o g /2} }[/tex] )
θ = tan⁻¹ ( [tex]tan ^{-1} (- \frac{3}{8} \sqrt{4} )= tan^{-1 } \ (- \frac{3}{4} )[/tex]
θ = -36.9º
The negative sign indicates that the angle is clockwise from the x-axis.
In conclusion, using the projectile launch we can find the correct answer for the question about the direction of the bullet when it hits the ground is:
D) θ = 37º measured clockwise from the x-axis.
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Need help ASAP, 1 MC
Answer:
The first one is the only one that is true all the time
Explanation:
The second one may be true if friction is high enough.
The other three are false all the time
Please help me! Some people have proposed a new way to build houses in areas that are likely to experience tsunamis. In this design, a house wouldn’t have solid walls on all four sides. Instead, some of the wall areas would be replaced by substances that water can travel through quickly, as shown in the diagram. How would this design help a house survive a tsunami? What drawbacks might there be to this design?
Answer:
I think some drawbacks are that since there are no solid walls meaning it is weak and if murphy's law is in place, the water will destroy the substance. Tsunami waves also happen very quickly so even if the water can travel thru the substance quickly, it probably won't be quick enough. This design could help if the wave is smaller because less destruction would occur.
Explanation:
yeah
Q1) Assertion : a vector can be resolved into maximum two components
Reason : in projectile motion the velocity is resolved into vertical and horizontal components
a) Both A and R are correct; R is the correct explanation of A
b) Both A and R are correct; R is not correct explanation of A
c) A is correct; R is not correct
d) A is not correct; R is correct
Q2) Assertion : speed is constant in uniform circular motion
Reason : acceleration is constant in uniform circular motion
a) Both A and R are correct; R is the correct explanation of A
b) Both A and R are correct; R is not correct explanation of A
c) A is correct; R is not correct
d) A is not correct; R is correct
Answer:
Explanation:
Q1) d) A is not correct; R is correct (sort of) but is not the reason for A.
A vector may be resolved into an infinite number of components.
Breaking a projectile motion into the vertical and horizontal components is the EASIEST way to solve it because acceleration can be assumed to be constant in both directions. Zero for horizontal and g(ravity) in the vertical. However it is not the ONLY way to do it. Other ways are much more complex.
Q2) a) Both A and R are correct; R is the correct explanation of A (sort of)
A is correct. Speed is constant in uniform circular motion.
R is correct if you call CENTRIPETAL acceleration constant. It is only constant in magnitude. The direction is always changing as the vector always points toward the center of rotation.
5. Which statement about the acceleration of an object is corr
a. The acceleration of an object is directly proportional to t
external force acting on the object and inversely propo
mass of the object.
b. The acceleration of an object is directly proportional to
external force acting on the object and directly propor
mass of the object.
c. The acceleration of an object is inversely proportional
external force acting on the object and inversely prop
mass of the object.
d. The acceleration of an object is inversely proportiona
external force acting on the object and directly propo
mass of the object.
Answer:
a
Explanation:
you will find out that an object that has more weight requires more energy to move than the one with less weight
American Football originated from which two sports?
A) Soccer and Rugby
B) Rugby and Basketball
C) Cricket and Soccer
D) Soccer and Volleyball
Answer:
b rugby and basketball
Explanation:
basket ball was made by a white man
American Football originated from Soccer and Rugby. Hence, option (A) is correct.
What is American Football?American football, sometimes known as gridiron, is a team sport played by two teams of eleven players on a rectangular field with goalposts at each end. It is known simply as football in the United States and Canada. The defense, the team without the ball, seeks to halt the offense's movement and seize control of the ball for themselves.
The offence, the team in possession of the oval-shaped football, attempts to advance down the field by running with the ball or throwing it. The offence is awarded a new set of four downs to resume the drive if they successfully gain at least 10 yards in four downs or plays. If they fail, they forfeit the ball to the defense.
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