Learning Goal: To understand the concept of moment of inertia and how it depends on mass, radius, and mass distribution.
In rigid-body rotational dynamics, the role analogous to the mass of a body (when one is considering translational motion) is played by the body's moment of inertia. For this reason, conceptual understanding of the motion of a rigid body requires some understanding of moments of inertia. This problem should help you develop such an understanding.
The moment of inertia of a body about some specified axis is I = cmr^2, where c is a dimensionless constant, m is the mass of the body, and r is the perpendicular distance from the axis of rotation. Therefore, if you have two similarly shaped objects of the same size but with one twice as massive as the other, the more massive object should have a moment of inertia twice that of the less massive one. Furthermore, if you have two similarly shaped objects of the same mass, but one has twice the size of the other, the larger object should have a moment of inertia that is four times that of the smaller one.
Two spherical shells have their mass uniformly distrubuted over the spherical surface. One of the shells has a diameter of 2 meters and a mass of 1 kilogram. The other shell has a diameter of 1 meter. What must the mass m of the 1-meter shell be for both shells to have the same moment of inertia about their centers of mass?
Answer:
m₂ = 4 kg
Explanation:
The moment of inertia is defined by
I = ∫ r² dm
for bodies with high symmetry it is tabulated, for a spherical shell
I = 2/3 m r²
in this case the first sphere has a radius of r₁ = 2m and a mass of m₁ = 1 kg, the second sphere has a radius r₂ = 1m.
They ask what is the masses of the second spherical shell so that the moment of inertia of the two is the same.
I₁ = ⅔ m₁ r₁²
I₂ = ⅔ m₂ r₂²
They ask that the two moments have been equal
I₁ = I₂
⅔ m₁ r₁² = ⅔ m₂ r₂²
m₂ = (r₁ / r₂) ² m₁
let's calculate
m₂ = (2/1) ² 1
m₂ = 4 kg
Which statement best describes covalent bonding?
A. two nonmetal atoms share electrons between them
B. many atoms give up electrons that can move among the atoms
C. two metal atoms share electrons between them
D. a metal atom transfers electrons to a nonmetal atom
Suppose that you make a series RC circuit with a capacitor and a known resistor that has a 5% tolerance: R= 5.20 ± 0.26kΩ. You plan is to measure the time constant of the circuit in order to determine the value of the capacitor. You do ten trials of your experiment and measure the time constant each time, and then you calculate the average and standard error of the ten results to determine that τ= 2.150 ± 0.002s.
Which of the following is the best estimate of the uncertainty on your determination of the value of your capacitor?
a. 1%
b. 0.1%
c. 5%
Answer:
correct answer is C
Explanation:
The time constant of an RC circuit is
τ = RC
so to find the capacitance
C = τ/ R
C = 2.150 / 5.20 10³
C = 4.13 10⁻⁴ F
to find the error we use the worst case
ΔC = | [tex]|\frac{dC}{d \tau }| \ \Delta \tau + | \frac{dC}{dR} | \ \Delta R[/tex]
the absolute value guarantees that we find the worst case, we evaluate the derivatives
ΔC = 1 /R Δτ + τ/R² ΔR
the absolute values of the errors are
Δτ = 0.002 s
ΔR = 0.3 kΩ
we substitute
ΔC = 0.002 /5.20 10³ + 2.150/(5.20 10³)² 0.3 10³
ΔC = 3.8 10⁻⁷ + 1.74 10⁻⁵
ΔC = 1.77 10⁻⁵ F
the uncertainty or error must be expressed with a significant figure
ΔC = 2 10⁻⁵ F
the percentage error is
Er% =[tex]\frac{\Delta C}{C} \ 100[/tex]
Er% = [tex]\frac{2 \ 10^{-5} }{ 4.13 \ 10^{-4} } \ 100[/tex]
Er% = 4.8%
the correct answer is C
An inventor claims to have developed a power cycle capable of delivering a net work output of 400 kJ for an energy input by heat transfer of 1200 kJ. The system undergoing the cycle receives heat from a source of 550K and rejects heat to a sink of 350K. Determine if this is a valid claim.
Answer: Valid claim
Explanation:
Given
Work output is [tex]W=400\ kJ[/tex]
Work input is [tex]Q=1200\ kJ[/tex]
The temperature of the source [tex]T_h=550\ K[/tex]
The temperature of the sink is [tex]T_l=350\ K[/tex]
Efficiency is given by
[tex]\eta =\dfrac{\text{W}}{\text{Q}}\times 100[/tex]
Insert the values
[tex]\Rightarrow \eta=\dfrac{400}{1200}\times 100\\\\\Rightarrow \eta=\dfrac{100}{3}\\\\\Rightarrow \eta=33.3\%[/tex]
For ideal cycle it is
[tex]\Rightarrow \eta=\dfrac{T_h-T_l}{T_l}\times 100\\\\\Rightarrow \eta=\dfrac{550-350}{550}\times 100\\\\\Rightarrow \eta=36.36\%[/tex]
The efficiency of the cycle is less than the ideal situation, therefore, it is valid claim.
