Answer:
D
Explanation:
If you need an explanation feel free to ask.
Two objects, X and Y, experience external net torques that vary over a period of 5 seconds. Object X has a moment of inertia I0, and Object Y has a moment of inertia 2I0. The average value of the magnitude of the external net torque exerted on Object X from time t=0 to t=5s is torquex. Similarly, the average value for ObjectY is torquey. The magnitudes of the angular momenta L of Objects X and Y versus t are shown in the graph. Which of the following expressions correctly relates torquey to torquex?
Explanation: ΔL = τ(average) * Δt
Change in angular momentum = average torque * change in time
solve for average torque for each objects
τ(average) = ΔL / Δt
Object y average torque
τy = ΔLy / Δt = 20 / 5 = 4
τy = 4
Object x average torque
τx = ΔLx / Δt = 10 / 5 = 2
τx = 2
Relates τy and τx
2τx = τy
Two objects, X and Y, experience external net torques that vary over a period of 5 seconds. Object X has a moment of inertia I0, and Object Y has a moment of inertia 2I0. The average value of the magnitude of the external net torque exerted on Object X from time t=0 to t=5s is torquex. Similarly, the average value for ObjectY is torquey.
The magnitudes of the angular momenta L of Objects X and Y versus t are shown in the graph. The precise relation between torquey and torquex is torquey = 2 * torquex.
To relate torquey to torquex, we are able to use the concept of angular momentum and torque. Angular momentum is described because the manufactured from the moment of inertia and angular velocity:
L = I * ω
Differentiating this equation with an appreciation of time, we get:
dL/dt = d(I * ω)/dt
Using the product rule of differentiation, we've got:
dL/dt = I * dω/dt + ω * dI/dt
Now, we realize that torque (τ) is described because of the charge of the exchange of angular momentum:
τ = dL/dt
Substituting the expression for dL/dt in terms of angular velocity and second of inertia:
τ = I * dω/dt + ω * dI/dt
Let's denote the common price of torque for item X as torquex. Since object X has a moment of inertia I0, we can write:
torquex = I0 * dω/dt + ω * dI0/dt
Now, let's consider item Y. It has a moment of inertia 2I0. Using the identical expression, we will write:
torquey = (2I0) * dω/dt + ω * d(2I0)/dt
torquey = 2I0 * dω/dt + ω * (2 * dI0/dt)
torquey = 2I0 * dω/dt + 2ω * dI0/dt
Comparing the expressions for torquex and torquey, we will see that:
torquey = 2 * torquex
Therefore, the precise relation between torquey and torquex is;
torquey = 2 * torquex.
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The correct question is;
"Two objects, X and Y, experience external net torques that vary over a period of 5 seconds. Object X has a moment of inertia I0, and Object Y has a moment of inertia 2I0. The average value of the magnitude of the external net torque exerted on Object X from time t=0 to t=5s is torquex. Similarly, the average value for ObjectY is torquey. The magnitudes of the angular momenta L of Objects X and Y versus t are shown in the graph. Which of the following expressions correctly relates torquey to torquex?"
A 250 kg cart is traveling at 8 m/s when it strikes a 100 kg cart at rest. After the elastic collision, the 250 kg cart continues to travel forward but at a lower velocity of 3 m/s. Determine the velocity of the 100 kg cart after the elastic collision.
Answer: In this scenario, we have two carts colliding with each other. One cart weighs 250 kg and is moving at a speed of 8 m/s, while the other cart weighs 100 kg and is initially at rest.
After the collision, the 250 kg cart continues moving forward, but at a slower speed of 3 m/s. We want to find out the speed at which the 100 kg cart moves after the collision.
To solve this, we use the principle that the total "push" or momentum before the collision should be the same as the total momentum after the collision.
Since the 100 kg cart is initially at rest, its momentum is zero. The momentum of the 250 kg cart before the collision is 250 kg * 8 m/s = 2000 kg·m/s.
After the collision, the momentum of the 250 kg cart becomes 250 kg * 3 m/s = 750 kg·m/s.
To find the momentum of the 100 kg cart after the collision, we subtract the momentum of the 250 kg cart after the collision from the total momentum before the collision: 2000 kg·m/s - 750 kg·m/s = 1250 kg·m/s.
Now, we divide this momentum by the mass of the 100 kg cart to find its velocity: 1250 kg·m/s / 100 kg = 12.5 m/s.
Therefore, the 100 kg cart moves at a velocity of 12.5 m/s after the collision, in the opposite direction of the 250 kg cart's motion.
