Answer:
400
Explanation:
Formula used in solution:
\(P = \frac{F}{A}\)
\(P - pressure,\: F - force,\: A - area\)
The given information:
\(F = 20N\)
\(A = 0.05m^{2}\)
Solution
\(P = \frac{F}{A} = \frac{20}{0.05} = 20 * 20 = 400\)
Answer:
\(Pressure = 400 \: Pascals\)
What is the mass, in kg, of a 136 pound gymnast on Earth?
Answer:
61.6886 kg
Explanation:
Answer:
61 kg
Explanation:
there ya go hope this was useful
A boy slides a book across the floor, using a force of 5 N over a distance of 2
m. What is the kinetic energy of the book after he slides it? Assume there is
no friction.
A. 5 J
B. 10 J
C. 20 J
D. 2.5 J
SUBMIT
The kinetic energy of the book after it is slids a distance of 2 meters will be 10 Joules.
How to determine the kinetic energy of an object?The work-energy theorem states that "the work done on an object is the change in its kinetic energy".
Hence;
Kinetic energy = work done
Note that: work-done is expressed as:
Work done = f × d
Where f is force applied and d is distance traveled.
Given that:
Force applied f = 5 newton
Distance d = 2 meters
Work done = ?
Plug these values into the above formula and solve for the workdone.
Work done = f × d
Work done = 5N × 2m
Work done = 10Nm
Work done = 10 Joules
Therefore, the kinetic energy is 10 Joules.
Option B) 10 J is the correct answer.
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which of the following would be most helpful for a baseball pitcher to know the exact speed of their pitch?
The greatest speed of a given pitch at any point from the moment it is released until it passes home plate is represented by velocity, one of the methods used to assess pitchers most commonly.
What is Velocity (VELO)?Pitching tracking in every MLB stadium was handled by PITCHf/x until Statcast was introduced. This system's reporting of each pitch's velocity at a distance of 50 feet from the rear tip of home plate rather than at the point of release set it apart from Statcast. Some organizations started utilizing 55 feet as the point of reference and extrapolating what the velocity would be at 55 feet based on the PITCHf/x data for the reported velocity at 50 feet in order to obtain velocity readings that were closer to pitchers' actual release positions.In contrast, Statcast can offer the maximum speed of a pitch at any point in its flight, with the highest speed always occurring at the release point due to physics, enabling a more accurate assessment of pitch velocity.To Learn more About velocity, refer To:
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Question
A 1.50 kg copper pipe at 800.0° C is immersed into a 20.0°C bucket of water with a mass of 5.00 kg. What is the final
temperature of the copper-water mixture if the specific heat of copper is 0.386- and the specific heat of water is
8°C
4.184?
To solve this problem, we need to use the principle of conservation of energy, which states that the total energy in a system is constant. In this case, the energy lost by the copper pipe as it cools down will be gained by the water as it heats up. We can use the equation:
Q_copper = -Q_water
where Q_copper is the heat lost by the copper pipe, and Q_water is the heat gained by the water. The negative sign indicates that the energy flows from the copper to the water.
The heat lost by the copper pipe can be calculated using the formula:
Q_copper = mcΔT
where m is the mass of the copper pipe, c is the specific heat of copper, and ΔT is the change in temperature. We can assume that the final temperature of the copper-water mixture is the same, so we can write:
Q_copper = mc(800.0 - T)
where T is the final temperature of the mixture.
The heat gained by the water can be calculated using the formula:
Q_water = mwCΔT
where mw is the mass of the water, C is the specific heat of water, and ΔT is the change in temperature. We can assume that the initial temperature of the water is 20.0°C, so we can write:
Q_water = mwC(T - 20.0)
Now we can substitute these equations into the conservation of energy equation:
mc(800.0 - T) = -mwC(T - 20.0)
Solving for T:
mc(800.0 - T) = mwC(T - 20.0)
1500.0 * 0.386 * (800.0 - T) = 5.00 * 4.184 * (T - 20.0)
231480 - 579.6T = 20.92T - 418.4
600.52T = 231898.4
T = 386.6°C
Therefore, the final temperature of the copper-water mixture is 386.6°C.