Science questions!! Please help!!
Post Assessment on Investigating the Immune System
please help!! Please choose the right answers!! Dont guess if you dont know the answers!!
Please please help me please please help please please help me please
Answer:
Electromagnetic waves do not require any medium to travel whereas mechanical waves must have a medium to propagate.
So, Basically, it is B I believe.
Hope It Helps!
4. When Tina went for a walk, she covered the first 300 m in 100 s and the next 200 m in 150
s. What was Tina's average speed?
A 1 m/s
B 2 m/s
C 3 m/s
D 5 m/s
2m/s
300m+200m=500m
100s+150s=250s
500m/250s= 2m/s
The average speed of tina will be 2m/s.
We have Tina who went for a walk.
We have to determine her average speed.
What is Average Speed ?Average speed is the rate of change of displacement with respect to time.
v(avg) = Δx/Δt
According to the question -
Total Distance covered = d = 500 m
Total time taken = t = 250 s
Average speed = 500/250 = 2 m/s
Hence, the average speed of tina will be 2m/s.
To solve more questions on Average speed, visit the link below-
https://brainly.com/question/22982282
#SPJ2
What is the centripetal force for a roller coaster if the mass is 10 kg and the normal force is 25 N?
Answer:
Fc = 123 Newton
Explanation:
Net force can be defined as the vector sum of all the forces acting on a body or an object i.e the sum of all forces acting simultaneously on a body or an object.
Mathematically, net force is given by the formula;
[tex] Fnet = Fapp + Fg[/tex]
Where;
Fnet is the net force.
Fapp is the applied force.
Fg is the force due to gravitation.
Given the following data;
Normal force = 25N
Mass = 10kg
To find the centripetal force;
From the net force, we have the following formula;
Fc = N + mg
Where;
Fc is the centripetal force.
N is the normal force.
mg is the the weight of the object.
Substituting into the formula, we have;
Fc = 25 + 10(9.8)
Fc = 25 + 98
Fc = 123 Newton
A weight lifter lifts a 1470N barbell above his head from the floor the a height of 2m. he holds the barbell there for 5 sec. how much work does he do?
Answer:
Workdone = 2940 Nm
Explanation:
Given the following data;
Force = 1470 N
Distance = 2m
Time = 5 seconds
To find the work done;
Mathematically, workdone is given by the formula;
Workdone = force * distance
Substituting into the formula, we have;
Workdone = 1470 * 2
Workdone = 2940 Nm
If two speeds are in exact opposite directions, the combined speed is the difference in the speeds.
A. True
B. False
Philosophy:The Big Picture Unit 7
Why does Marx’s workers’ paradise resolve the problems of capitalism?
I KNOW C IS INCORRECT SO CHOOSE OUT OF A,B OR D
A. Everything is free, and no one has to work.
B. Workers are divided into three classes, much like in Plato’s ideas.
C. There is no currency in the paradise so no economic problems.
D. People work for their own good instead of a factory owner’s.
Answer:
B
Explanation:
If you cross of what you don't think are the answers then it makes it easier to narrow it down to what the answers are.
Hope this helps!
Two creatures sit on a horizontal frictional rotating platform. The platform rotates at a constant speed. The creatures do not slip off as it rotates.
ASSUME:
Red has a mass of 5 kg
Red is 1.5 m from the center
Red has a speed of 9 m/s
Blue has a mass of 25 kg
Blue has a speed of 1.8 m/s
The force of friction on Red is EQUAL to the force of friction on Blue
DETERMINE:
How far from the center is Blue
Answer:
M v^2 / R = centripetal force
For Red: M v^2 / R = 5 * 9^2 / 1.5 = 270
For Blue M v^2 / R = 270 = 25 * 1.8^2 / Rb
So Rb = 25 * 1.8^2 / 270 = .3 m
A film of oil lies on wet pavement. The refractive index of the oil exceeds that of the water. The film has the minimum nonzero thickness such that it appears dark due to destructive interference when viewed in visible light with wavelength 678 nm in vacuum. Assuming that the visible spectrum extends from 380 to 750 nm, what is the longest visible wavelength (in vacuum) for which the film will appear bright due to constructive interference
Answer:
Explanation:
For destructive interference , the condition is
2μt = nλ
2μt = n x 678
For constructive interference , the condition is
2μt = (2n+1)λ₁ /2
n x 678 = (2n+1)λ₁ /2
λ₁ = 1356 n / ( 2n + 1 )
λ₁ = 1356 / ( 2 + 1/n )
For longest wavelength , denominator should be smallest or n should be largest . The longest value of n is infinity so
λ₁ = 1356 / 2
= 678 nm .