2. The second year of Peixotto Media's incorporation, the board of directors
announce that they will issue cash dividends to their shareholders. At this point,
shareholders own 70,000 shares of stock in the corporation. The dividends will be 10
cents per share.
a. How should Savannah journalize the declaration and payment of this dividend? (4
points)
b. Now, imagine that Peixotto Media had chosen to pay its shareholders a stock
Qividend instead of cash dividend. At the time, their stock is valued at $7.25 per
share. They choose to pay a 5 percent dividend. How would Savannah journalize the
declaration and payment of this dividend? (4 points)
c. Elena and Josh both own common stock in Peixotto Media. Elena owns 300
shares and Josh owns 75 shares. Compute the dividends payable to both
shareholders. Show your work. (2 points)
a. Savannah would debit retained earnings and credit dividends payable for the declaration of a cash dividend, and debit dividends payable and credit cash for the payment, b. To declare and pay a stock dividend, Savannah would debit retained earnings and credit common stock dividend distributable for declaration, then debit common stock dividend distributable and credit common stock for payment, and c. Dividends payable to shareholders like Elena and Josh can be computed by multiplying the number of shares owned by the dividend per share.
Dividends Payable is a liability account used to record the amount of dividends that a company owes to its shareholders but has not yet paid out. It represents the obligation of the company to pay out the declared dividend amount to its shareholders, and the balance is typically cleared out when the dividend payment is made. Companies usually set a record date and payment date to declare and pay dividends respectively.
a. To journalize the declaration and payment of the cash dividend, Savannah would make the following entries:
Declaration:
Debit: Retained Earnings
Credit: Dividends Payable
Payment:
Debit: Dividends Payable
Credit: Cash
b. To journalize the declaration and payment of the stock dividend, Savannah would make the following entries:
Declaration:
Debit: Retained Earnings
Credit: Common Stock Dividend Distributable (70,000 x 5% = 3,500 shares)
Payment:
Debit: Common Stock Dividend Distributable
Credit: Common Stock ($7.25 x 3,500 shares)
c. To compute the dividends payable to Elena and Josh, we would use the following formula:
Dividends Payable = Number of Shares x Dividend per Share
For Elena:
Dividends Payable = 300 shares x $0.10 per share = $30.00
For Josh:
Dividends Payable = 75 shares x $0.10 per share = $7.50
Therefore, To declare and pay a cash dividend, Savannah would debit retained earnings and credit dividends payable for declaration, and debit dividends payable and credit cash for payment. To declare and pay a stock dividend, Savannah would debit retained earnings and credit common stock dividend distributable for declaration, then debit common stock dividend distributable and credit common stock for payment. Dividends payable to shareholders like Elena and Josh can be computed by multiplying the number of shares owned by the dividend per share.
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How many kilocalories of heat would be needed to melt 0.32 kg of ice at 0°C and increase the temperature to 25°C? The specific heat of water is 1 cal/g.°C, specific heat of ice is 0.5 cal/g.°C, the latent heat of ice to water is 80 cal/g. Keep one digit after the decimal.
Which statement best suscribes what happens during chemical change?
Chemical change involves the rearrangement of atoms or molecules in a substance, resulting in the formation of new substances with different properties than the original substance.
A chemical change in a chemical reaction is a process where one or more substances undergo a chemical transformation, resulting in the formation of new substances with different chemical and physical properties than the original substances. During a chemical change, the atoms or molecules of the reacting substances are rearranged through chemical reactions, leading to the breaking and forming of chemical bonds and the release or absorption of energy.
Chemical changes occur when a material's chemical makeup is changed, creating one or more new compounds with qualities that are distinct from those of the original substance. Chemical reactions that result in the breaking and building of chemical bonds occur when the atoms or molecules of the substances involved are reorganized during a chemical shift. The release or absorption of energy in the form of heat, light, or sound is typically accompanied by this process.
Therefore, Rearranging atoms or molecules in a substance causes chemical change, which creates new compounds with differing properties from the original one.
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Which of the following is true about mixtures and compounds?
OA. A compound forms when different substances chemically combine to form a new substance.
B. A mixture contains different substances that are not chemically combined with one another.
OC. Mixtures and compounds are both made of two or more different substances.
D. all of these
If the magnification is -4 then is the image larger or smaller and is it inverted or upright
If the magnification is -4 the the image is larger and is it inverted in nature.
The magnification of the body is given is -4, here the signs show the nature of the image and the numerical value is the times to which the object has been magnified. Here, it is inverted because there is negative sign and it is enlarged as the magnification is more than 1.
Therefore, a magnification of -4 indicates that the image is both inverted and larger than the object. The resultant picture will be a larger, inverted version of the object if it is seen via a lens or mirror with a magnification of -4.