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♥️ \({\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\\)
2. For electric circuit shown in Figure find currents in each resistor.
The current flowing in the 2Ω and 1Ω is 1.14 A and the current flowing in the 3Ω and 4Ω is 0.286 A.
What is the current flowing in each resistor?The value of the current in each resistor is calculated by applying Kirchoff voltage law as follows;
The total voltage in loop 1 is calculated as;
2 + 4 - I₁R₁ - (I₁ - I₂)R₂ - I₁R₃ = 0
6 - 2I₁ - 3(I₁ - I₂) - 1₁ = 0
The current flowing in loop 2 is calculated as;
I = V/R
I₂ = ( 6 V - 4 V ) / (3 + 4)
I₂ = 0.286 A
The value of the current flowing in loop 1 is calculated as;
6 - 2I₁ - 3(I₁ - I₂) - 1₁ = 0
6 - 2I₁ - 3(I₁ - 0.286) - 1₁ = 0
6 - 3I₁ - 3₁ + 0.858 = 0
-6I₁ = -6.858
I₁ = 6.858 / 6
I₁ = 1.14 A
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A car travels at a speed of 55 km/hr and slows down to 10 km/hr in 20 seconds. What is the acceleration?
Answer:
a = 0.62 [m/s²]
Explanation:
To solve this problem we must use the following equation of kinematics. But first, we must convert speeds from kilometers per hour to meters per second.
\(v_{f} =v_{o} -a*t\)
\(55[\frac{km}{hr}]*\frac{1hr}{3600s}*\frac{1000m}{1km} =15.27[\frac{m}{s} ]\\10[\frac{km}{hr} ]*\frac{1hr}{3600s}*\frac{1000m}{1km} = 2.77[\frac{m}{s} ]\)
where:
Vf = final velocity = 2,77 [m/s]
Vo = initial velocity = 15.27 [m/s]
t = time = 20 [s]
a = acceleration [m/s²]
Now replacing:
\(2.77=15.27-a*(20)\\20*a=12.49\\a = 0.62[m/s^{2}]\)
Answer:
It would be 10.00
Explanation:
Hope this helps its different for everyone what was it for u it was D for me
An imported sports car is being carried by plane. The cargo plane is traveling 54 m/s at an altitude of 256 m. The heavy crate containing the car accidentally slips off the back of the plane when it’s directly above your house. How far from your house did it land?
Given,
The initial horizontal velocity of the car, u=54 m/s
The height from which the car was dropped, h=256 m
The initial vertical velocity of the car will be zero.
Thus from the equation of motion, the height from which the car was dropped can be written as
\(h=\frac{1}{2}gt^2\)Where g is the acceleration due to gravity and t is the time it takes for the car to reach the ground.
On substituting the known values,
\(\begin{gathered} 256=\frac{1}{2}\times9.8\times t^2 \\ t=\sqrt[]{\frac{256\times2}{9.8}} \\ =7.23\text{ s} \end{gathered}\)The range of flight of car, i.e., the distance between your house and the point where the car lads is given by,
\(R=ut\)On substituting the known values,
\(\begin{gathered} R=54\times7.23 \\ =390.42\text{ m} \end{gathered}\)thus the car will land at a distance of 390.42 m away from your house.
Help needed! I'm kind of stuck on this question for the 9th-grade Physical Science Ionic/Covalent Bonding question.
Answer:
no one
neon is a stable atom, thus, it’s valence shell is filled (8 electrons on the outermost shell), which is why it’s in group 8 (also referred to as group 0 or 18) which is the group for noble gases
since neon has 8 electrons in the outermost shell it doesn’t need any more electrons, thus, neon doesn’t need to react (and anyway can’t react) with any element.
A lorry of mass 2000kg moving with a speed of 50kmh' collides with a drum of mass 25kg at a police checkpoint. The velocity of the lorry after the impact is 34kmh'. What is the velocity of the drum?
