A rectangular gasoline tank can hold 36.0 kg of gasoline when full. what is the depth of the tank (in m) if it is 0.450 m wide by 0.900 m long? m (b) what is the volume of the tank (in gal)? (it is suitable for a passenger car.) gal

(1)   Through the Second Law of motion, the equation  for Force is:

                                 F = m x a

Where m is mass and a is acceleration (deceleration)

(2)   Distance is calculated through the equation,

                             D = Vi^2 / 2a

Where Vi is initial velocity

(3)   Work is calculated through the equation,

                          W = F x D

Substituting the known values,

Part A:

(1)     F = (85 kg)(2 m/s^2) = 170 N

(2)     D = (37 m/s)^2 / (2)(2 m/s^2)  = 9.25 m

(3)     W = (170 N)(9.25 m) = 1572.5 J

Part B:

(1)    F = (85 kg)(4 m/s^2) = 340 N

(2)   D = (37 m/s)^2 / (2)(4 m/s^2) = 4.625 m

(3)    W = (340 N)(4.625 m) = 1572.5 J

We have that the velocity  two block system   is mathematically given as

vcm= -16 m/s

Velocity  two block system

Question Parameters:

With a mass of 4.0 kg, is moving with a speed of 2.0 m/s while block B , with a mass of 8.0 kg, is moving in the opposite direction with a speed of 3.0 m/s.

Generally the equation for the Velocity   is mathematically given as

vcm = (m1*v1) + (m2*v2)

vcm = ((4*2)-(8*3))

vcm= -16 m/s

And the direction is

dcm = in the direction of block B

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Answer: Option (1)

Explanation: A spring tide occurs when the sun, earth and the moon are collinear. It is the condition in which the gravitational pull is exerted on earth by both the sun as well as the moon, from opposite sides. Due to this, there occurs a high tide, in comparison to the regular tide, because of the combination of both the gravitational force. It occurs two time a year on each of the lunar month.

Thus, the correct answer is option (1).

A spring tide, characterized by higher tides due to the alignment of the Sun, Moon, and Earth, occurs about 26 times a year at every full and new moon. Neap tides occur when the Moon is at first or last quarter, resulting in lower than usual tides.

A spring tide occurs about 26 times per year, at every full and new moon. The term 'spring tides' is connected not to the season but to the idea that higher tides 'spring up'. During a spring tide, the Sun, Moon, and Earth are aligned, causing the Sun's and Moon's gravitational pulls to reinforce each other. This creates higher than usual tides as tidal bulges occur on both sides of the Earth.

In contrast, when the Moon is at first or last quarter (at right angles to the Sun's direction), neap tides occur. At this time, the Sun's tides partially cancel out the Moon's tides, resulting in lower than usual tides. The actual magnitude of these tides can be affected by the distances from the Earth to the Moon and Sun.

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Among all the given options, the correct option is option A. Distance, displacement, or acceleration can be used to describe motion.

Physical quantity concepts like velocity, velocity, distance, displacement, or acceleration can be used to describe motion. Sir Isaac Newton provided the correct definition of motion. These quantities are all explained in terms of the same parameter, time.

The proportion of the total all quantities to the entire number of quantities is what is simply meant by the word "average." In Physics, an alternative strategy is used. Let's first define velocity precisely as well as speed and how the two are related before moving on to average velocity.

Total Displacement = Area under v-t graph

=πr²/2

=π×1²/2

=π/2m

Average velocity = Total Displacement / total time

= π/2/2 = π/4m/s

Therefore, the correct option is option A.

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Final answer:

The speed of the surface current near Tokyo, Japan can vary depending on various factors such as tides and weather conditions. However, a typical range for surface currents in the ocean is around 1-2 meters per second or 2-4 knots.

Explanation:

The speed of the surface current near Tokyo, Japan can vary depending on various factors such as tides and weather conditions. However, a typical range for surface currents in the ocean is around 1-2 meters per second or 2-4 knots.

It's important to note that the speed of surface currents can change and is not constant. Factors such as the Earth's rotation, wind patterns, and the shape of the coastline can influence the speed and direction of surface currents.

Ultimately, it is recommended to consult local oceanographic data or resources for more precise and up-to-date information on the speed of the surface current near Tokyo, Japan.