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Need some guidance and help
The image distance is the distance of the image formed to the lens.
option C.
What is an image distance?The distance between the point of incidence of a lens and the point where the image is formed is called image distance.
The image distance, that is the distance of the image formed by a lens for a given object distance (u) and the focal length (f) of the lens, is given by the following lens formula;
1/f = 1/v + 1/u
where;
f is the focal length of the lensu is the object distance - distance of the object to the lensv is the image distance - the distance of the image formed to the lensThus, based on the formula and explanation given above, we can conclude that object distance is the distance of the object to the lens and image distance is the distance of the image formed to the lens.
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In the above example, the 9.012 represents the
The medium in which electromagnetic waves and mechanical waves travel is one of their primary distinctions. Light and other electromagnetic waves, including radio waves, can move through void space without the aid of a physical medium.
They may move through vacuum, air, or other materials and are made up of oscillating electric and magnetic fields. The propagation of mechanical waves, such as sound or water waves, on the other hand, depends on a physical medium.
To transport energy, they rely on particle interactions and displacements in the medium. Since mechanical waves need a physical medium to carry their energy, they cannot move through a vacuum.
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List the following in order of increasing mass: an atomic nucleus, a cell, an electron, a DNA molecule.
The order of increasing mass is:
An electron < An atomic nucleus < a DNA molecule < a cell.
An electron is a fundamental particle with a negative charge and has a very small mass of order [tex]10^{-31}\ kg[/tex]. Which makes it the lightest in the group.
An atomic nucleus consists of protons and neutrons which both individually have larger mass than an electron. The order of magnitude of the nucleus's mass is [tex]10^{-27}\ kg[/tex] or higher.
A DNA molecule is a polymer chain of nucleotides and it carries genetic information. It contains many atoms, therefore it makes sense that it should have more mass than an atomic nucleus. Each human cell has about DNA of mass of order [tex]10^{15}\ kg[/tex].
Lastly, A cell has the most mass in the given list since it encompasses everything else in the list.
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The image below shows sound waves traveling through air.
Which point is the source of the sound?
The point on the image that is the source of the sound / sound waves travelling would be B. 2.
Where do sound waves originate ?When a sound is produced, such as a musical note or spoken word, it initiates a disturbance at the source, which sets the surrounding particles in motion. As these particles oscillate back and forth, they generate regions of compression and rarefaction, resulting in the formation of longitudinal waves.
The propagation of sound waves emanates from a central source, radiating outward in a spherical pattern, thereby creating an expanding wavefront. This fundamental principle of wave behavior stems from the point-source nature of sound waves, wherein they originate from a central locus and disperse in all directions.
This central source in the image is 2.
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which of the following is an example of a physical change of matter
An example of a physical change of matter is (c) Melting ice.
Explanation: Melting ice is an example of a physical change of matter. When ice melts, it undergoes a change in state from a solid to a liquid, but its chemical composition remains the same. The water molecules in ice rearrange themselves to form liquid water, but no new substances are formed. This change can be reversed by cooling the liquid water to below its freezing point, causing it to solidify back into ice. Physical changes do not involve a change in the chemical identity of the substance, only a change in its physical properties, such as shape, size, or state.
In contrast, options a) Burning wood, b) Digesting food, and d) Rusting iron involve chemical changes. Burning wood involves a chemical reaction where wood reacts with oxygen to produce carbon dioxide, water vapor, and ash. Digesting food involves the breakdown of complex molecules into simpler ones through chemical reactions in the body. Rusting iron is a chemical reaction where iron reacts with oxygen and moisture in the air to form iron oxide.
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Note: The complete question is:
Which of the following is an example of a physical change of matter?