The velocity of the drum after the collision with a lorry of 2000 kg mass is determined as 1,280 km/h.
What is the velocity of the drum?The velocity of the drum after the collision is calculated by applying the principle of conservation of linear momentum as follows;
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where;
m₁ is the mass of the lorrym₂ is the mass of the drumu₁ and u₂ are the initial velocitiesv₁ and v₂ are the final velocitiesThe velocity of the drum after the collision is calculated as;
2000 (50) + 25(0) = 2000(34) + 25v₂
100,000 = 68,000 + 25v₂
25v₂ = 32,000
v₂ = 32,000/25
v₂ = 1,280 km/h
Thus, the final velocity of the drum after the collision is calculated by applying the principle of conservation of linear momentum.
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The velocity of the drum after the collision, given that a 2000 kg lorry moving with a speed of 50 Km/h collides with it, is 1280 Km/h
How do I determine the velocity of the drum after collision?The following data were obtained from the question given above:
Mass of lorry (m₁) = 2000 KgInitial velocity of car (u₁) = 50 Km/hMass of drum (m₂) = 25 KgInitial velocity of truck (u₂) = 0 Km/hFinal velocity of lorry (v₁) = 34 Km/hFinal velocity of drum (v₂) = ?The law of conservation of linear momentum states as follow:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Inputting the given parameters, the velocity of the drum after the collision can be obtain as follow:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
(2000 × 50) + (25 × 0) = (2000 × 34) + (25 × v₂)
100000 + 0 = 68000 + 25v₂
Collect like terms
25v₂ = 100000 - 68000
25v₂ = 32000
Divide both sides by 25
v₂ = 32000 / 25
v₂ = 1280 Km/h
Thus, the velocity of the drum after collision is 1280 Km/h
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The rabbit flea Spilopsyllus has a mass of 0.45 mg. It can jump vertically to aheight of about 3.5 cm. Biologists have hypothesized that the energy for the jump is most likely derived from the elastic potential energy stored in the resilin pads ofthe two rear legs of the flea. Each pad is estimated to have a volume of about and its strain typically reaches a value of 100%. The elastic modulus of resilience is about . Is the hypothesis plausible
Answer:
Therefore The hypothesis is not plausible Because
\(P.E \geq P.E_e\)
\(P.E=12.435*10^{-5}J \geq 1.4*10^{-7}J\)
Explanation:
From the question we are told that:
Mass \(M=0.45mg\)
Jump height \(h=3.5cm \approx 0.03m\)
Percentage strain \(\mu =100\%\)
Generally the equation for potential energy is mathematically given by
\(P.E=mgh\)
\(P.E=0.45*10^{-3}*9.8*0.03\)
\(P.E=12.435*10^{-5}J\)
Generally the equation for Elastic potential energy is mathematically given by
\(P.E_e=0.5*stress*strain *volume\)
\(P.E_e=0.5*1*2*10^6*1*1.4*10^{-4*(10^-3)^3}\)
\(P.E_e=1.4*10^{-7}J\)
The hypothesis is only plausible at conditions where
\(P.E\leq P.E_e\)
Therefore The hypothesis is not plausible Because
\(P.E \geq P.E_e\)
\(P.E=12.435*10^{-5}J \geq 1.4*10^{-7}J\)
Which equation below is not valid for relating velocity,
time, displacement, and constant (or average)
acceleration?
Answer:(vi^2+d)^2=vf+a^2+2t
Explanation:
Barney walks at a velocity of 1.7 meters/second on an inclined plane which has an angle of 18.5 with the ground what is the horizontal component of Barney’s velocity
Answer:
Explanation:
The horizontal velocity is 1.61.
Earth rotate once every 24 hours. In a reference frame fixed to Earth, how far does
a point on the equator move in 1 hour? RE = 6.34×106 m
In a reference frame fixed to Earth, a point on the equator moves zero distance in 1 hour.
What is the frame of reference?A frame of reference in physics is made up of an abstract coordinate system and the collection of physical reference points that fix the coordinate system specifically and regulate measurements inside it.
