A 2.12 kg hollow cylinder with inner radius 0.28 m and outer radius 0.57 m rolls with- out slipping when it is pulled by a horizontal string with a force of 33.3 N , as shown in the diagram below 2.12 kg 33.3 N 0.57 m- 3 0.28 m What is the acceleration of the cylinder's center of mass ? Its moment of inertia about the center of mass is Answer in units of 1 2 m(R out ^ 2 +R in ^ 2 ); m / (s ^ 2) .
Answers
The first step is to find the net torque on the cylinder. Since the cylinder is rolling without slipping, the friction force between the cylinder and the ground produces no torque. Therefore, the only torque is due to the tension in the string. The torque due to the tension is given by:
τ = rFsinθ
where r is the radius of the cylinder (in this case, we use the average radius R = (R_out + R_in)/2), F is the tension force, and θ is the angle between the force and the lever arm (which is perpendicular to the cylinder's axis). Since the force is horizontal, θ = 90° and sinθ = 1. Therefore:
τ = RF
Next, we can use Newton's second law for rotational motion, which states that the net torque is equal to the moment of inertia times the angular acceleration:
τ = Iα
where I is the moment of inertia about the center of mass and α is the angular acceleration. Since the cylinder is rolling without slipping, the linear acceleration a of the center of mass is related to the angular acceleration by:
a = Rα
Substituting these equations, we get:
RF = I(Rα)
a = Rα
Solving for α, we get:
α = F/(I/ R)
where I is the moment of inertia about the center of mass, which can be found using the formula for a hollow cylinder:
I = 1/2m(R_out^2 + R_in^2)
Substituting the given values, we get:
I = 1/2(2.12 kg)(0.57 m^2 + 0.28 m^2) = 0.755 kgm^2
R = (0.57 m + 0.28 m)/2 = 0.425 m
Substituting these values, we get:
α = (33.3 N)/(0.755 kgm^2/0.425 m) = 184.6 rad/s^2
Finally, we can use the equation a = Rα to find the linear acceleration:
a = (0.425 m)(184.6 rad/s^2) = 78.5 m/s^2
Therefore, the acceleration of the cylinder's center of mass is 78.5 m/s^2, and the answer in the specified units is:
78.5 m/s^2 = 78.5/(1/2(0.755 kg)(0.57^2 m^2 + 0.28^2 m^2)) m/s^2 = 0.341 m/(s^2).
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Related Questions
give scientific reasons when the body falls freely to the ground its motion as the uniform acceleration
Answers
Answer:
When an object falls freely to the ground, its acceleration is uniform. Hint: When an object falls freely on the ground, the force of the gravity works on it. So the acceleration on the object is the acceleration due to gravity. So the acceleration is uniform on the freely falling body.
What role do decisions play in wellness?
Answers
Answer: If you make certain decisions like changing your diet (for good or worse) increasing physical activity, or playing more video games, things like these can affect your wellness and health for the worse or better.
Answer:
health is the answer to what the role is play in wellness
how do light dependent reactions differ from the calvin cycle
Answers
Light-dependent reactions involve the conversion of light energy into chemical energy, while the Calvin cycle is a series of biochemical reactions that utilize the chemical energy produced in the light-dependent reactions to convert carbon dioxide into glucose.
During light-dependent reactions, light energy is absorbed by chlorophyll and other pigments in the thylakoid membranes of chloroplasts, resulting in the production of ATP and NADPH. These energy-rich molecules are then used in the Calvin cycle. The Calvin cycle, also known as the dark reactions or the light-independent reactions, takes place in the stroma of chloroplasts. It uses ATP and NADPH, along with carbon dioxide, to produce glucose through a series of enzymatic reactions.
In summary, light-dependent reactions capture light energy and convert it into chemical energy, while the Calvin cycle uses that chemical energy to fix carbon dioxide and produce glucose. These two processes work together in photosynthesis to convert light energy into usable chemical energy for the plant.