a) Burning wood
b) Digesting food
c) Melting ice
d) Rusting iron
2. How much heat energy is required to change an ice cube of mass m=720g from ice at a temperature of -10˚C to water at temperature of 15˚C? (specific heat capacity of ice=2220J/kgK, specific heat capacity of water=4187J/kgK and the latent heat fusion of ice=3330J/K)
The amount of heat required to change the ice cube of mass 720 g from ice at a temperature of -10 ˚C to water at temperature of 15 ˚C is 300963.6 J
How do i determine the heat required?First, we shall obtain the heat required to change the ice from -10 ˚C to 0 °C. Details below:
Mass of ice (M) = 720 g = 720 / 1000 = 0.72 KgInitial temperature of ice (T₁) = -10 °CFinal temperature of water (T₂) = 0 °CChange in temperature of water (ΔT) = 0 - (-10) = 10 °CSpecific heat capacity of ice (C) = 2220 J/KgKHeat (H₁) =?H₁ = MCΔT
H₁ = 0.72 × 2220 × 10
H₁ = 15984 J
Next, we shall obtain the heat needed to melt the ice. Details below:
Mass of ice (m) = 0.72 KgLatent heat of fusion (ΔHf) = 333000 J/KgHeat (H₂) =?H₂ = m × ΔHf
H₂ = 0.72 × 333000
H₂ = 239760 J
Next, we shall determine the heat required to change the water from 0 °C to 15 °C. Details below:
Mass of water (M) = 0.72 KgInitial temperature of water (T₁) = 0 °CFinal temperature of water (T₂) = 15 °CChange in temperature of water (ΔT) = 15 - 0 = 15 °CSpecific heat capacity of water (C) = 4187 J/gK Heat (H₃) =?H₃ = MCΔT
H₃ = 0.72 × 4187 × 15
H₃ = 45219.6 J
Finally, we shall determine the heat required to change the ice from -10 ˚C to water at temperature of 15 ˚C Details below:
Heat required to change the ice from -10 ˚C to 0 °C (H₁) = 15984 JHeat required to melt the ice (H₂) = 239760 JHeat required to the water from 0 °C to 15 °C (H₃) = 45219.6 JTotal heat required (Q) =?Q = H₁ + H₂ + H₃
Q = 15984 + 239760 + 45219.6
Q = 300963.6 J
From the above calculations, we can conclude that the heat required to change the ice from -10 ˚C to water at 15 ˚C is 300963.6 J
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c) A steel ring of radius 444mm is to be slipped on to a brass wheel of radius 450mm. To what maximum temperature
should the steel ring be heated to enable fitting? What will be the stresses in the materials on cooling if the cross-
sectional dimension of the steel ring is 20mm x 5mm and that of the brass wheel is 20mm x 40mm? (E for steel is
200GPa, E for brass is 95GPa and coefficient of expansion for steel is 12 x 10-6/°C (12 Marks)
&
10cm=16m
According to the information, the steel ring should be heated to a maximum temperature of approximately 50.67°C to enable fitting; and the stresses in the materials on cooling will be approximately 17.04 MPa in the steel ring and 2.11 MPa in the brass wheel.
How to calculate the linear thermal expansion?To enable fitting, the steel ring needs to expand in size so that its inner diameter matches the outer diameter of the brass wheel. We can use the formula for linear thermal expansion:
ΔL = α * L0 * ΔTWhere ΔL is the change in length, α is the coefficient of linear expansion, L0 is the initial length, and ΔT is the change in temperature. By substituting the given values and solving for ΔT, we find that the steel ring needs to be heated to a maximum temperature of approximately 50.67°C.
How to calculate the stress in the materials?The stresses in the materials can be calculated using the formula:
Stress = (Force / Area)Since the dimensions of the cross-sections are given, we can calculate the areas of the steel ring and brass wheel. The force can be calculated using the equation:
Force = Young's modulus * Change in length / Initial lengthBy substituting the given values for Young's modulus, change in length, and initial length, we can calculate the forces in both materials. Finally, by dividing the forces by their respective areas, we can determine the stresses in the steel ring and brass wheel, which are approximately 17.04 MPa and 2.11 MPa, respectively.
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Hi
Please help on question asap if the answer is correct I'll rate you five stars a thanks and maybe even brainliest!
What do you notice about the values?
0.9 amps ÷0.03v=30 ohms.
1.9amps÷0.07v=27.149 ohms
3.1. amps ÷0.10v =31 ohms
3.9. amps ÷ 0.12v =032.5 ohms
5. amps ÷0.15v=33.33 ohms
6.1. amps ÷0.19v=32.1053 ohms
The resistance values from the givens are having a consistent value ranging from 27 to 33 ohms depending upon the supply of voltage and current.
Ohm's law gives the relation between the voltage, current, and resistance. Ohm's law states that the applied voltage is directly proportional to the current flow in the conductor. Thus, V∝I, V is the voltage and I is the current.
Ohm's law can also be written as, V = IR, where R is the resistance and the unit of resistance is ohm. The resistance is the factor that resists or opposes the current flow in the curcuit. When resistance increases, current flow in the circuit decreases and vice-versa.
From the given values, the resistance values changes when there is a change in voltage and current. The current and voltage have linear relationship, and these calculations make the idealsitic assumptions and can not hold true in practical applicaitons, when woeking with non-ohmic or non-linear components.
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Suppose that a car is initially moving at a speed of 100 m / s to the right. Take right a positive. The driver hits the brakes, and the car comes to a stop in a time of 20 s. What is the acceleration of the car?