When we take a reference frame fixed to Earth, the displacement due to earth's rotation can not be measured. So, any point on earth remains in rest through out the day with respect to the reference frame fixed to Earth. Hence, a point on the equator moves no distance in 1 hour in a reference frame fixed to Earth.
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19. If an atom has an atomic number of 6 and a
mass number of 14, how many protons,
electrons, and neutrons are in the atom?
Answer:
protons: 6
electrons: 6
neutrons: 8
Explanation:
atomic number -> number of protons -> 6
mass number -> number of protons + number of neutrons
so 14-6 = 8. 8 neutrons
this atom is neutral (net charge is 0), so the number of electrons is the same as the number of protons, which is 6
A bike accelerates from 0 m/s to 15 m/s over the span of 5 seconds. How fast is the bike
traveling after 2.5 seconds?
The bike is travelling at 22.5 m/s after 2.5 s
What is acceleration?This is defined as the rate of change of velocity which time. It is expressed as
a = (v – u) / t
Where
a is the acceleration v is the final velocity u is the initial velocity t is the time How to determine the acceleration Initial velocity (u) = 0 m/sFinal velocity (v) = 15 m/sTime (t) = 5 sAcceleration (a) =?a = (v – u) / t
a = (15 – 0) / 5
a = 3 m/s²
How to determine the final velocity in the first 2.5 s Initial velocity (u) = 15 m/sAcceleration (a) = 3 m/s²Time (t) = 2.5 s Final velocity (v) = ?a = (v – u) / t
3 = (v – 15) / 2.5
Cross multiply
v – 15 = 3 × 2.5
v – 15 = 7.5
Collect like terms
v = 7.5 + 15
v = 22.5 m/s
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2 The deposit cylinder of a teller drive-in window at a bank travels through the tube at a constant speed of 4 meters per second. If it takes 17 seconds to travel from the car to the teller. What is the length of the tube the cylinder travels through.
The length of the tube the cylinder travels through 68 m
Constant speed of Cylinder v = 4 m/s
acceleration of Cylinder a = 0 \(m/s^2\)
time taken during travel t = 17 Seconds
Since acceleration is constant, hence as per the equation of motion
\(S = vt + \frac{1}{2}at^2\)
\(S = 4\times17 + \frac{1}{2}(0)17^2\)
S = 68 m
What is acceleration ?The acceleration is positive when the object is speeding up and negative when speeding down. According to Newton’s Second Law, the net unbalanced force which acts on the object causes this to happen. Thus, it can be said that acceleration is a vector quantity. It is so because it changes the time rate of change of velocity. Mainly, Uniform acceleration, non-uniform acceleration, and average acceleration are the three types of accelerated motions.
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____ is factual information not subject to bias.
Interpretation
Analysis
Data
Opinion
Answer:
Data
Explanation:
Data is factual information not subject to bias.
This ultimately implies that, data connotes fact, thus, it is an information that is credible, accurate, a statement of truth, evidential and proven.
In Computer programming, a data dictionary can be defined as a centralized collection of information on a specific data such as attributes, names, fields and definitions that are being used in a computer database system.
In a data dictionary, data elements are combined into records, which are meaningful combinations of data elements that are included in data flows or retained in data stores.
This ultimately implies that, a data dictionary found in a computer database system typically contains the records about all the data elements (objects) such as data relationships with other elements, ownership, type, size, primary keys etc. This records are stored and communicated to other data when required or needed.
How bullet train and a circuit breaker work on the magnet effect of current
A block with mass 0.500 kg
sits at rest on a light but not long vertical spring that has spring constant 70.0 N/m
and one end on the floor.
