which of the following statement best describes the laws of conservation mass?

Final answer:

The speed of the raindrops relative to the ground is 12.7 m/s and the angle is 90°.

Explanation:

To determine the speed and angle of the raindrops relative to the ground, we can use the concept of relative velocity. When driving north at a speed of 21 m/s, the observer sees the raindrops at an angle of 36° with the vertical. This means that the raindrops are falling at a velocity perpendicular to the observer's motion.

Using trigonometry, we can find the vertical component of the raindrop's velocity:

Vertical Component: vvertical = v x sin(θ) = 21 m/s x sin(36°) = 12.7 m/s

Since the raindrops are falling straight down when driving in the opposite direction, the vertical component of the raindrop's velocity relative to the ground is 0. Therefore, the speed of the raindrops relative to the ground is 12.7 m/s, and the angle with respect to the ground is 90°.

a. The rate at which the tank is filled is 16.5 gallons per second. b. The rate at which the tank is filled is 0.0273 cubic meters per second. c. It would take approximately 36.6 seconds to fill a 1.00 m³ volume at the same rate.

a. To calculate the rate at which the tank is filled in gallons per second, we need to convert the time from minutes to seconds and divide the volume of the tank by the time taken to fill it.
1 gallon = 231 cubic inches

30 gallons = 30 x 231 cubic inches = 6930 cubic inches

Rate = Volume / Time

= 6930 cubic inches / (7 minutes x 60 seconds/minute)

= 16.5 cubic inches/second

b. To calculate the rate at which the tank is filled in cubic meters per second, we need to convert the volume from gallons to cubic meters and divide it by the time taken to fill the tank.

1 cubic meter = 1000 liters
1 gallon = 3.785 liters
30 gallons = 30 x 3.785 liters = 113.55 liters
1 liter = 0.001 cubic meters
113.55 liters = 113.55 x 0.001 cubic meters = 0.11355 cubic meters
Rate = Volume / Time

= 0.11355 cubic meters / (7 minutes x 60 seconds/minute)

= 0.0273 cubic meters/second

c. To determine the time interval required to fill a 1.00-m³ volume at the same rate, we need to divide the volume by the rate.

Time = Volume / Rate

= 1.00 m³ / 0.0273 cubic meters/second

= 36.6 seconds

Answer:

Kinetic Energy (K.E) of the car is 630000 J

Explanation:

Kinetic energy (K.E) of a body is the energy of the body in motion and it is given by the product of half its mass (m) and the square of its velocity (v). It is expressed in Joules.

Mathematically written as;

K.E = [tex]\frac{1}{2}[/tex] x m x [tex]v^{2}[/tex]

According to the question,

The mass m of the car is 1400kg

=> m = 1400kg

The speed (velocity) of the car is 30m/s

=> v = 30m/s

Substituting these values into the equation above gives;

K.E = [tex]\frac{1}{2}[/tex] x 1400 x [tex]30^{2}[/tex]

K.E = 630000 J

Therefore the kinetic energy of the car is 630000Joules

The kinetic energy of a 1400 kg car traveling at 30 m/s is calculated using the kinetic energy formula, resulting in a total energy of 630,000 Joules or 630 kJ.

The answer is 630,000 Joules or 630 kJ.

Kinetic energy is a fundamental concept in physics, representing the energy of an object in motion. It depends on two factors: the object's mass (m) and its velocity (v). The formula for kinetic energy is KE = 0.5 * m * v^2. Essentially, the greater an object's mass or speed, the more kinetic energy it possesses. This energy is vital in understanding various natural phenomena, such as the motion of vehicles, the flight of birds, and the behavior of particles in atomic and subatomic physics. It is also crucial in engineering and everyday applications.