The required acceleration of the car, when the driver hits the brake, is [tex]-5 m/s^2[/tex], the negative sign indicates that the car is slowing down.
From the question we can see that the:
initial velocity(u) is + 100 m/s (to the right)
Final velocity (v) is 0 since the car comes to stop
Time (t) is 20 s
We can use the formula
a= (v-u)/t to find the acceleration(a) of the car.
Now Substituting the values in the formula given above we get:
a=(0-100)/20
a= [tex]-5m/s^2[/tex]
Therefore, the acceleration of the car is [tex]-5 m/s^2[/tex]. The negative sign in the answer indicates that the acceleration is in the opposite direction to the initial velocity, which means that the car is slowing down or decelerating.
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A hot water tap delivers water at the rate of 20kg per minute at 80°C. A cold water tap delivers cold water at the rate of 10kg per minute at 20 °C. If both tabs are open for 3 minutes, calculate the final temperature of the mixture of cold and hot water.
The final temperature of the mixture of cold and hot water is 60°C.
To calculate the final temperature of the mixture of hot and cold water, we can use the principle of conservation of energy. The heat gained by the cold water is equal to the heat lost by the hot water.
Given:
Rate of hot water flow (m₁) = 20 kg/min
The initial temperature of hot water (T₁) = 80°C
Rate of cold water flow (m₂) = 10 kg/min
The initial temperature of cold water (T₂) = 20°C
Duration (t) = 3 minutes
Let's calculate the heat gained by the cold water and the heat lost by the hot water using the formula:
Heat gained = mass * specific heat capacity * temperature change
For the cold water:
Heat gained by cold water = m₂ * specific heat capacity * (final temperature - T₂)
For the hot water:
Heat lost by hot water = m₁ * specific heat capacity * (T₁ - final temperature)
Since the heat gained by the cold water is equal to the heat lost by the hot water, we can set up the equation:
m₂ * specific heat capacity * (final temperature - T₂) = m₁ * specific heat capacity * (T₁ - final temperature)
Let's substitute the given values and solve for the final temperature:
10 kg/min * specific heat capacity * (final temperature - 20°C) = 20 kg/min * specific heat capacity * (80°C - final temperature)
Simplifying the equation:
10 * (final temperature - 20) = 20 * (80 - final temperature)
10 * final temperature - 200 = 1600 - 20 * final temperature
30 * final temperature = 1800
final temperature = 1800 / 30
final temperature = 60°C
Therefore, the final temperature of the mixture of hot and cold water after 3 minutes will be 60°C.
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A plate of iron at 20 °C has shown in the figure below. If the temperature
raised to 100 °C and the coefficient of linear expansion of iron is 1.1 x 10-7 o
1, then what is the final area of the plate?
(5
2 m
2 m
The final area of the plate is 4.0000352 [tex]m^2[/tex] if the temperature raised to 100 °C and the coefficient of linear expansion of iron is 1.1 x 10-7.
Expecting that the plate of iron is rectangular, we can involve the recipe for warm extension of solids to compute the last region of the plate. The equation for direct warm development is given by ΔL = αLΔT, where ΔL is the adjustment of length, α is the coefficient of straight extension, L is the first length, and ΔT is the adjustment of temperature.
Since the region of the plate is given by A = L*W, where L is the length and W is the width, we can involve the equation for straight warm extension to compute the adjustment of length of the plate and afterward use it to compute the last region.
ΔL = αLΔT = [tex](1.1 x 10^-7 m/oC)(2 m)(80 oC) = 1.76 x 10^-5 m[/tex]
The last length of the plate is L + ΔL = 2 m + 1.76 x [tex]10^-5[/tex] m = 2.0000176 m (approx.)
The last width of the plate is thought to be unaltered as it isn't impacted by the adjustment of temperature.
Thusly, the last region of the plate is A = L*W = (2.0000176 m)(2 m) = 4.0000352 [tex]m^2[/tex] (approx.)
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proof(how this formula comes )
vector
u.v=|u||v|cosβ
The formula you mentioned is known as the dot product formula or the scalar product formula. It is used to find the angle between two vectors u and v.
Let's start by defining the vectors u and v. Suppose we have two vectors u and v in a two-dimensional space.
u = (u1, u2)
v = (v1, v2)
The dot product of these vectors is defined as:
u . v = |u| |v| cos(β)
where |u| and |v| are the magnitudes of the vectors u and v respectively, and β is the angle between the vectors u and v.