How much elastic potential energy is stored in the spring when the block is sitting at rest on it? (for this I got 0.172 J and it was correct)
A second identical block is dropped onto the first from a height of 4.40 m
above the first block and sticks to it. What is the maximum elastic potential energy stored in the spring during the motion of the blocks after the collision? (for this I got 21.7 J but it was wrong)
What is the maximum distance the first block moves down after the second block has landed on it? (for this I got 0.788 m but it was wrong)
The elastic potential energy stored in the spring when the block is sitting at rest on it is 0.172 J, the maximum elastic potential energy stored in the spring during the motion of the blocks after the collision is 1.84 J, and the maximum distance the first block moves down after the second block has landed on it is 0.185 m.
How is elastic potential energy stored in a spring?Elastic potential energy is stored in a spring when it is compressed or stretched from its rest position.
How is the maximum elastic potential energy stored in the spring during the motion of the blocks after the collision calculated?The maximum elastic potential energy stored in the spring during the motion of the blocks after the collision is calculated as the difference between the total initial mechanical energy and the total final mechanical energy, where the total initial mechanical energy is the sum of the potential energy of the two-block system at the highest point of the motion and the kinetic energy of the two-block system just before impact, and the total final mechanical energy is the sum of the potential energy of the two-block system at the maximum compression of the spring and the elastic potential energy stored in the spring at that point.
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Light travels about 180 million kilometers in 10 minutes. How far does it travel in 1 minute? How far does it travel in 1 second? Show your reasoning
I need help
Explanation:
180 million km = 10 min
? = 1 min
180 million x 10 = 1,800,000,000 km
180 million km = 600s
? = l s
108,000,000,000km
The NEC states the resistance of 4/0 coated
copper conductors is 0.0626 ohms per 1000
feet. What would be the total resistance of the
three 4/0 conductors installed in parallel, if the
total length for each of the three conductors is
323 feet?
Answer:
The resistance of 4/0 coated copper conductors is given as 0.0626 ohms per 1000 feet. To find the total resistance of the three 4/0 conductors installed in parallel, we can use the formula for combining resistances in parallel.
Since the total length for each of the three conductors is 323 feet, the resistance of each conductor can be calculated as follows:
Resistance of one conductor = (0.0626 ohms / 1000 feet) * 323 feet
To find the total resistance when the conductors are in parallel, we use the formula:
1/Total Resistance = 1/Resistance of Conductor 1 + 1/Resistance of Conductor 2 + 1/Resistance of Conductor 3
Total Resistance = 1 / (1/Resistance of Conductor 1 + 1/Resistance of Conductor 2 + 1/Resistance of Conductor 3)
Substituting the values, we get:
Total Resistance = 1 / (1/((0.0626 ohms / 1000 feet) * 323 feet) + 1/((0.0626 ohms / 1000 feet) * 323 feet) + 1/((0.0626 ohms / 1000 feet) * 323 feet))
Simplifying the expression will give us the total resistance of the three 4/0 conductors installed in parallel.
Based on the diagram, what is the difference in how economic decisions are made in a mixed economy and a market economy? E.1.2
How Economic Decisions are Made
By the Government,
command
economy
By the Consumers
mixed
economy
market.
economy
O Consumers make all economic decisions in a mixed economy, while the government makes all economic decisions in a market economy.
Government and consumers make economic decisions in a mixed economy, while consumers make economic decisions in a market economy.
Government makes all economic decisions in a mixed economy, while consumers make all economic decisions in a market economy.
O Consumers make economic decisions in a mixed economy, while consumers and government make economic decisions in a market economy.
Based on the diagram, the correct statement is: Government and consumers make economic decisions in a mixed economy, while consumers make economic decisions in a market economy.
How do we explain?In a mixed economy, economic decisions are made by both the government and consumers.
The government plays a significant role in regulating and influencing economic activities through policies, regulations, and interventions.
In market economy, economic decisions are primarily made by consumers. The market forces of supply and demand dictate the allocation of resources, production levels, and pricing.
The freedom to buy and sell whatever they choose is what ultimately determines how commodities and services are produced and distributed.
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Hi please answer the question labeled d
If Q1 is 5 times larger than Q2 the force that Q1 exerts on Q2 is?