The kinetic energy of an object can be calculated using the formula: Kinetic Energy = 0.5 * mass * speed². In this case, the mass of the car is 1400 kg and the speed is 30 m/s. To calculate the kinetic energy, you would substitute these values into the formula:

Kinetic Energy = 0.5 * 1400 kg * (30 m/s)²

Therefore, Kinetic Energy = 0.5 * 1400 * 900

So, the kinetic energy of the car is 630,000 Joules or 630 kJ.

Hence The answer is 630,000 Joules or 630 kJ.

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Light is actually both a particle and a wave. It is essentially made of particles called photons which move or flow in waves. Due to it being a particle, its movement can also be hindered by other particles, hence the answer is:

D) The gas would transmit the fastest because there are the fewest particles to interfere with the waves.

Answer: D.The gas would transmit the fastest because there are the fewest particles to interfere with the waves.

Explanation: Usatestprep

Answer:

Our answer is 3380kg

Explanation:

The force required to move the truck at constant speed in the given case is.

F=Mg sin∅ =(9100kg)(9.8m/s²)sin15° =2.31×10⁴ N

The net force on the truck after the mass is fell down from the truck is

Fnet =F- mg sin∅

ma= F-mg sin∅

m(1.5m/s²) =( 2.31 × 10⁴N) -m(9.8m/s²)sin 15°

Solve for m.

m((1.5m/s²) +(9.8m/s²)sin 15°) =(2.31 ×10⁴ N))

m = 5720kg

Mass of load is.

Δm =M -m =(9100kg) -(5720kg) =3380kg

People who have color vision deficiency typically lack one or more of the three cones that are sensitive to a particular wavelength is the true statement.

Color vision deficiency is the inability to distinguish certain shades of color. Color blindness is used to describe this visual condition, but very few people are completely color blind.

Color vision is possible due to photoreceptors in the retina of the eye known as cones. These cones have light-sensitive pigments that enable us to recognize color.

Each cone is sensitive to either red, green or blue light. The cones recognize these lights based on their wavelengths.

The pigments inside the cones register different colors and send that information through the optic nerve to the brain.

Most people with color vision deficiency can see colors. The most common form of color deficiency is red-green. It does not mean people with this deficiency cannot see these colors altogether, they simply have a harder time differentiating between them, which can depend on the darkness or lightness of the colors.

Another form of color deficiency is blue-yellow. It is a rarer and more severe form of color vision loss than just red-green deficiency as people with blue-yellow deficiency frequently have red-green blindness, too. In both cases, people with color-vision deficiency often see neutral or gray areas where color should appear.

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Final answer:

Increasing the temperature and decreasing the solvent density are two processes that increase the motion of molecules, facilitating increased diffusion rates.

Explanation:

The two processes that increase the motion of molecules are raising the temperature and decreasing the solvent density. When the temperature is increased, it provides more energy to the molecules, thus making them move faster and increasing the rate of diffusion. On the other hand, a lower solvent density means that the molecules have fewer obstructions to navigate through, allowing them to move more freely and thus increasing diffusion rate.

For instance, heating water can increase the kinetic energy of its molecules, leading to a faster spread of those molecules through the environment. Conversely, if water is very dense, such as saltwater compared to fresh water, molecules of a solute would diffuse more slowly due to the increased resistance.

Answer:

A. Shale

Explanation: Sedimentary rocks are converted into metamorphosed rocks under high temperature and pressure. Shale is a sedimentary rock which get converted into slate under high temperature and pressure. Shale is a sedimentary rock made up of volcanic ash or clay while slate is a fine- grained , homogeneous metamorphosed rock. Slate can be found in many colors such as- grey, green, pale to brown.

The resistance [tex]\( r_2 \)[/tex] is greater than the resistance [tex]\( r_1 \)[/tex] by the square of the turns ratio of the transformer.