Now, let's derive this formula. The dot product of two vectors u and v is given by:
u . v = (u1 × v1) + (u2 × v2)
The magnitude of a vector is given by:
|u| = sqrt(u1² + u2²)
|v| = sqrt(v1² + v2²)
We can use the dot product and magnitude equations to obtain:
cos(β) = (u . v) / (|u| × |v|)
Multiplying both sides by |u| × |v| gives us:
|u| × |v| × cos(β) = u . v
Therefore, we have derived the dot product formula:
u . v = |u| × |v| × cos(β)
This formula can be used to find the angle between two vectors u and v in any two-dimensional or three-dimensional space.
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The complete question is-
Write the proof of the formula
u.v=|u||v|cosβ
I NEED HELP WITH THIS QUESTION
The charge R is positive and the charge L is negative hence, the correct option is option D.
The electric charges are of two types and they are positive and negative charge. There is an attractive force between the two charges. The electric field is formed around the charges and the electric field is denoted by using field lines around it.
The field lines are emerging from positive charge and end up in a negative charge. The field lines never intersect with each other. Hence, from the given, the field lines emerging from the positive charge(R) and end up in the negative charge(L).
Hence, the ideal solution is option D.
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The side of a cube of metal is measured to be (1.00±0.06) cm and its mass is measured to be (41.0±0.4) g. Determine the uncertainty in the density of the solid in kilograms per cubic meter.
The density of the solid is (4.10 ± 0.78) × 10^3 kg/m^3.
To calculate the density of the cube below formula can be used:
ρ = m/V
where ρ is density, m is mass, and V is volume. For a cube, the volume is given by:
V = (side)^3
Therefore, the uncertainty in density can be calculated using the formula:
δρ/ρ = sqrt[(δm/m)^2 + 3(δs/s)^2]
where δρ is the uncertainty in density, δm is the uncertainty in mass, δs is the uncertainty in side, and s is the value of the side.
Now, putting in the given values:
s = (1.00 ± 0.06) cm = 0.01 ± 0.0006 m
m = (41.0 ± 0.4) g = 0.0410 ± 0.0004 kg
Volume, V = (0.01 m)^3
= 1.0 × 10^-6 m^3
Therefore, the density is:
ρ = m/V
= 0.0410 kg/1.0 × 10^-6 m^3
= 4.10 × 10^4 kg/m^3
Now substituting the values and calculating the uncertainty in density:
δρ/ρ = sqrt[(δm/m)^2 + 3(δs/s)^2]
δρ/ρ = sqrt[(0.0004/0.0410)^2 + 3(0.0006/0.01)^2]
δρ/ρ = 0.019
Therefore, the uncertainty in density is:
δρ = (0.019)(4.10 × 10^4 kg/m^3)
= 779 kg/m^3
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A uniform bar, of mass M, with seven evenly spaced holes is held by sliding the bar over a horizontal peg through one of the seven holes. The peg passes through hole C, and a cylinder hangs from a hook placed through hole B as shown above. The mass of the bar is equal to the mass of the cylinder, and the location of the center of mass of the bar is at the center of hole D. In this configuration, the bar-cylinder system remains motionless but is free to rotate around the peg in hole C. Frictional forces acting on the bar are negligible. In a clear, coherent paragraph-length response that may also contain equations, explain why the bar does not rotate in this configuration.
In this configuration, the bar-cylinder system is in static equilibrium, which means that the net force and the net torque acting on the system are both zero. The system remains motionless and does not rotate around the peg in hole C because the weight of the cylinder hanging from hole B and the weight of the bar itself create equal and opposite torque around the peg.
To understand why the system is in equilibrium, we can consider the forces and torques acting on the system. Let's assume that the weight of the bar is W, and the weight of the cylinder is also W. When the system is hung in this configuration, the weight of the cylinder hanging from hole B creates a clockwise torque around the peg, while the weight of the bar creates a counter-clockwise torque around the same peg. The two torques cancel each other out, resulting in zero net torque.
The location of the center of mass of the bar at the center of hole D ensures that the weight of the bar acts vertically downward through the center of hole D. Since the peg passes through hole C, the weight of the bar does not act at a distance from the peg, and so it does not create any torque around the peg.
Therefore, the bar-cylinder system remains in equilibrium and does not rotate around the peg in hole C because the weight of the cylinder and the weight of the bar create equal and opposite torques around the peg, resulting in zero net torque. The location of the center of mass of thebar at the center of hole D ensures that the weight of the bar itself does not create any torque around the peg. Hence, the system remains motionless and balanced in this configuration.
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Car A is moving at a speed of 45km/h towards car B which is moving at a speed of 55km/h. if the two car were initially separated at a distance of 150km, determine how long it will take the two cars to meet?
The time taken by the cars to meet is 5.4 x 10³ s.