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Which of the following metals is the most important in atomic research
Uranium
Beryllium
Silver
Copper
Answers
Answer:
Uranium
Explanation:
The most important in atomic research is Uranium, Uranium Can be used as fuel for nuclear power plants and the nuclear reactors that run naval ships and submarines, so option A is correct.
What are atoms?The atom is the smallest unit of matter that may be divided without generating particles with an electrical charge. Additionally, it is the tiniest material with characteristics similar to chemical elements. As a result, the atom acts as the basic building block of chemistry.
Space makes up the majority of an atom. The rest is made up of a positively charged nucleus made up of protons and neutrons that are surrounded by a cloud of negatively charged electrons. The nucleus is small and dense when compared to electrons, which are the lightest charged particles in nature. Electric forces, link electrons to the nucleus of atoms, causing them to be drawn to any positive charge.
Uranium that has been "enriched" to have a higher concentration of U-235 can power nuclear power plants, and It can also be applied to nuclear weapons.
Therefore, uranium is the most important in atomic research.
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why do blazars, quasars, and double radio sources seem to have different and distinct properties, if they are caused by the same process?
Answers
Blazars, quasars, and double radio sources appear to have different and distinct properties despite being caused by the same process, which is the accretion of matter onto a supermassive black hole at the center of a galaxy.
The variation in properties can be attributed to the orientation of the objects with respect to the observer. Blazars are a subclass of quasars, and their emission is highly beamed towards us due to a favorable alignment, resulting in intense and variable radiation across the electromagnetic spectrum. This beaming effect causes blazars to appear brighter and exhibit rapid fluctuations compared to other quasars. On the other hand, quasars are more commonly observed as bright, distant objects emitting substantial amounts of radiation, but without the extreme variability of blazars.
Double radio sources, such as radio galaxies, are a different manifestation of the same process. They occur when two jets of relativistic particles are ejected from the vicinity of the supermassive black hole, resulting in extended radio emission. The properties of double radio sources depend on factors such as the power of the jets, their orientation, and the surrounding environment. These sources can exhibit a wide range of morphologies, including symmetrical lobes, double-lobed structures, and complex radio structures, which differ from the compact and highly variable emissions seen in blazars.
While blazars, quasars, and double radio sources arise from the same underlying mechanism of accretion onto a supermassive black hole, their distinct properties emerge due to the orientation of the emitting regions, the beaming effect in blazars, and the formation of extended radio structures in double radio sources.
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Maude worked as a lead animator in an animation company. However, she could not exercise her freedom while working on projects because she was bound by the decisions made by the company. Fed up with this, Maude quit her job and started an independent animation firm where she accepts only those projects that allow her a free rein in terms of creativity. In the given scenario, Maude most likely started her own firm because it offered _____.
Answers
In the given scenario, Maude most likely started her own firm because it offered independence.
What is the main motivation behind people choosing to start their own businesses?
What you may think is not what drives entrepreneurs to launch their own enterprises. The freedom, satisfaction, and flexibility that being their own boss affords is the main motivation for the majority of people.
Many business owners decide to launch their ventures alone because they desire complete control and because coordination is easier.
Every method for beginning a business has advantages and disadvantages. The appropriate type of ownership will be determined by a number of variables, including the business's industry, capital needs, owners' liability for profits, regulatory requirements, business continuity, and transferability of interests, among others.
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Light rays from a candle flame are incident on a convex mirror. After reflecting from the mirror, these light rays converge and form a real image diverge and form a virtual image diverge and form a real image 1 converge and form a virtual image
Answers
When light rays from a candle flame are incident on a convex mirror, they diverge and form a virtual image. A convex mirror is characterized by its reflective surface that curves outward, causing light rays to spread out upon reflection. This spreading out of light rays results in the formation of a virtual image.
A virtual image is an image that cannot be projected onto a screen or captured on a surface. It appears to be behind the mirror and is formed by extending the diverging rays backward. In the case of a convex mirror, the virtual image is always upright and reduced in size compared to the object.
The formation of a virtual image in a convex mirror is a result of the mirror's shape, which causes light rays to diverge. This property makes convex mirrors useful in applications such as rear-view mirrors in vehicles, where a wide field of view is necessary.