At thermal equilibrium, when the colder object has a higher heat capacity than the hotter object, the final temperature of the system will be closer to the initial temperature of the colder object.

Thermal Equilibrium of Two Objects

When two objects with different initial temperatures are placed in thermal contact and isolated from their surroundings, they will exchange heat until reaching thermal equilibrium. Specifically, the zeroth law of thermodynamics states that if two systems are in thermal contact and no heat flows between them, they are at the same temperature, implying they have reached thermal equilibrium.

The object with the higher heat capacity can absorb more heat without a significant increase in temperature.

The concept of thermal equilibrium in thermodynamics states that objects in contact will approach the same temperature, following the zeroth law of thermodynamics.

In the scenario, where the heat capacity of the colder object B is much greater than that of the hotter object A, and both objects are allowed to reach thermal equilibrium, the final temperature of the system will be closer to the initial temperature of object B, the colder object. This is because the object with the greater heat capacity will undergo a smaller change in temperature for the same amount of heat exchange, compared to the object with the smaller heat capacity.

Calculate the magnitude and direction of the acceleration of a proton placed in an electric field of 500 N/C.

Magnitude of Acceleration: The magnitude of the acceleration of the proton can be calculated using Newton's second law, F = ma, where F is the force experienced by the proton in the electric field. Given that the electric field intensity is 500 N/C and the charge of a proton is 1.6 x 10^-19 C, you can find the acceleration.

Direction of Acceleration: The direction of the acceleration will be the same as the direction of the force experienced by the proton in the electric field, which is determined by the positive charge of the proton relative to the field lines.

The acceleration of a proton in a 500 N/C electric field is calculated using the charge of the proton and its mass, along with the given field intensity. The proton's charge is 1.60 x 10^-19 C, and its mass is 1.67 x 10^-27 kg. The proton accelerates in the same direction as the electric field.

To calculate the magnitude and direction of the acceleration of a proton in an electric field, we can use the formula for force F exerted on a charge q in an electric field E: F = qE. Next, we use Newton's second law of motion, which states that the force F on an object is equal to its mass m times its acceleration a: F = ma. Since the two expressions are both equal to the force F, we can set them equal to each other to find the acceleration: ma = qE. For a proton, the charge q is equal to the elementary charge, which is approximately 1.60 x 10-19 C. Hence, the acceleration a is found by rearranging the formula to a = qE/m.

The mass of a proton is approximately 1.67 x 10-27 kg. Substituting the given electric field intensity of 500 N/C, the charge of a proton, and the mass into the formula, we get:

a = (1.60 x 10-19 C) \\* (500 N/C) / (1.67 x 10-27 kg)

Calculating this, we get the acceleration a of the proton. Since the proton is positively charged, it will accelerate in the same direction as the electric field. This gives us both the magnitude of the acceleration and its direction.

Final answer:

The initial speed of a flea as it leaves the ground to reach a height of 0.550 meters is approximately 3.29 meters per second, calculated using the formula v = √{2gh}, where g is the acceleration due to gravity and h is the height.

Explanation:

The question asks us to find the initial speed of a flea as it leaves the ground to reach a height of 0.550 meters. To solve this, we can use the physics concept of kinematic equations, specifically the one that relates initial velocity, acceleration due to gravity, and maximum height achieved by a projectile. The formula we will use is: v = √{2gh}, where v is the initial velocity, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the maximum height (0.550 m).

Substituting the given values into the formula, we get:
v = √{2*9.81*0.550} = 3.29 m/s.

Therefore, the initial speed of the flea as it leaves the ground is approximately 3.29 meters per second.

The maximum amount by which the wavelength of an incident photon could change in Compton scattering depends on the angle of scattering and can be calculated using the given formula.

In Compton scattering, the wavelength of an incident photon can change. The maximum change in wavelength, or shift, can be determined by using the formula:

Change in wavelength (Δλ) = Compton wavelength (λc) * (1 - cosθ)

Where λc is the Compton wavelength, given by:

In this formula, h is Planck's constant, m is the mass of the scattering particle (in this case, the atom with a mass of 36.0 u), and c is the speed of light.

The maximum amount by which the wavelength of an incident photon could change depends on the angle of scattering (θ) and can be calculated using the formula mentioned above.

In Physics, the work done on a system is calculated using the formula W = P∆V. Using a conversion factor to change atmospheres to Joules/liter, the total work done by the piston as the cylinder's volume changed was approximately 744.55 Joules.

