(a) The potential energy of the tank of water with respect to the floor is 294,000 J.
(b) The potential energy of the tank of water with respect to the basement is 392,000 J.
What is the potential energy?
The potential energy of the tank of water with respect to the floor can be calculated as follows:
Potential energy = mgh
where;
m is the mass of the water, g is the acceleration due to gravity, and h is the height of the tank with respect to the floor.We can first find the mass of the water using the density of water, which is approximately 1000 kg/m³:
Mass of water = density x volume
Mass of water = 1000 kg/m³ x 2500 L
Mass of water = 2500 kg
Now we can calculate the potential energy:
Potential energy = 2500 kg x 9.8 m/s² x 12.0 m
Potential energy = 294,000 J
The potential energy of the tank of water with respect to the basement can be calculated in a similar way. We can first calculate the height of the tank with respect to the basement:
Height of tank with respect to basement = 12.0 m + 4.0 m
Height of tank with respect to basement = 16.0 m
Now we can calculate the potential energy using the same formula as before:
Potential energy = 2500 kg x 9.8 m/s² x 16.0 m
Potential energy = 392,000 J
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A 400Hz tuning fork is vibrating, producing a sound wave in the
air.
What is the wavelength of the sound wave (in given units)? In centimeters ?
The wavelength of the sound wave that has a frequency of 400Hz is 7.5 × 10⁵m.
How to calculate wavelength?Wavelength is the length of a single cycle of a wave, as measured by the distance between one peak or trough of a wave and the next.
It is often designated in physics as λ, and corresponds to the velocity of the wave divided by its frequency.
According to this question, a 400Hz tuning fork is vibrating, producing a sound wave in the air. The wavelength is calculated as follows:
λ = 3 × 10⁸ ÷ 400
λ = 7.5 × 10⁵m
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Let E =3i^+1j^ and F =1i^−3j^.
A. Find the magnitude of E.
B. Find the magnitude of F.
C. Find the magnitude of G =E +F.
D. Find the magnitude of H =−E −2F.
The given vectors E and F are in Cartesian form. To find their magnitudes, we can use the formula:
|v| = √(vx² + vy²)
where vx and vy are the x and y components of the vector.
What is the Cartesian algebra?Cartesian algebra, also known as coordinate algebra or analytic geometry, is a branch of mathematics that deals with the use of algebraic equations to describe geometric shapes and their properties. It is named after the French philosopher and mathematician René Descartes, who developed the Cartesian coordinate system, which provides a way to describe the position of points in space using numbers.
A. Magnitude of E:
|E| = √((3i)² + (1j)²)
= √(9i² + 1j²)
= √(9 + 1)
= √(10)
Therefore, the magnitude of E is √(10).
B. Magnitude of F:
|F| = √((1i)² + (-3j)²)
= √(1 + 9)
=√(10)
Therefore, the magnitude of F is √(10).
C. Magnitude of G = E + F:
G = E + F = (3i + 1i) + (1j - 3j)
= 4i - 2j
|G| = √((4i)² + (-2j)²)
=√(16 + 4)
= √(20)
= 2√(5)
Therefore, the magnitude of G is 2√(5).
D. Magnitude of H = -E - 2F:
H = -E - 2F = (-3i - 2i) + (-1j + 6j)
= -5i + 5j
|H| = √(-5i)² + (5j)²)
= √(25 + 25)
= √(50)
= 5√(2)
Therefore, the magnitude of H is 5√(2).
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A battery is connected to an electrical circuit. During each second, 2.3 coulombs of charge pass through the battery when the switch is closed. The battery supplies energy to each coulomb of charge at a rate of 4.2J C^-1. Take 1 C = 6.24 x 10^18 electrons
State the potential difference across the battery
Answer:
The potential difference across the battery can be calculated using the equation:
Potential difference (V) = Energy supplied (J) / Charge (C)
Energy supplied during each second = 2.3 coulombs * 4.2 J/C = 9.66 J
Therefore, the potential difference across the battery would be:
Potential difference (V) = 9.66 J / 2.3 C = 4.2 V
So the potential difference across the battery is 4.2 volts.