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what is the force felt by a doubly ionized particle in a 2,000-n/c electric field? (note: the charge of an electron is e = 1.6 × 10−19 c.)
Answers
The force felt by a doubly ionized particle in a 2,000 N/C electric field is calculated by using Coulomb's law of electrostatics, which is found to be 6.4 × 10^-16 N.
According to Coulomb's law of electrostatics, the force (F) acting on a charged particle due to an electric field (E) is given by F = q x E, where F is the force, q is the charge of the particle, and E is the electric field intensity.
To calculate the force felt by a doubly ionized particle in a 2,000 N/C electric field, we need to first find the charge of the particle.
The charge of an electron is e = 1.6 × 10−19 C.
Since the particle is doubly ionized, its charge will be 2e = 3.2 × 10−19 C.
Now we can use the formula for force F = q x EF = 3.2 × 10^-19 C × 2,000 N/C = 6.4 × 10^-16 N.
Therefore, the force felt by a doubly ionized particle in a 2,000 N/C electric field is 6.4 × 10^-16 N.
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The half-life of radium-226 is 1590 years. (a) A sample of radium-226 has a mass of 100mg. Find a formula for the mass of the sample that remains after t years. (b) Find the mass after 1000 years correct to the nearest milligram. (c) When will the mass be reduced to 30mg ?
Answers
The formula for the mass remaining after t years for a sample of radium-226 with an initial mass of 100mg is given by \($M(t) = 100 \times 0.5^{t/1590}$\). After 1000 years, the mass is approximately 87mg. The mass will be reduced to 30mg after approximately 2167 years.
(a) The decay of radium-226 follows an exponential decay model, where the amount of radium remaining decreases by half every 1590 years. The formula for the mass remaining after t years can be derived using the half-life concept. Let M(t) represent the mass remaining after t years, then the equation can be written as \($M(t) = 100 \times 0.5^{t/1590}$\). Here, 100 represents the initial mass of the sample, and 0.5 is the decay constant derived from the half-life.
(b) To find the mass after 1000 years, we substitute t = 1000 into the formula: \($M(1000) = 100 \times 0.5^{1000/1590}$\). Evaluating this expression gives us approximately 87mg.
(c) To determine when the mass will be reduced to 30mg, we need to solve the equation \($M(t) = 30$\) for t. Substituting M(t) and rearranging the equation gives us \($100 \times 0.5^{t/1590} = 30$\). Solving this equation, we find t ≈ 2167 years. Therefore, it will take approximately 2167 years for the mass of the radium-226 sample to be reduced to 30mg.
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what behavior is mostly strongly associated with introversion in a personality.
Answers
Answer:
Need quiet to concentrate
Are reflective
Are self-aware
Take time making decisions
Feel comfortable being alone
Don’t like group work
Prefer to write rather than talk
And maybe even feel tired after being in a crowd
Explanation:
A rocket burns fuel at a rate of 239 kg/s
and exhausts the gas at a relative speed of
6 km/s.
Find the thrust of the rocket.
Answer in units of MN.
Answers
The Thrust on the rocket is 1.434 MN.
To calculate the thrust of a rocket, we use the formula below
Thrust: This is the force that moves an aircraft through the air.
⇒Formula
T = M'×v.................... Equation 1⇒ Where:
T = Thrust of the rocketM' = Fuel ejection ratev = gas exhaust velocityFrom the question,
⇒ Given:
M' = 239 kg/sv = 60 km/s = 6000 m/s⇒ Substitute these values into equation 1
T = 239(6000)T = 1434000 NT = 1.434 MNHence, the Thrust on the rocket is 1.434 MN.
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Give an example of metals which is the best conductor of heat and shining non metal..
NEED HELP PLZ
Answers
Answer:
silver and copper
Explanation:
A ball accelerates from rest down a ramp at 2.4 m/s^2. Write an equation that could be used to determine the balls finals position, assuming the positive direction points down the ramp.