The work done on a system in physics is given by formula W = P∆V, where P is pressure and ∆V is the change in volume. Considering the conversion factor of 1 atm equaling 101.3 J/liter in this context, we apply this formula to find the work done. Given that the pressure equals 15.0 atm, which is equal to 1519.5 Joules per liter, and the change in volume equals 0.490 liters (0.640 liters - 0.150 liters), we multiply these values together to determine the work to be approximately 744.55 Joules.

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Gravity is a force attracting two masses, with strength depending on their mass and distance apart. Air resistance affects how objects fall, especially lighter ones. A creative example is traveling by balloons, where releasing air and gravity interact to influence descent.

Explanation of Gravity

Gravity is a fundamental force that causes two objects with mass to be attracted to one another. It is why objects fall to the ground when released, and it keeps planets in orbit around stars. The force of gravity depends on the mass of the objects and the distance between them. According to Newton's law of gravity, the more mass an object has, the more powerful its gravitational pull. According to Einstein's theory of general relativity, gravity is the result of massive objects causing a curvature in spacetime.

Effect of Mass on Gravity

The force of gravity is directly proportional to the mass of the objects involved, meaning that larger masses will exert a stronger gravitational pull. If you were to calculate the gravitational pull between two objects, you would use the equation F = G (m1 * m2) / r², where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers of mass.

Role of Air Resistance

Air resistance acts against the force of gravity, especially on light or low-density objects. It is this resistance that explains why a feather falls more slowly than a bowling ball, despite gravity pulling on all objects equally. Air resistance depends on the speed and surface area of the falling object, as well as the density of the air.

Creative Example of the Force of Gravity

Imagine a world where everyone travels by balloons. The only way to move downward is by releasing some of the air from your balloon. Here, the force of gravity and the mass of the person in the balloon interact to determine how quickly they descend, with air resistance playing a part depending on the size and shape of the balloon.

To solve this problem, we know that:

1 Albert = 88 meters

1 A = 88 m

The first thing we have to do is to square both sides of the equation:

(1 A)^2 = (88 m)^2

1 A^2 = 7,744 m^2

Since it is given that 1 acre = 4,050 m^2, so to reach that value, 1st let us divide both sides by 7,744:

1 A^2 / 7,744 = 7,744 m^2 / 7,744

(1 / 7,744) A^2 = 1 m^2

Then we multiply both sides by 4,050.

(4050 / 7744) A^2 = 4050 m^2

0.523 A^2 = 4050 m^2

Therefore 1 acre is equivalent to about 0.52 square alberts.

The roller coaster's path is represented by two vectors: a horizontal and an inclined one. The inclined path is further broken into its vertical and horizontal components. By summing up the squares of the total horizontal and vertical distances (after calculating these components) and taking the square root, the magnitude of the resultant vector equates to 323.95 feet.

The question relates to the calculation of the magnitude of a resultant vector, which is a concept in physics. The roller coaster's path can be represented as two vectors - the horizontal and the inclined path. The magnitude of the resultant vector can be calculated using the Pythagorean theorem, which is commonly used in physics to determine the resultant of perpendicular vectors.

The horizontal displacement is 200 feet. However, the vertical displacement is part of the inclined path, which needs to be broken down into its components to get the vertical and horizontal distances. The vertical distance covered in the inclined path can be calculated as 135 sin(30) = 67.5 feet and the horizontal distance as 135 cos(30) = 116.7 feet. Thus, the total horizontal distance becomes 200 + 116.7 = 316.7 feet.

The resultant vector, which represents the total path covered by the roller coaster, can be calculated by adding the squares of the total horizontal and vertical distance and then taking the square root of the sum. Using the Pythagorean theorem, the magnitude of the resultant vector becomes √(316.7² + 67.5²) = 323.95 feet.

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Answer: The correct answers are "chemical energy into electrical energy" and then "the electrical energy into light energy".

Explanation:

In the battery-powered flashlight, the battery supplies the chemical energy which makes the electrons to flow in the circuit and constitutes the current.

Then, the flashlight flashes the light in this way.

In the battery-powered flashlight, firstly, the chemical energy gets converted into electrical energy and then the electrical energy  gets converted into light energy.