Compared to the audible range for the average human ear, infrasonic waves have a
A. Lower frequency & longer wavelength
B. Higher frequency & shorter wavelength
C. Lower frequency & shorter wavelength
D. Higher frequency & longer wavelength
The Lower frequency & longer wavelength is the correct option (a).
What is frequency ?
The frequency is expressed in Hertz. A sound wave's frequency is determined by how many vibrations it produces ( f ). Another way to think of frequency is as the quantity of waves that pass a specific spot in a second.
What is wavelength ?
The distance between identical points (adjacent crests) in adjacent cycles determines how far a waveform signal has travelled in space or over a wire. In wireless systems, this length is often expressed in metres (m), centimetres (cm), or millimetres (mm).
Therefore, The Lower frequency & longer wavelength is the correct option (a).
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The temperature of the water was
originally 16.0°C. The specific heat of
water is approximately 4.18 J/g °C.
What is the change in thermal energy?
Assume the mass of the water is 1.00
kg. (Show your work!)
Answer: 4182 J/kg°C
Explanation: molar heat capacity is J/mole C not J/gC. 4.18 J/gC x (18.0 g / mole) = 75.2 J/moleC
I need help figuring this question out?
The momentum of the driver is 1,750 kgm/s.
What is the momentum of the driver?Momentum refers to an object's tendency to maintain its velocity (or speed) in a straight line unless acted upon by an external force.
The magnitude of momentum is determined from the product of mass and velocity of the object.
The momentum of the driver is calculated as follows;
P = mv
where;
m is the mass of the driverv is the speed of the driverP = 70 kg x 25 m/s
P = 1,750 kgm/s
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Below are free-body diagrams for three electric charges that lie in the same plane. Their relative positions are unknown.
Below are free-body diagrams for three electric ch
Along which of the lines (A to H) in the figure(Figure 1)should charge 2 be placed so that the free-body diagrams of charge 1 and charge 2 are consistent?
Figure 2:
Below are free-body diagrams for three electric ch
Along which of the lines (A to H) in the figure(Figure 2)should charge 2 be placed so that the free-body diagrams of charge 1 and charge 2 are consistent?
In Figure 1, charge 2 should be placed along line D to make the free-body diagrams of charge 1 and charge 2 consistent.
The electric field lines produced by charge 2 should point towards charge 1 to provide the attractive force between them. As shown in the free-body diagram of charge 1, the electric field lines point towards the left, which means that charge 2 should be placed on the left side of charge 1. Similarly, in Figure 2, charge 2 should be placed along line F to make the free-body diagrams of charge 1 and charge 2 consistent. The electric field lines produced by charge 2 should point towards the left to provide the attractive force between them. In Figure 1, charge 2 should be placed along line D to make the free-body diagrams of charge 1 and charge 2 consistent.
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What is the case of hose pipe in Newton's third law of motion?
Newton's third law of motion states that "for every action, there is an equal and opposite reaction." In the case of a hose pipe, this law applies to the forces involved in the flow of water through the hose.
When water is flowing through the hose, it is being accelerated by the pressure difference between the inlet and outlet of the hose. As the water moves through the hose, it exerts a force on the walls of the hose, pushing them outwards. This is the "action" described in Newton's third law.
According to the law, there must be an equal and opposite "reaction" force. In this case, the reaction force is the force that the hose exerts on the water. The force of the hose pushing outwards is equal and opposite to the force of the water pushing inwards.
This reaction force is what allows the water to flow through the hose. Without it, the water would not be able to move through the hose and would instead remain stationary.
So, in summary, in the case of a hose pipe, Newton's third law of motion applies to the forces involved in the flow of water through the hose. The force that the water exerts on the hose is equal and opposite to the force that the hose exerts on the water, and this allows the water to flow through the hose.
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i need help asappp
Lots of scientists had worked on the periodic table other than Mendeleev. What did Dmitri Mendeleev do that set him apart from all of the other scientist?
How do you think Mendeleev was able to so accurately estimate the properties of undiscovered elements?
What do you think would have changed if all of the scientist had worked closely together to figure out the best way to arrange the periodic table? Do you think collaboration is always the best answer
Answer:
Explanation:
1. Mendeleev predicted that there would be more chemical elements to come
2. by looking at the chemical properties
3. i think if all of them came together it would probably still look about the same tho ik it has changed over the years soo
A is thrown up into the air with initial vem/s. How fast is the ball moving when it first reachemeters?