Biodiversity decline poses a problem in an ecosystem because
Answer:
Biodiversity decline continues due to a rapidly expanding human population. Habitat is damaged in order to meet growing needs for agriculture, urban development, water and materials. Fish, wildlife and plants are overharvested, despite mounting evidence that many harvesting practices are unsustainable.
How many tons and pounds (like together, not two different numbers) is 9,920 pounds? Please help,
Answer:
About 5 tons (4.96)
Suppose a 118kg watermelon is held 5m above the ground before sliding along a frictionless ramp to the ground. How high above the ground is the watermelon at the moment it's kinetic energy is 4,610J
This question involves the concepts of kinetic energy, potential energy, and the law of conservation of energy.
The watermelon is "1.02 m" above the ground.
The total energy of the watermelon can be found by its potential energy at the highest point:
Total Energy = mgh
where,
m = mass = 118 kgg = 9.81 m/s²h = height = 5 mTherefore,
Total Energy = (118 kg)(9.81 m/s²)(5 m)
Total Energy = 5787.9 J
LAW OF CONSERVATION OF ENERGYNow, according to the law of conservation of energy, at the given point:
Total Energy = Kinetic Energy + Potential Energy
5787.9 J = 4610 J + mgh'
[tex]h'=\frac{5787.9\ J-4610\ J}{(118\ kg)(9.81\ m/s^2)}[/tex]
h' = 1.02 m
Learn more about the law of conservation of energy here:
https://brainly.com/question/2264339
The amount of energy for a coulomb of charge at one end of a conductor is 40 joules. The amount of energy for a coulomb of charge at the other end of the conductor is 20 joules. The potential difference across the ends of the conductor is ______.
A.) 60 joules per coulomb
B.) 60 joules
C.) 20 joules per coulomb
D.) 20 joules
A box proceeds along the x-axis and the figure below shows a record of its velocity as a function of time. Every grid line along the vertical axis corresponds to 2.00 m/s and each gridline along the horizontal axis corresponds to 0.500 s. (Enter your answer in m/s^2. Indicate the direction with signs of your answers. Note that t=0 at the intersection of the axes.) a) Determine the average acceleration of the box in the time interval t=0 to t=2.50 s. b) Determine the average acceleration of the box in the time interval t=2.50 s to t=7.50 s. c) Determine the average acceleration of the box in the time interval t=0 to t=10.0 s
Answer:
The answer is "[tex]\bold{0, 12.8 \ \frac{m}{s^2}, and \ 6.4 \ \frac{m}{s^2}}[/tex]"
Explanation:
For point a:
The average time interval acceleration for the box [tex]t = 0\ to\ t = 250 \ s:[/tex]
[tex]\to \alpha_{0 \ to \ 2.50}=\frac{v_f - v_i}{t_f-t_i}=\frac{0-0}{2.50-0}=0[/tex]
For point b:
The average time interval acceleration for the box
[tex]t = 250 \ s\ to\ t = 750 \ s :[/tex]
[tex]\to \alpha_{2.50 \ to \ 7.50}=\frac{v_f - v_i}{t_f-t_i}=\frac{32-(-32)}{7.50-2.50}=12.8 \ \frac{m}{s^2}[/tex]
For point c:
The average time interval acceleration for the box [tex]t = 0\ to \ t = 10 \ s :[/tex]
[tex]\to \alpha_{2.50 \ to \ 7.50}=\frac{v_f - v_i}{t_f-t_i}=\frac{32-(-32)}{10-0}=6.4 \ \frac{m}{s^2}[/tex]
Directions: Fill in the blank with the correct word. Choose from the list of possible answers in the word bank below:
atoms
compound
element
heterogeneous
homogeneous
mixture
molecule
particles
solution
suspension
1. An _______________ is made up of just one kind of atom.
2. Matter is made up of tiny _______________.
3. In a mixture called a ________________ the particles are larger and can settle out.
4. A _______________ of water is made up of two hydrogen atoms and one oxygen atom.
5. Two or more elements chemically combined form a _______________.
6. _______________ are the building blocks of matter.
7. Seawater is an example of a _______________ mixture because it is the same throughout.
8. Vegetable soup is an example of a _______________.
9. In a _______________ one substance is dissolved in another.
10. A mixture that is not the same throughout is called a _______________ mixture.
Answer:
1).atoms (3). mixture. (5). Element
2). particles (4). molecules (6). suspension
Explanation:
(7). Homogeneous (8). Heterogeneous
(9). compound (10). solutions
A ball is kicked at 10.4 m/s at an angle of 32 degrees to the horizontal
how long (time) is the ball in the air?
find the horizontal displacement (range) of the ball
Answer:
3M/S
Explanation:
HELP ME PLEASEEEEEEEEEEEEEE
Answer:
probably won't help now but the answer is the 4th one lol
Explanation:
When silver nitrate and beryllium chloride react, silver chloride and beryllium nitrate form. What are the coefficients in this equation? (Note: Be sure to keep the reactants and products in the same order that they appear in the question.)