Answers
Answer:
x=2.4t+4.9t^2
Explanation:
This equation is one of the kinematic equations to solve for distance. The original equation is as follows:
X=Xo+Vt+1/2at^2
We know that the ball starts at rest meaning that its initial velocity and position is zero.
X=0+Vt+1/2at^2
Since it is going down the ramp, you can use the acceleration of gravity constant. (9.81 m/s^2) and simplify that with the 1/2.
X=Vt+4.9t^2
Note: Since the positive direction in this problem is down, you are adding the 4.9t^2, but if a question says that the downward direction is negative, you would subtract those values.
Now, substitute in your velocity value.
X=2.4t+4.9t^2
I NEED HELP PLEASE, THANKS! :)
Holiday lights are often connected in series and use special lamps that short out when the potential difference across a lamp increases to the line voltage. Generate an explanation why and explain why these light sets might blow their fuses after many bulbs have failed.
Answers
Answer:
if there isn't a shorting mechanism, the whole sets will be blown out several lamps and then shortened, the overall resistance of the remaining operating lamps will be decreased resulting in an increased working current that is adequate to blast the fuse
As a sample of water is heated, the energy is used to overcome the attractions between the molecules so that they begin to move past one
another. Then, the kinetic energy of its molecules increases. Which sections
of the heating curve illustrate this process?
Answers
Answer:
D. A followed by B
Explanation:
You can see at section A solid Ice at temperature 0°C gets heated up for and all the energy generated from heating up the ice is used to break the bonds which holds the ice together as a solid .
while at Section B the liquid water at 100°C changes to vapor because the heat energy applied here breaks intermolecular bonds c.
The section where A is followed by C of the heating curve illustrate this process. The correct option is D.
What is heating curve?The heating curve represents the association between the supply temperature of the heating system and the external air temperature.
As can be seen in section A reliable Ice at 0°C is heated, and all of the energy generated by heating the ice is used to shatter the bonds that hold the ice together as a solid.
While in Section B, liquid water at 100°C transforms to vapor because the heat energy applied here shatters the intermolecular bonds c.
Thus, the correct option is D.
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please I need it now
write an essay of 350 words on thank God it is a dream
Answers
Answer:
............. really?
What is the radius object in circular motion with a tangential velocity of 18.5m/s that takes 28 seconds to make one revolution?
Answers
The radius of the object in circular motion is 82.1 meters, under the condition that a tangential velocity of 18.5m/s in the given duration of 28 seconds.
Hence using all the given information to derive a particular formula:
v = 2πr/T
Here,
v = tangential velocity,
r = radius of the circular path
T= time period of circular motion.
Restructuring the formula to evaluate r
r = vT/2π
Staging the given values in the provided formula
r = (18.5 m/s) x (28 s) / (2π)
r = 518/2(3.14)
Applying simplification to the expression
r ≈ 82.1 m
Then, the radius of the object is approximately 82.1 meters.
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The complete question is
What is the radius of the object in circular motion with a tangential velocity of 18.5m/s that takes 28 seconds to make one revolution?
There is an elephant shaped weather vane at the top of a corn dryer tower that is 45 m high. If the weather vane weighs 190 N, what is the Potential Energy that the weather vane has?Potential Energy = Weight x HeightWeight = Potential Energy / HeightHeight = Potential Energy / WeightWeight = Mass x 10Mass = Weight / 10
Answers
Given,
The weight, W = 190 N
The height, H = 45 m
The potential energy is calculated by the formula,
\(PE=\text{Weight}\times Height\)Calculate the potential energy by substituting the given values.
\(\begin{gathered} PE=190\text{ N}\times45\text{ m} \\ PE=8,550\text{ J} \end{gathered}\)Thus, the potential energy is 8,550 Joules.
A. It Implies That M Is Finitely Generated. B. It Implies That M Has Nonzero Elements Of Nonzero Order. C. When Every Non-Null Element Has Null . D. In The Case That The Ring R Is A Body. E. None Of The Above Alternatives Gives A
Which of the following alternatives give a true statement. Justify your answer.