Once the ball is thrown, the only force acting on it is gravity, which means that it's acceleration is -9.81 m/s² (negative means downward).
List the known and unknown quantities from the question.
u = initial velocity = 20 m/s
v = final velocity = ? m/s
g = acceleration due to gravity = -9.81 m/s²
t = time interval = ? s
s displacement = 11 m
Before calculating the time it takes for the ball to reach 11 m, the final velocity needs to be calculated using the following kinematic equation.
v² = u² + 2gs
v = √(u² + 2gs)
= √((20 m/s)² + (2x-9.81 m/s² x 11 m)) = 13.57 m/s V=
Calculate the time it takes the ball to reach 11 m using the following kinematic equation.
V = u + gt
Solve for t.
t = (v-u)/g
t (13 57 m/s - 20 m/s)/(-981 m/s²) = 0.655 s
Applying the maximum force you can exert, the heaviest box you can push at constant speed across a level floor with coefficient of kinetic friction μ has weight ω. Another box sits on a ramp that is inclined at an angle of β
above the horizontal. The coefficient of kinetic friction between the box and the ramp is μ.
If you apply the same magnitude maximum force, now parallel to the ramp, that you applied to the box on the floor, what is the heaviest weight box that you can push up the ramp at constant speed? (in both cases assume you can give enough extra push to get the box started moving)
The heaviest box you can push up the ramp at constant speed with a maximum force F is: ω = F / (μ sin(β))
Let F be the maximum force applied to the box, and let N be the normal force between the box and the ramp.
We can use the following equation to solve for the maximum weight of the box on the ramp:
F + μN = ω sin(β)
Where ω is the weight of the box, and β is the angle of the ramp.
hence, the heaviest box you can push up the ramp at constant speed with a maximum force F is:
ω = F / (μ sin(β))
What is speed?
Speed is the rate of change of an object's position over time, or the rate at which an object moves. Speed is a scalar quantity and is measured in metres per second (m/s).
Therefore, The heaviest box you can push up the ramp at constant speed with a maximum force F is: ω = F / (μ sin(β))
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Which two elements have similar properties and 8 electrons in their outmost shells?
Answer:
neon and argon
Explanation:
because they are inert gas
What are the main forces involved in a flying plane?
Answer:
There are four main forces involved in the flight of an airplane: lift, weight, thrust, and drag.
Explanation:
1. Lift: Lift is the force that opposes the weight of an aircraft and keeps it in the air. It is generated by the wings as they move through the air and is affected by factors such as the shape of the wings, the angle of attack, and the speed of the aircraft.
2. Weight: Weight is the force of gravity acting on an aircraft and pulling it downward. It is proportional to the mass of the aircraft and the acceleration due to gravity.
3. Thrust: Thrust is the forward force generated by the engines of an aircraft. It must be greater than the drag force in order to maintain forward flight.
4. Drag: Drag is the aerodynamic force that opposes the forward motion of an aircraft. It is caused by the friction of the air moving past the surface of the aircraft and is affected by factors such as the speed of the aircraft, its shape, and the altitude.
These four forces are in a constant state of balance during flight, with the pilot adjusting the thrust and angle of attack to maintain a stable flight.
If air resistance exerts a constant force of 200 N on a car, what amount of forward force from the engine is
needed to make a 1000 kg car accelerate at 10 m/s² forward? Is this force constant or increasing?
The forward force is 10200 N.
What is the forward force?The term "forward force" is not commonly used as a specific term, but it could refer to any force that acts in the direction of motion of an object. For example, the force generated by a car's engine that propels it forward is commonly referred to as the "driving force," which could be considered a type of forward force.