(greater than, smaller than, or exactly the same as) the force that Q2 exerts on Q1.
part a) If Q increases by 5 times its original value, the electrostatic force (F) will increase5 times as well.
part b) If r is halved (reduced by 2), the force will become four times stronger (since 2² = 4).
part c) If Q1 is positive and Q2 is negative, the charges will attract each other.
part d) If the force that Q1 exerts on Q2 is 5 times larger than the force that Q2 exerts on Q1 is same.
What is electrostatic force?The electrostatic force is described as the force of attraction or repulsion between two charged particles.
With regards to Coulomb's Law, we have that the electrostatic force between two charges separated by a distance is :
Force = k * (Q1 * Q2) / r²
Where:
F_ = electrostatic force
k = electrostatic constant
Q1 and Q2 = magnitudes of the charges
r = distance
for case a:
If one of the charges, Q1 or Q2, increases by 5 times then the electrostatic force will also increase by 5 times.
case b)
If the distance between the charges, r, is halved, the electrostatic force will become four times stronger because (1/r²).
for case c.
if Q1 is positive and Q2 is negative, the charges will attract each other because of magnetic laws.
for case d.)
If the force that Q1 exerts on Q2 is 5 times larger than the force that Q2 exerts on Q1 is same as there is a resulting stronger gravitational or electromagnetic force.
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Suppose the student in (Figure 1) is 68kg, and the board being stood on has a 12kg mass. What is the reading on the left scale? What is the reading on the right scale?
The equilibrium conditions allow to find the results for the balance forces are:
F₁ = 225.4 N F₂ = 558.6 N
When the acceleration is zero we have the equilibrium conditions for both linear and rotational motion.
∑ F = 0
∑ τ = 0
Where F are the forces and τ the torques.
The torque is the product of the force and the perpendicular distance to the point of support,
The free-body diagrams are diagrams of the forces without the details of the bodies, see attached for the free-body diagram of the system.
We write the translational equilibrium condition.
F₁ - W₁ - W₂ + F₂ = 0
We write the equation for the rotational motion, set our point of origin at scale 1, and the counterclockwise turns are positive.
F₂ 2 - W₁ 1 - W₂ 1.5 = 0\(\frac{W_1 \ 1 + W_2 \ 1.5}{2}\)
Let's calculate F₂
F₂ = \(\frac{W_1 \ 1 + W_2 \ 1.5 }{2}\)
F₂ = (m g + M g 1.5)/ 2
F₂ = \(\frac{(12 + 68 \ 1.5 ) \ 9.8}{2}\)
F₂ = 558.6 N
We substitute in the translational equilibrium equation.
F₁ = W₁ + W₂ - F₂
F₁ = (m + M) g - F₂
F₁ = (12 +68) 9.8 - 558.6
F₁ = 225.4 N
In conclusion using the equilibrium conditions we can find the forces of the balance are:
F₁ = 225.4 N F2 = 558.6 N
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jet of water squirts out horizontally from a hole near the bottom of the tank in the figure. if the hole has a diameter of 3.50 mm, what is the height, h, of the water level in the tank?
The water level of the tank is 9 x 10^-2m.
What is Bernoulli’s principle?
The Bernoulli equation can be seen as a statement of the energy conservation principle that applies to flowing fluids. Fluid pressure decreases in areas where the flow velocity is increased, which is the qualitative behavior that is typically referred to as the "Bernoulli effect."
Here,
→ Time taken for a fluid h = Vyt + gr² Particle to reach the ground 2 9.81 m 52 2 Im Velocity 2 initial vertical is ZeroS
62 0.455 -0
n = VatUn 2 n ヒ 0.6 0.45 2 2
1.33 m/s
Bernoulli equation between the exit hole at the bottom and the free Surface in the top lank:- Sw. g. 7, 8. Vn x Sw xg x y z
2Swg (y₁ - Y₂) = Sw Un 3 2 Sw
(J₁-92) 2 S w Vn гу hrank = Sw v₁²
2гд
2(1.3312 2x9.81 0.09 m 2
Ans ures h tank 29×10-2 m
Therefore, the water level of the tank is 9 x 10^-2m
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Can someone explain how to do the algebra for this question? I know everything else, I just don’t know how to rearrange the question to solve for v.