A modulus M over a ring R has a finite basis:
a. It implies that M is finitely generated.
b. It implies that M has nonzero elements of nonzero order.
C. When every non-null element has null .
d. in the case that the ring R is a body.
e. None of the above alternatives gives a true statement.
Which of the following statements are true?
a. If a subset of a module generates that whole module, then the subset cannot be
empty.
b. Every submodule S of a module M verifies the inequality C. Two different subsets of M have to generate two different submodules of M.
d. If S generates a submodule N of the module M, then contains S.
e. Neither statement is true.
Answers
The correct answer is e. None of the above alternatives gives a true statement. None of the statements in options a, b, c, and d are true when it comes to a modulus M over a ring R having a finite basis.
When a modulus M can be formed entirely from a finite set of elements, the modulus M is said to be finitely generated. M's finite basis does not, however, automatically imply that M is finitely generated. A basis is a set of linearly independent elements, and it might not be enough to produce all of the components of the modulus.
According to the assertion in option b, M must include nonzero items of nonzero order if it has a finite basis. This is untrue, though. The smallest positive number k, such that the element raised to the power of k equals the identity element, is referred to as the order of an element.
According to option c, every non-null element in a modulus with a finite basis has a null. Nevertheless, this claim is likewise untrue. It is possible for a modulus with a finite basis to have non-null elements without a null element.
According to option d, a ring R is a body, or a field, and only then can a modulus have a finite basis. However, this assertion is also untrue. Even though the ring R is not a field, a modulus can nonetheless have a finite basis. None of the given alternatives provides a true statement about a modulus M over a ring R having a finite basis.
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How does the ratio of tin to copper affect the properties of the alloy bronze?
Answers
Answer:
Stronger and harder than either of the pure metals
Explanation:
help as soon u can pls! due in 45 mins!!
Which statement correctly represents a mineral?
1. any naturally forming substance made from one element
2. any chemical substance which forms naturally in the Earth
3. an element which is made into an object
4. any substance which develops in the ground
Answers
Minerals are any chemical substance which forms naturally in the Earth
Define mineral.
Minerals are those substances found in foods and in the earth that our systems require for healthy growth and development. Calcium, phosphate, potassium, sodium, chloride, magnesium, iron, zinc, iodine, chromium, copper, fluoride, molybdenum, manganese, and selenium are among the nutrients that are crucial for good health.
Compounds found only in living creatures are typically not considered minerals according to geological definitions. However, some minerals, like calcite, are frequently biogenic or, in terms of chemistry, are organic molecules (such as mellite). Additionally, living things frequently produce inorganic crystals (like hydroxylapatite), which are also found in rocks.
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What Determines the amount of TE of an object
Answers
Answer:
To find the volume of a rectangular object, measure the length, width and height. Multiply the length times the width and multiply the result by the height. The result is the volume. Give the result in cubic units, such as cubic centimeters.
Explanation:
Answer:
Kinetic energy is the energy possessed by an object due to its motion. If an object is moving, then it has kinetic energy. The amount of kinetic energy depends on mass and speed.
Explanation:
A gas of volume 2 m^3 at 27°C is (a) heated to 327°C, (b) cooled to - 123°C, at constant pressure.What are its new volumes?
Answers
Answer:
A. 4 m³
B. 1 m³
Explanation:
A. Determination of the new volume.
Initial Volume (V₁) = 2 m³
Initial temperature (T₁) = 27 °C + 273 = 300 K
Final temperature (T₂) = 327 °C + 273 = 600 K
Final volume (V₂) =?
V₁ / T₁ = V₂ / T₂
2 / 300 = V₂ / 600
Cross multiply
300 × V₂ = 2 × 600
300 × V₂ = 1200
Divide both side by 300
V₂ = 1200 / 300
V₂ = 4 m³
B. Determination of the new volume.
Initial Volume (V₁) = 2 m³
Initial temperature (T₁) = 27 °C + 273 = 300 K
Final temperature (T₂) = –123 °C + 273 = 150 K
Final volume (V₂) =?