We have to note that the Fnet = ma
= 1000 * 10 = 10000 N
Thus;
Fnet = Force force - Resistance force
Forward force = Fnet + Resistance force
= 10000 + 200
= 10200 N
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The amount of forward force from the engine needed to make the 1000 Kg car accelerate 10 m/s² forward is 10200 N
How do I determine the forward force needed to accelerate the car?First, we shall obtain the net force acting on the 1000 Kg car. Details below:
Mass of car (m) = 1000 KgAcceleration of car (a) = 10 m/s²Net force (F) =?Net force = mass × acceleration
Net force = 1000 × 10
Net force = 10000 N
Finally, we shall obtain the forward force needed to accelerate the car. This is illustrated below:
Net force = 10000 NResistant force = 200 NForward force = ?Net force = Forward force - resistant force
10000 = Forward force - 200
Collect like terma
Forward force = 10000 + 200
Forward force = 10200 N
Thus, the forward force needed is 10200 N
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Part A The integral with respect to time of a force applied to an object is a measure called impulse, and the impulse applied to an object during a time interval determines its change in momentum during the time interval. The safety of a t-shirt launcher, used to help get crowds cheering at baseball games, is being evaluated. As a first step in the evaluation, engineers consider the design momentum of the launched t-shirts. The springs in the launcher are designed to apply a variable force to a t-shirt over a time interval of tu=0.5 s. The force as a function of time is given by F(t) = at' + b, where a = -28 N/s' and b = 7.0 N. F (t) dt. By applying the given time The momentum of the t-shirt will be its initial momentum (po = 0) plus its change in momentum due to the applied impulse: pj=po+ S dependent function for F(t) and performing the integration, which of the following is the correct expression for p/? View Available Hint(s) P = 0+ )6 0+*+8 +b)16 0+(+3 + bt) 0+ +) Submit Previous Answers ✓ Correct We check that we have obtained the correct form of the integral by performing differentiation of t + bt with respect to t, which gives at +b= F(t) as expected. Correct If the Jadarian-Ruby had been properly maintained, GAJMO Nermalloy would be able to successfully complete the delivery mission. The result can be found using KE2 = KE + F(2) dr. When F(2) is constant, F(2) = Fo, and the result of the integral is simply FoAr. That is, the measure of work represented by the integral is exactly the measure of the rectangle with height Fo and width Ar. For functions of other forms, rectangles only approximate the measure, and the integral allows us to evaluate the measure in the limit that the rectangles have infinitesimal width and the measure becomes exact. Part E Evaluate the final kinetic energy of the supply spacecraft for the actual tractor beam force, F(x) = ax + 8. View Available Hint(s) KE = 1.07. 1010 J Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining
The final kinetic energy of the supply spacecraft is [tex]6.4 *10^{11} J[/tex] and final kinetic energy of the supply spacecraft can be found using the work-energy principle.
The work done by the tractor beam force can be found by integrating the force with respect to distance. Since the force is a function of x, we need to express the distance traveled by the spacecraft as a function of x. We know that the spacecraft starts from rest at x = 0 and moves a distance of [tex]4.0 * 10^5 m[/tex], so we have:
[tex]x = 0 + (1/2)ax^2 + 8x[/tex]
We can simplify this expression to:
[tex]x = (1/2)ax^2 + 8x[/tex]
Now we can express the work done by the tractor beam force as an integral:
W = ∫ F(x) dx from [tex]x = 0[/tex] to [tex]x = 4.0 * 10^5 m[/tex]
W = ∫ (ax + 8) dx from [tex]x = 0[/tex] to [tex]x = 4.0 * 10^5 m[/tex]
[tex]W = (1/2) a (4.0 * 10^5)^2 + 8 (4.0 *10^5)[/tex]
[tex]W = 6.4 * 10^{11} J[/tex]
The work done by the tractor beam force is [tex]6.4 * 10^{11} J[/tex].
Since the work done on the spacecraft is equal to the change in kinetic energy of the spacecraft, we have:
W = KE2 - KE
where KE is the initial kinetic energy of the spacecraft, which is zero.
Therefore, the final kinetic energy of the spacecraft is:
[tex]KE2 = W = 6.4 *10^{11} J[/tex]
So the final kinetic energy of the supply spacecraft is [tex]6.4 * 10^{11} J[/tex].
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6.
(3 points) What is the mass in g of 500.0 mL of propylene glycol,
which has a density of 1.036 g/mL? Express your answer to the
correct number of significant figures.
Taking into account the definition of density, the mass of 500.0 mL of propylene glycol, which has a density of 1.036 g/mL, is 518 g.
Definition of densityDensity is the amount of matter in a given space and is defined as the amount of mass of a substance per unit volume.