Answer:
Refer to the step-by-step Explanation.
Step-by-step Explanation:
Simplify the equation with given substitutions,
Given Equation:
\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)
Given Substitutions:
\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)
Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)
Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the left-hand side of the equation:
\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
Simplifying the third term.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)
"R²'s" cancel, we are left with:
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)
We have like terms, combine them.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)
Each term has an "m" in common, factor it out.
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)
Now we have the following equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the right-hand side of the equation:
\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)
\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)
Now we have the equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
\(\hrulefill\)
Now solving the equation for the variable "v":
\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
Dividing each side by "m," this will cancel the "m" variable on each side.
\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)
Subtract the term "gh" from either side of the equation.
\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)
Multiply each side of the equation by "10/7."
\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)
Now squaring both sides.
\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)
Thus, the simplified equation above matches the simplified equation that was given.
______________________________
A Stone Is Dropped Into a Deep Water Well. The Sound of The Stone Hitting The Water Is Heard After 3.4 Seconds. Determine The Depth of The Water Well.
N.B. The Correct Answer Will Receive 30 Points & The Brainliest Title.
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A Stone Is Dropped Into a Deep Water Well. The Sound of The Stone Hitting The Water Is Heard After 3.4 Seconds. then The Depth of The Water Well is 56.6 m.
In terms of physics, sound is a vibration that travels through a transmission medium like a gas, liquid, or solid as an acoustic wave. Sound is the receipt of these waves and the brain's perception of them in terms of human physiology and psychology. Only acoustic waves with frequencies between about 20 Hz and 20 kHz, or the audio frequency range, may cause a human to have an auditory sensation. These correspond to sound waves in air with an atmospheric pressure of 17 metres (56 ft) to 1.7 centimetres (0.67 in) in wavelength. Ultrasounds are sound waves with a frequency higher than 20 kHz that are inaudible to humans. Infrasound refers to sound frequencies below 20 Hz. Animals of different species have different hearing ranges. Acceleration of the stone is 9.8 m/s²
according to kinematics,
s = ut + 1/2 at²
s = 1/2 ×9.8×3.4²
s = 56.6 m
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a
Gold-198 has a half-life of approximately 3 days. If a 100g sample of gold-198 decays for
9 days, approximately how much gold-198 remains in the sample?
o 13 g
o 25 g
o 33 g
o 50g
Answer:
13 g
Explanation:
Gold-198 has a half-life of approximately 3 days. If a 100 g sample of gold-198 decays for 9 days, approximately how much gold-198 remains in the sample?
13 g
What is kci and o2 classified as
KCl ( potassium chloride ) is classified as solid substance while O₂ ( oxygen molecule ) is classified as gaseous substance.
What is KCl?
KCl is an abbreviation for potassium chloride. Potassium chloride ( KCl ) naturally occurs as a white or colorless solid that has a powdery, crystalline appearance.
Potassium chloride ( KCl ) is one of the important raw materials required in the manufacture of potassium metal.
The metal halide salt KCl is also used in the manufacture of soaps.
The chemical formula of potassium chloride ( KCl ), consists of one potassium ( K ) atom and one chlorine ( Cl ) atom.
O₂ is a substance that is known as oxygen molecule and it usually exist in gaseous state.
Thus, we can conclude that we can classify O₂ ( oxygen molecule )which is known as oxygen molecule as gas, and KCl ( potassium chloride ) known as potassium chloride as solid substance.
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Which occupies more volume: 3m^3, or 100 ft^3?
Answer:
3 m³ will occupy more volume.
Explanation:
We need to tell which occupies more volume : 3m³ or 100 ft³.
To compare, we first make the units same.
We know that,
1 m = 3.28 feet
1 m³ = 35.31 foot³
3 m³ = 105.94 foot³
Now, we can compare 105.94 foot³ and 100 ft³. It can be clear that 3 m³ will occupies more volume.