V₁ / T₁ = V₂ / T₂
2 / 300 = V₂ / 150
Cross multiply
300 × V₂ = 2 × 150
300 × V₂ = 300
Divide both side by 300
V₂ = 300 / 300
V₂ = 1 m³
Question 2 (1 point)
(01.01 MC)
Blake is a member of the cross-country track team and runs six days a week. He also helps around the house by washing his family's cars,
mowing the grass, and taking out the garbage and recycling. Which of the following describes a possible benefit of Blake's physical activity
point)
O
a
Blake may be less likely to commit to a healthy future.
Ob
Blake may have a decreased chance of disease.
Oc
Blake may require more assistance performing daily tasks.
O
Blake may struggle to achieve healthy body fat levels.
Answers
Answer: Blake may have a decreased chance of disease.
Explanation:
Research has shown that on average, a person who engages in more physical activity will live longer than a person who does not with one reason for this being that engaging in physical activity helps reduce the risk of diseases such as; heart disease, diabetes, and many forms of cancer.
Obesity (risk factor) and high blood pressure are also reduced by engaging in physical activity.
How is heat transmitted?
Answers
Order the mechanical following waves from least energy to most energy.
Answers
Answer:
middle
top
bottom
under neith middle
A physical quantity X is connected from X = ab2/C. Calculate percentage error in X, when percentage error in a,b,c are 4,2 and 3 respectively.
Answers
Answer: 11%
Explanation:
Given that
X = ab^2/C. Calculate percentage error in X, when percentage error in a,b,c are 4,2 and 3 respectively.
Percentage error of b = 2%
Percentage error of b^2 = 2 × 2 = 4
When you are calculating for percentage error that involves multiplication and division, you will always add up the percentage error values.
Percentage error of X will be;
Percentage error of a + percentage error of b^2 + percentage error of c
Substitute for all these values
4 + 4 + 3 = 11%
Therefore, percentage error of X is 11%
which of the following best explains why mars' and venus' surface temperatures vary, despite both planets having atmospheres that contain mostly carbon dioxide?
Answers
Mars has a thin atmosphere unlike Venus hence their surface temperature varies despite both Mars and Venus having atmospheres with mostly Carbon Dioxide
Venus and Mars are the solar system's planets, and their temperatures differ. Mars has a thin atmosphere that cannot withstand much heat.
Mars is the fourth planet in the solar system, also known as the red planet . It contains less oxygen gas than carbon dioxide. It is has a thin atmosphere and is made up of various gases.
Unlike Venus, Mars' thin atmosphere cannot retain heat and instead radiates it back into space. Venus has a thick atmosphere. It traps heat and raises the surface temperature. Mars' atmospheric particles cannot store energy and thus vary in temperature.
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Can you please help me on all of these!!!! Please
Answers
Answer:
differ from mechanical waves in that they do not require a medium to propagate. This means that electromagnetic waves can travel not only through the air and solid materials but also through the vacuum of space.
Explanation:
This means that electromagnetic waves can travel not only through the air and solid materials but also through the vacuum of space.
a 2n and 6 n force pull on an object to the right and a 4 n force pulls to the left a 0.5 kg object. what is the net force on the object?
Answers
The net force acting on the object is 8N - 4N = 4N. This means that there is a net force of 4N acting to the right on the 0.5 kg object.To sum up, the net force acting on the object is 4N to the right.
In order to determine the net force on an object, you need to determine the sum of all the forces acting on the object, including the direction of the forces. For the given scenario of a 2N and 6N force pulling to the right and a 4N force pulling to the left on a 0.5 kg object, the net force can be determined as follows. The two forces acting to the right are 2N and 6N, so the total force acting to the right is 2N + 6N = 8N.
Similarly, the force acting to the left is 4N, so the total force acting to the left is 4N. Since the forces are in opposite directions, we can subtract the smaller force from the larger force to get the net force acting on the object. Therefore, the net force acting on the object is 8N - 4N = 4N. This means that there is a net force of 4N acting to the right on the 0.5 kg object.
To sum up, the net force acting on the object is 4N to the right.
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