In other words, density is defined as the amount of mass in a certain volume of a substance.
The expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:
density= mass÷ volume
Mass of propylene glycolIn this case, you know that:
Density= 1.036 g/mLVolume= 500 mLReplacing in the definition of density:
1.036 g/mL= mass÷ 500 mL
Solving:
mass= 1.036 g/mL×500 mL
mass= 518 g
Finally, the mass is 518 g.
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3.1 Displacement, Velocity, and Acceleration
A turtle's velocity changes from v₁ = 1.0 mm/s at 0 = 0° to v₂ - 1.2 mm/s at 0= 20°. What is the change in the turtle's velocity?
Answer:
Explanation:
Displacement, velocity, and acceleration are fundamental concepts in physics that describe the motion of objects.
Velocity is a vector quantity that describes the rate of change of an object's position in a particular direction. It is defined as the displacement (the change in position) divided by the time it took to cover that displacement.
Acceleration is the rate of change of velocity, or the rate at which an object changes its speed or direction of motion. It is a vector quantity that is defined as the change in velocity divided by the time it took to achieve that change.
The change in velocity, also known as the delta velocity, is the difference between the initial velocity (v₁) and the final velocity (v₂). In this case, the change in velocity can be calculated as follows:
Δv = v₂ - v₁ = 1.2 mm/s - 1.0 mm/s = 0.2 mm/s
So, the turtle's velocity changes by 0.2 mm/s from 1.0 mm/s to 1.2 mm/s at 0=20°.
In summary, velocity describes the rate of change of an object's position, acceleration describes the rate of change of velocity, and the change in velocity is the difference between the final and initial velocities.
the perception that seemingly infertile couples who adopt a child are subsequently more likely to conceive a child themselves best illustrates
The perception that seems infertile couples who adopt a child are generally more likely to conceive a progeny themselves best describes an illusory correlation.
What is an illusory correlation?Illusory correlation when we overexcite to one outcome and ignore the other. In psychology, it states that the relationship between the variables, even such a relation does not exist.
In the given passage couples who adopt a child are subsequently more likely to conceive a child themselves best explains, suggesting the illusory correlation.
Therefore, this passage suggests an illusory correlation.
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Both Josef Loschmidt and Amedeo Avogadro contributed to our understanding of basic molecular numbers sizes reaction ratios. Neither scientist discovered avogadro’s number in the form we use today (6.02 x 10^23). Still, there’s controversy over the name of this number. Research the contributions of these two scientists and how Avogadro’s number got its name. Note the name you think is the number should be called provide key details about each scientist contribution to this concept and give a solid rationale for your case and Namingthe number.
Avogadro's number, which is equal to [tex]6.02214076 \times 10^23[/tex] Is the quantity of units in one mole of any material (defined as its molecular weight in grams).
What Avogadro’s number in the form we use today?Avogadro made the right assumption that equivalent quantities of gases at the same pressure and temperature contain an equal number of molecules. Avogadro proposed a theory in 1811 that his contemporaries disregarded for many years.
In order to determine how many particles there are in a cubic centimetre of gas under ideal conditions, Loschmidt employed the kinetic molecular theory in 1865. The acknowledged value of this quantity—now known as the Loschmidt constant is [tex]2.6867773 \times 10^25 m-3.[/tex]
Therefore, equal volumes of gases at the same temperature and pressure should contain equal numbers of molecules, as Avogadro rightly theorized. It is [tex]6.02214076 \times 10^23[/tex] Or Avogadro's number.
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A string wraps around uniform cylinder of mass M; which rests on fixed plane The string passes up over massless pulley and is connected t0 mass m, as shown in the figure. Assume that the cylinder rolls without slipping on the plane, Jd that the string is parallel to the plane What is the acceleration of the mass m? What is the condition on the ratio M /m for which the cylinder accelerates down the plane? (don't forget to include friction)
The cylinder rolls on the plane without slipping, and the string is parallel to the plane. Assume the cylinder has a radius of R and an inertia moment about its center of mass of I.
Tension in the string (T), the gravitational force on mass m (mg), and the frictional force on the cylinder from the plane are the forces acting on the system (f).