Answer:

speed or velocity

Explanation:

The ratio of distance travels to the time taken is called speed.

Speed = distance traveled / time taken

Speed is a scalar quantity and its SI unit is m/s.

If the direction of distance given then it is velocity.

Velocity is defined as the ratio of displacement to the time taken.

Velocity is a vector quantity and its SI unit is m/s.

There are many ways to solve this but I prefer to use the energy method. Calculate the potential energy using the point then from Potential Energy convert to Kinetic Energy at each points.

PE = KE

From the given points (h1 = 45, h2 = 16, h3  = 26)

Let’s use the formula: 

v2= sqrt[2*Gravity*h1]  where the gravity is equal to 9.81m/s2

v3= sqrt[2*Gravity*(h1 - h3 )] where the gravity is equal to 9.81m/s2

v4= sqrt[2*Gravity*(h1 – h2)] where the gravity is equal to 9.81m/s2

Solve for v2

v2= sqrt[2*Gravity*h1]      

    = √2*9.81m/s2*45m

v2= 29.71m/s

v3= sqrt[2*Gravity*(h1 - h3 )   

    =√2*9.81m/s2*(45-26)

    =√2*9.81m/s2*19 

v3=19.31m/s

v4= sqrt[2*Gravity*(h1 – h2)]        

    =√2*9.81m/s2*(45-16)

    =√2*9.81m/s2*(29)

v4=23.85m/s

To calculate the speed at points 2, 3, and 4 of the roller-coaster car, we can use the principle of conservation of mechanical energy. At point 1, the car is released from rest, so its initial velocity is 0 m/s. Therefore, its potential energy at point 1 is equal to its total mechanical energy at point 1. Using the principle of conservation of mechanical energy again, we can find the speed at points 2, 3, and 4.

To calculate the speed at points 2, 3, and 4 of the roller-coaster car, we can use the principle of conservation of mechanical energy. At point 1, the car is released from rest, so its initial velocity is 0 m/s. Therefore, its potential energy at point 1 is equal to its total mechanical energy at point 1:

Using the principle of conservation of mechanical energy again, we can find the speed at point 2:

Similarly, we can find the speed at point 3 using the same principle:

Finally, the speed at point 4 can be found:

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The first step in solving this problem is to calculate for the volume of ice: 
V = A w

V = 1 m^2 (0.010 m)

V = 0.010 m^3

 
At 0°C, the density of solid block of ice is: d = 917 kg / m^3 

Therefore the mass of the solid ice is:

m = 917 kg / m^3  * 0.010 m^3

m = 9.17 kg

The heat of fusion of ice is equivalent to 333.55 kJ/kg, therefore: 
Phase change enthalpy = 333.55 kJ/kg (9.17 kg)

Phase change enthalpy = 3,058.65 kJ = 3,058,650 J

 
Using 1kW/m^2 insolation energy: 
1kW/m^2 * (.05) * sin(90°-37°) = 39.93 Watts = 39.93 Joule/s m² 

Therefore the time required to melt the ice is:

t = (3,058,650 J) / [39.93 Joule/s m² * (1 m^2)]
t = 76,600.3 s = 21 hours 16 min 40 seconds

To calculate the time it takes for the sun to melt the block of ice, we need to calculate the amount of heat transfer. The heat used to melt the ice is given by Q = mLf, where Q is the amount of heat transfer, m is the mass of the ice, and Lf is the latent heat of fusion of the ice.

To calculate the time it takes for the sun to melt the block of ice, we need to calculate the amount of heat transfer. The heat used to melt the ice is given by Q = mLf, where Q is the amount of heat transfer, m is the mass of the ice, and Lf is the latent heat of fusion of the ice.

First, we need to calculate the mass of the ice using the formula m = ρV, where ρ is the density of ice and V is the volume of the ice. Since the thickness of the ice is given as 1.0 cm and the area is 1.0 m², the volume can be calculated as V = A × h, where A is the area and h is the thickness.

Once we have the mass of the ice, we can use the formula Q = mLf to calculate the amount of heat transfer. Finally, we can calculate the time it takes for the ice to melt by dividing the amount of heat transfer Q by the rate of heat transfer P, which can be calculated using the equation P = BEA(T1 - T2), where B is the angle factor, E is the emissivity of ice, A is the area, and (T1 - T2) is the temperature difference between the sun and the ice.

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