Speed of car A, v₁ = 45 km/h = 12.5 m/s
Speed of car B, v₂ = 55 km/h = 15.27 m/s
Distance between the cars, d = 150 km = 15 x 10⁴m
The expression for the time taken by the cars to meet can be given as,
Time = Distance/Average speed
t = d/(v₁ + v₂)
Applying the values of d, v₁ and v₂.
t = 15 x 10⁴/(12.5 + 15.27)
t = 15 x 10⁴/27.77
t = 5.4 x 10³ s
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The diagram shows two sets of vectors that result in a
single vector.
R
100 m
200 m
250 m
50 m
What are the first two steps for finding the magnitude of
the resultant vector?
find the square of the first horizontal vector and the
square root of the first vertical vector
O find the square root of the first horizontal vector and
the square root of the second horizontal vector
O find the sum of the two horizontal vectors and the
sum of the two vertical vectors
O find the difference between the two horizontal vectors
and the difference between the two vertical vectors
The magnitude of the resultant vector is obtained by finding the sum of two horizontal vectors and the sum of two vertical vectors. Thus, option C is correct.
The resultant vector is the single vector that has the same effect in the number of vectors collectively produced. The resultant vector in the horizontal and vertical direction is obtained by drawing a diagonal and hence by using the Pythagoras theorem.
To find resultant vector is obtained by finding the sum of two horizontal vectors and vertical vectors and then using the Pythagoras theorem.
Thus, the ideal solution is option C.
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PLEASE HELP
S
ai
5
The regular polygon has the following measures.
a = 9√3 m
s = 18 m
Segment a is drawn from the center of the polygon
perpendicular to one of its sides.
What is the vocabulary term for segment a?
What is the area of the polygon?
Round to the nearest tenth and include correct units.
Segment a, which is drawn from the center of the polygon perpendicular to one of its sides, is called the apothem.
The typical hexagon has a surface area of around 874.6 square meters.
How to determine area of a hexagon?To find the area of a regular polygon, use the formula:
Area = (1/2) x Perimeter x Apothem
Find the perimeter of the polygon. Since the polygon has n sides, use the formula:
Perimeter = n x s
where s = length of one side.
Since s = 18m, find n by using the formula:
n = 360° / (180° - (360° / n))
where n = number of sides.
Plugging in the values:
n = 360° / (180° - (360° / n))
n = 360° / (180° - (360° / 6))
n = 6
So the polygon has 6 sides, which makes it a hexagon.
Now find the perimeter:
Perimeter = n x s
Perimeter = 6 x 18
Perimeter = 108m
Next, find the apothem, use the formula:
Apothem = s / (2 x tan(π/n))
Plugging in the values:
Apothem = 18 / (2 x tan(π/6))
Apothem = 9√3 m
Now use the formula for the area:
Area = (1/2) x Perimeter x Apothem
Area = (1/2) x 108 x 9√3
Area ≈ 874.6 m²
Therefore, the area of the regular hexagon is approximately 874.6 square meters.
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You will need to know that Force (N) is equal to mass (kg) multiplied by acceleration (m/s2) for this problem. A fearless space explorer has discovered a new planet with a frictionless surface! He pushes a large crate with a mass of 220kg a distance of 5.3 km, as he does so, it accelerates at a rate of 2m/s2. How much work has our intrepid hero done?
The intrepid hero has done 2.332 x Joules of work in pushing the crate.
To ascertain the work done by the traveler, we first need to find the power he applied on the case. As per Newton's subsequent regulation, force is equivalent to mass times speed increase, so the power applied by the traveler on the container is:
Force = mass x speed increase = 220 kg x 2 = 440 N
Then, we really want to work out the distance the case was moved. The pilgrim pushed the box a distance of 5.3 km, or 5,300 m.
At long last, we can compute the work done by the pioneer utilizing the equation:
Work = force x distance = 440 N x 5,300 m = 2.332 x 10^6 Joules
Thusly, the valiant legend has done 2.332 x Joules of work in pushing the case.
The space pilgrim takes care of business on the case by applying a power that makes it speed up. The work done is equivalent to the power duplicated by the distance over which the power is applied. Involving the recipe for force, F=ma, and the given qualities for mass and speed increase, we can ascertain the power applied. Then, at that point, involving the recipe for work, W=Fd, and the given distance, we can ascertain the work done. The work done by the adventurer is 2.332 x J.
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I need help. I don’t understand.
The voltage drop across R3 is 34.5 volts.
Voltage, also known as electric potential difference, is a measure of the difference in electric potential energy between two points in an electrical circuit, and it is measured in volts. It is the driving force that moves electric charges through a circuit, from a higher potential to a lower potential.