The tension in the string (T) is balanced by the gravitational force on mass m because the string is parallel to the plane (mg). As a result, we can write:
T = mg
To find the acceleration of mass m, we can use Newton's second law for the vertical motion of mass m:
mg - T = ma
Substituting T with mg, we get:
a = g - g(M/m)
where M/m is the ratio of the masses of the cylinder and the mass, respectively.
To find the condition on the ratio M/m for which the cylinder accelerates down the plane, we need to apply Newton's second law for the rotational motion of the cylinder. The torque acting on the cylinder is due to the frictional force f, which is given by:
f = μN
where μ is the coefficient of static friction, and N is the normal force on the cylinder from the plane. Since the cylinder rolls without slipping, the frictional force f is equal to the force due to the tension in the string, which is mg.
Therefore, we can write:
mg = f = μN
The normal force N is equal to the weight of the cylinder, which is Mg. Therefore, we can write:
mg = μMg
Simplifying, we get:
μ = m/M
For the cylinder to accelerate down the plane, the frictional force must be less than or equal to the maximum static frictional force, which is given by:
f_max = μ_s N
where μ_s is the coefficient of static friction. Therefore, we need to have:
f <= f_max
Substituting f and f_max, we get:
mg <= μ_s Mg
Substituting μ = m/M, we get:
mg <= μ_s Mg
Simplifying, we get:
m/M <= μ_s
Therefore, the condition on the ratio M/m for which the cylinder accelerates down the plane is:
M/m > μ_s
where μ_s is the coefficient of static friction between the cylinder and the plane.
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.Impulse is equal to ... (pick TWO answers) * A.the change in momentum of an object. B.the change in mass of an object. C.the change in volume of an object. D.a force applied to an object for a period of time. E.the original momentum of the object.
The impulse is force × time. Option D
What is Impulse in Physics?In physics, impulse is a quantity that describes the change in momentum of an object that results from a force acting on it for a period of time. Mathematically, impulse is defined as the product of force and the time interval over which it acts:
Impulse = force × time
The unit of impulse is the newton-second (N·s) in the SI system of units.
Impulse is closely related to the concept of momentum, which is the product of an object's mass and velocity. When a force acts on an object, it causes a change in the object's momentum. The magnitude of this change is equal to the impulse that the force imparts on the object.
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The tires of a car make 73 revolutions as the car reduces its speed uniformly from 94.0 km/h to 60.0 km/h. The tires have a diameter of 0.84 m.
Part C: If the car continues to decelerate at this rate, how far does it go? Find the total distance.
Express your answer to three significant figures and include the appropriate units.
If the car continues to decelerate at this rate then the total distance of car is 324.91 meters.
What is decelerate?
When an object slows down, it undergoes deceleration, which is the opposite of acceleration. There are usually two ways that acceleration slows down. The first occurs when an object slows down by itself. Gravity, friction, or momentum loss could be to blame. The second is when the object is subjected to an external force, such as when a car driver applies the brakes or a pilot deploys the air brakes in an airplane. A journey that is both safe and successful requires deceleration, which is an essential component of movement.
When the vehicle revs at 73, then :d₁ = R × θ
= 0.42×73×2× π
= 192.6 m
Using 2nd kinematic equation for distance traveled in next 16 sec:
θ₁ = wi × t + (1/2)× α ×t²
θ₁ = 39.69 × 16 + (1/2) × (-2.5) × 16²
= 315.04 rad
d₂ = R× θ₁
= 0.42× 315.04
= 132.31 m
So total stopping distance = 192.6 + 132.31
= 324.91 m
Therefore, the total distance is 324.91 m.
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A compound has a molar mass of 123. 22 g/mol. What is the molecular formula of a substance that has this molar mass?.
If the given compound has a molar mass of 123.22 g/mol then, SrS is the molecular formula of a substance that has this molar mass. Therefore, option c is the correct answer according to the given information.
The molecular formula is defined as the number of atoms present in the molecules of a chemical compound when the two molecules of different substances are combined together. The molecular mass is the mass of a given molecule measured in daltons.
The molar mass of Strontium = 87.22g/mol
The molar mass of Sulfur = 32 g/mol.
The total molecular mass of these two combined compounds
= Strontium + Sulfur = SrS
SrS = 87.22 + 32 = 123.22g/mol.