A. 2,1,1,2
B. 1,2,2,1
C. 1,2,1,2
D. 2,1,2,1
Answer:
D. 2,1,2,1
Explanation:
The equation of the reaction is; 2AgNO3 + BeCl2 + ---------》2AgCl + Be(NO3)2
The rule applied in balancing chemical reaction equation is that the number of atoms of each element on the reactants side must be the same as the number of atoms of the same element on the products sides.
If this rule is properly applied to the reaction between silver nitrate and beryllium chloride to form silver chloride and beryllium nitrate , the coefficients in the equation are; 2,1,2,1
Which of the following does NOT create a mechanical wave? Text to speech
A. a shaking rope
B. a guitar being played
C. dropping a rock in a pond
D. light coming through a window
Answer:
light coming through a window
NO LINKS PLEASE; On the calendar, the full moon is shown happening on the eleventh of the month. What moon would you see around the date shown with the question mark?
First Quarter
New Moon
Waxing Crescent
Waning Gibbous
Wanning gibbous
hope it helps u
Plz mrk me brainlest
Identify and describe one past geologic process that formed copper ore deposits.
Answer:
tornado and land
Explanation:
The ratio of carbon-14 to nitrogen-14 in an artifact is 1:7. Given that the half-
life of carbon-14 is 5730 years, how old is the artifact?
Definitely will be giving brainliest!! Thanks!!
Answer:
17,190 years old
Explanation:
A p e x
In a Young's double-slit experiment the separation distance y between the second-order bright fringe and the central bright fringe on a flat screen is 0.0176 m, when the light has a wavelength of 425 nm. Assume that the angles are small enough so that is approximately equal to . Find the separation y when the light has a wavelength of 614 nm.
Answer:
Y = 0.0254 m = 25.4 mm
Explanation:
The formula for the fringe spacing in Young's Double-slit experiment is given by the following formula:
[tex]Y = \frac{\lambda L}{d}[/tex]
where,
Y = fringe spacing = 0.0176 m
λ = wavelength = 425 nm = 4.25 x 10⁻⁷ m
L = Distance between screen and slits
d = slit separation
Therefore,
[tex]\frac{0.0176\ m}{4.25\ x\ 10^{-7}\ m} = \frac{L}{d}\\\\\frac{L}{d} = 41411.76[/tex]
Now, for:
λ = 614 nm = 6.14 x 10⁻⁷ m
[tex]Y = (6.14\ x\ 10^{-7}\ m)(41411.76)\\[/tex]
Y = 0.0254 m = 25.4 mm
The volume of a piece of rock was 18.0 cm^3. The student measured the mass of the piece of rock as 48.6 g. Calculate the density of the rock in g/cm^3.
Answer:
Density of rock piece = 2.7 g/cm³
Explanation:
Given:
Volume of rock piece = 18 cm³
Mass of rock piece = 48.6 gram
Find:
Density of rock piece
Computation:
We know relation between density, mass and volume,
Density = Mass / Volume
Density of rock piece = Mass of rock / Volume of rock
Density of rock piece = 48.6 / 18
Density of rock piece = 2.7 g/cm³
arcsin 0.9331 in degrees
Answer:
68.9233231661
Explanation:
Just put it into your calculator, shift sin should do it but it will come up like this: [tex]sin^{-1}[/tex] which is the same as arcsin
Match these items.
1. effect observed when light from an object in cool air passes through warm air
2. line perpendicular to a surface
3. splitting of light into its component colors angle of incidence
4. alignment of light into a single vibrational direction
5. larger angle as light passes from air to water
6. cause of the sky's color
7. bouncing of light rays reflection
8. bending of light between media
9. ratio of speeds of light
10. inability of light to escape a low-velocity medium due to a large angle of approach refraction
a. scattering
b.dispersion
c.angle of incidence
d.index of refraction
e.mirage
f.reflection
g.normal
h.total inertial reflection
i.polarization
j.refraction
Answer:
1. effect observed when light from an object in cool air passes through warm air
→ h. total internal reflection
2. line perpendicular to a surface
→ g. normal.
3. splitting of light into its component colors angle of incidence
→ b. dispersion.
4. alignment of light into a single vibrational direction
→ i. polarization
5. larger angle as light passes from air to water
→ c. angle of incidence
6. cause of the sky's color
→ f. reflection
7. bouncing of light rays reflection
→ f. reflection
8. bending of light between media
→ j. refraction.
9. ratio of speeds of light
→ d. index of refraction.
10. inability of light to escape a low-velocity medium due to a large angle of approach refraction
→ scattering.