To determine the voltage drop across R3 in this circuit, we need to first find the equivalent resistance of R2, R3, and R4, since they are connected in parallel. We can then find the total resistance of the circuit by adding the equivalent resistance in series with R1, and finally use Ohm's Law to calculate the voltage drop across R3.
The equivalent resistance of R2, R3, and R4 in parallel can be calculated as:
1/R_parallel = 1/R2 + 1/R3 + 1/R4
1/R_parallel = 1/20 + 1/25 + 1/10
1/R_parallel = 0.15
R_parallel = 1/0.15
R_parallel = 6.67 ohm
The total resistance of the circuit can be found by adding R1 and the equivalent resistance in series:
R_total = R1 + R_parallel
R_total = 15 + 6.67
R_total = 21.67 ohm
Now we can use Ohm's Law to calculate the current flowing through the circuit:
I = ET / R_total
I = 30 / 21.67
I = 1.38 A
Finally, we can use Ohm's Law again to calculate the voltage drop across R3:
V_R3 = I * R3
V_R3 = 1.38 * 25
V_R3 = 34.5 V
Therefore, the voltage drop across R3 is 34.5 volts.
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A 24.0kg dog running at a speed of 3.0 m/s jumps onto a stationary skateboard that has a mass of 3.6 kg. How long will it take a force with a magnitude of 9.0N to stop the skateboard and dog?
Given: ?
Unknown: ?
Solve and show your work
The time will take a skateboard and dog with force 9N to stop the skateboard and dog is 8 seconds.
The force is defined as the push or pull of an object. The force equals the mass and acceleration of the object obtained from Newton's second law. Acceleration defines the change in velocity by the time taken. The force is defined as the rate of change of momentum and time. Momentum is defined as the product of mass and velocity and the unit of momentum is Kg.m/s.
From the given,
mass of dog (m) = 24 kg
The initial speed of dog (u) = 3 m/s
mass of skateboard and dog = 3 + 24 = 27 kg.
The final speed of dog (v) = 0 m/s
Force = 9N
time =?
F = dp/dt, rate of change of momentum and time.
F(dt) = dp
dt = (dp)/F
=(Pf - Pi)/F
Pf is the final momentum and Pi is the initial momentum.
Pi = m×v = 24×3 = 72 kg.m/s²
Pf = m×v = 27×0 =0 kg.m/s²
dt = (0-72)/9
= 8s
Thus, the time taken to stop the skateboard and dog is 8s.
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Push: Explain Newton's Third Law
Explain how a rocket taking off can be an example of Newton's Third Law of Motion.
Every action have equal and opposite reaction. for example when we fire bullet from a gun, the gun will recoil back and bullet moves forward. In case of rocket, rocket is fired, thrust is reaction of force applied by the gas on the floor.
A push or a pull that an object experiences as a result of interacting with another item is known as a force. Interactions result in forces! As was covered in Lesson 2, certain forces are the result of contact interactions (reaction, frictional, tensional, and applied forces are examples of contact forces), whilst other forces (gravitational, electrical, and magnetic forces) are the consequence of action-at-a-distance interactions. Newton postulated that whenever objects A and B interact, they exert forces on one another. You put a downward force on the chair when you sit on it, and the chair responds by exerting an upward force on your body. This contact creates two forces: one force on the chair and one force on your body.
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A falling object accelerates from
-10.0 m/s to -30.0 m/s. How much
time does that take?
(Unit = s)
Remember: Falling = -v
a = -9.80 m/s²
Lost height = -Ay
Be careful with minus signs!!!/for acellus
It takes 2.04 seconds for the object to accelerate from -10.0 m/s to -30.0 m/s.
Velocity is a measure of an object's speed in a specific direction. It is calculated by dividing the distance traveled by the time taken and specifying the direction of the motion.
We can use the following formula to find the time taken for an object to change velocity under constant acceleration:
Δv = a × Δt
where Δv is the change in velocity, a is the acceleration, and Δt is the time taken.
In this case, the initial velocity is -10.0 m/s, and the final velocity is -30.0 m/s. So, the change in velocity is:
Δv = (-30.0 m/s) - (-10.0 m/s) = -20.0 m/s
The acceleration of the falling object is -9.80 m/s² (negative because the object is falling downward).
Now, we can rearrange the formula to solve for Δt:
Δt = Δv / a
Substituting the values we have:
Δt = (-20.0 m/s) / (-9.80 m/s²) = 2.04 seconds
Therefore, The object accelerates from -10.0 m/s to -30.0 m/s in 2.04 seconds.
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