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The complete question is-
A compound has a molar mass of 123.22 g/mol. what is the molecular formula of a substance that has this molar mass?
A. CoH4
B. PSF3
C. SrS
D. ZrO2
The mass of Jupiter is 1/1047 of the Sun's mass (that's 0.000955). We want to confirm this using Newton's version of Kepler's Third Law, following the examples in Lecture 7. We'll use the approximate data for two different moons of Jupiter to see how close the results are. Pick the closest answer in each case: (a) Ganymede is the third moon from the inside. It has an orbital period around Jupiter of approximately 0.0194 Earth years. Its semimajor axis is 0.0071 AU. Which of these comes closest to the mass of Jupiter (in solar masses) when using these data → [Select ] 0.000951 (b) Europa is the second moon from the inside. It has an ork 0.000989 approximately 0.0096 Earth years. Its semimajor axis is 0.0045 AU. Which of these comes closest to the mass of Jupiter (in solar masses) when using these data? [Select] Hint: See also example 3.4 in the textbook.
These come closest to the mass of Jupiter as (a) 0.000951; (b) 0.000955.
what is Kepler's law?Kepler's laws describe the motion of planets in their orbits around the sun.
This question involves using Newton's version of Kepler's Third Law to calculate the mass of Jupiter. Kepler's Third Law states that the square of the period of revolution of a planet/moon around a central object is proportional to the cube of the semimajor axis of the orbit. Newton's version of the law introduces the masses of the two objects in the equation, allowing us to solve for the mass of the central object (in this case, Jupiter) if we know the period and semimajor axis of a moon's orbit around it.
For part (a), we are given the period and semimajor axis of Ganymede's orbit and asked to select the closest answer for the mass of Jupiter when using this data. By plugging the values into Newton's version of Kepler's Third Law and solving for Jupiter's mass, we get an answer of 0.000951 solar masses.
For part (b), we are given the period and semimajor axis of Europa's orbit and asked to select the closest answer for the mass of Jupiter when using this data. Again, by plugging the values into the equation and solving for Jupiter's mass, we get an answer of 0.000989 solar masses.
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. Find the net resistance of 113 such strands if they are placed side by side to form a cable of the same length as a single strand.
The net resistance of 113 strands placed side by side is 1/113th of the resistance of a single strand.
Assuming that each strand has the same resistance, the net resistance of 113 strands placed side by side can be found by calculating the equivalent resistance of a parallel combination of 113 resistors. The formula for calculating the equivalent resistance of a parallel combination of resistors is:
1/R = 1/R1 + 1/R2 + ... + 1/Rn
where R is the equivalent resistance, and R1, R2, ..., Rn are the resistances of the individual components.
In this case, we have 113 strands, so n = 113. Since the strands are placed side by side, they are in parallel, so we can use the above formula to find the equivalent resistance:
1/R = 1/R1 + 1/R2 + ... + 1/R113
R = 1 / (1/R1 + 1/R2 + ... + 1/R113)
Since we don't know the resistance of a single strand, we cannot calculate the exact value of the net resistance. However, if we assume that each strand has the same resistance, we can use the formula for the equivalent resistance of n equal resistors in parallel:
1/R = n / R1
R = R1 / n
Substituting n = 113, we get:
R = R1 / 113
This means that the net resistance of 113 strands placed side by side is 1/113th of the resistance of a single strand.Assuming that each strand has the same resistance, the net resistance of 113 strands placed side by side can be found by calculating the equivalent resistance of a parallel combination of 113 resistors. The formula for calculating the equivalent resistance of a parallel combination of resistors is:
1/R = 1/R1 + 1/R2 + ... + 1/Rn
where R is the equivalent resistance, and R1, R2, ..., Rn are the resistances of the individual components.
In this case, we have 113 strands, so n = 113. Since the strands are placed side by side, they are in parallel, so we can use the above formula to find the equivalent resistance:
1/R = 1/R1 + 1/R2 + ... + 1/R1₁₃
R = 1 / (1/R₁ + 1/R₂ + ... + 1/R1₁₃)
Since we don't know the resistance of a single strand, we cannot calculate the exact value of the net resistance. However, if we assume that each strand has the same resistance, we can use the formula for the equivalent resistance of n equal resistors in parallel:
1/R = n / R₁
R = R1 / n
Substituting n = 113, we get:
R = R₁ / 113
This means that the net resistance of 113 strands placed side by side is 1/113th of the resistance of a single strand.
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A battery is connected to an electrical circuit. During each second, 2.3 coulombs of charge pass through the battery when the switch is closed. The battery supplies energy to each coulomb of charge at a rate of 4.2J C^-1. Take 1 C = 6.24 x 10^18 electrons
State the potential difference across the battery
The potential difference across the battery is 4.2 volts.
What is potential difference?
Potential difference is described as the amount of work energy required to move an electric charge from one point to another.
The unit of potential difference is the volt.
The potential difference across the battery is calculated using the equation:
V = W / Q
Workdone = Q * Vbattery = 2.3 C * 4.2 J/C = 9.66 J
Therefore, the voltage across the battery can be calculated as:
V = W / Q = 9.66 J / 2.3 C = 4.2 V
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Jumping Off. A person of mass m jumps off a ledge that is a distance h off the ground. Their legs are straight in the air, but as they land, they bend their knees at the instant they touch the ground. Treated as a particle, they move an additional distance d downward as they hit the ground before coming to a complete stop. * Find an expression for the person's acceleration after they touch the ground in terms of g, h and d. * Draw a FBD of the person while they are in contact with the ground. Find an expression for the amount of force they apply on the ground to stop in distanced in terms of m, g, h, and d. * If the person is able to apply a force equal to 5.00 times their weight with their legs, what would the required distance to stop be if they jumped from a height of 3.00 m?
The expression for the person's acceleration after they touch the ground in terms of g, h and d is a = 2gh / (2h/g + sqrt(2gh + 2gd).
What is an acceleration?An acceleration refers to the change in velocity with respect to time in terms of speed and direction. In the case given here, assuming no air resistance, the potential energy of the person at the top of the ledge is converted into kinetic energy just before they hit the ground.
Let's consider the motion of the person after they touch the ground. We assume that the person's acceleration is constant during the time they move a distance d. Let a be the acceleration of the person after they touch the ground, and let t be the time it takes for them to come to a complete stop. Then:
⇒ d = 1/2 × a t²........... (1)
⇒ v = at........(2)
⇒ h + d = 1/2 gt² + vt......... (3)
where, v is the velocity of the person just before they touch the ground, and g is the acceleration due to gravity.
Therefore,
t = (sqrt(2gh + 2gd + v²) – v) / g
a = 2(d + h) / t² – g
Substituting v = sqrt(2gh):
a = 2gh / (2h/g + sqrt(2gh + 2gd))
Therefore, the acceleration of the person after they touch the ground is:
a = 2gh / (2h/g + sqrt(2gh + 2gd))
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A ball with momentum must also have?
A. Kinetic energy
B.Thermal energy
C.Gravitational potential energy
D.Elastic energy
c. i) A block of mass of 2 kg with constant velocity is pushed along a table by a
force of 5N, what is the magnitude of the force opposing its motion?
Answer:
The Force of Friction:
Friction is a self-adjusting force. The block in the question is moving with constant velocity under the force of 5 N. This implies that the force of kinetic friction acting on the block is also 5 N, acting opposite to the applied force and net force on the block is
What is the power of x? Explain how similar and different is the excel equation is to equation 3. [5 points]
equation 3 is V=kQ/d
The power of x is the exponent of x in an equation. The power of x (x^n) is the result of multiplying a number (x) by itself (n) times. For example, in an equation of the form x^a, the power of x is a.
For example, if x = 2 and n = 3, then x^n = 8 (2 x 2 x 2).
The Excel equation is similar to the equation V=kQ/d in that they both contain variables (x, k, Q, and d) and the goal is to calculate a result (x^n, V). However, the Excel equation is specific to the power of x and is used to calculate the result of multiplying a number by itself a certain number of times. The equation V=kQ/d is used to calculate velocity based on a constant (k), a quantity (Q), and a distance (d). However, the equation V=kQ/d does not involve x, and it is used to calculate the voltage, V, in a circuit. The power of x is simply a mathematical notation used to indicate the number of times a variable is multiplied by itself, while the equation V=kQ/d is used to calculate the voltage in a specific circuit.
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