Let's denote the turns ratio of the step-up transformer as [tex]n[/tex], which is the ratio of the number of turns in the secondary winding [tex]\( N_s \)[/tex] to the number of turns in the primary winding [tex]\( N_p \)[/tex]. Therefore, [tex]\( n = \frac{N_s}{N_p} \).[/tex]

Since it is a step-up transformer, [tex]\( n > 1 \).[/tex]

The voltage across the secondary winding [tex]\( V_s \)[/tex] is equal to the voltage across the primary winding [tex]V_p[/tex] multiplied by the turns ratio [tex]n[/tex]. Thus, [tex]\( V_s = n \cdot V_p \).[/tex]

The current in the secondary winding [tex]\( I_s \)[/tex] is related to the current in the primary winding [tex]\( I_p \)[/tex] by the inverse of the turns ratio, due to the conservation of power in an ideal transformer (neglecting losses). Therefore, [tex]\( I_s = \frac{I_p}{n} \).[/tex]

The power delivered to both resistors must be the same because the current in both cases is measured to be the same, and power is the product of voltage and current. Hence, [tex]\( P = V_s \cdot I_s = V_p \cdot I_p \).[/tex]

Now, let's calculate the resistance of the resistors using Ohm's law, which states that [tex]\( V = I \cdot R \)[/tex], where [tex]V[/tex] is the voltage, [tex]I[/tex] is the current, and [tex]R[/tex] is the resistance.

 For resistor 1 connected across the secondary:

[tex]\( R_1 = \frac{V_s}{I_s} \)[/tex]

Substituting [tex]\( V_s = n \cdot V_p \) and \( I_s = \frac{I_p}{n} \)[/tex] into the equation, we get:

[tex]\( R_1 = \frac{n \cdot V_p}{\frac{I_p}{n}} = n^2 \cdot \frac{V_p}{I_p} \)[/tex]

For resistor 2 connected directly across the wall socket:

[tex]\( R_2 = \frac{V_p}{I_p} \)[/tex]

Since the currents are the same [tex](\( I_s = I_p \))[/tex], we can equate the powers:

[tex]\( V_s \cdot I_s = V_p \cdot I_p \)[/tex]

Substituting [tex]\( V_s = n \cdot V_p \) and \( I_s = I_p \),[/tex] we get:

[tex]\( n \cdot V_p \cdot I_p = V_p \cdot I_p \)[/tex]

This simplifies to:

[tex]\( n = 1 \)[/tex]

However, this is not possible since [tex]\( n > 1 \)[/tex] for a step-up transformer. The mistake here is that we assumed [tex]\( I_s = I_p \)[/tex] without considering the turns ratio. The correct approach is to use the power equation:

[tex]\( P = V_s \cdot I_s = V_p \cdot I_p \)[/tex]

Since [tex]\( V_s = n \cdot V_p \) and \( I_s = \frac{I_p}{n} \),[/tex] we have:

[tex]\( n \cdot V_p \cdot \frac{I_p}{n} = V_p \cdot I_p \)[/tex]

This simplifies to:

[tex]\( V_p \cdot I_p = V_p \cdot I_p \)[/tex]

Now, using the resistance formula for both resistors, we have:

[tex]\( R_1 = \frac{V_s}{I_s} = \frac{n \cdot V_p}{\frac{I_p}{n}} = n^2 \cdot \frac{V_p}{I_p} \)[/tex]

[tex]\( R_2 = \frac{V_p}{I_p} \)[/tex]

Comparing [tex]\( R_1 \) and \( R_2 \), we find: \( R_1 = n^2 \cdot R_2 \)[/tex]

Since [tex]\( n > 1 \)[/tex], it follows that [tex]\( R_1 > R_2 \)[/tex]. However, we are asked how [tex]\( r_2 \)[/tex]compares to [tex]\( r_1 \)[/tex], which means we need to express [tex]\( R_2 \)[/tex] in terms of [tex]\( R_1 \)[/tex]:

[tex]\( R_2 = \frac{R_1}{n^2} \)[/tex]

Therefore, [tex]\( r_2 \) is less than \( r_1 \)[/tex] by a factor of [tex]\( n^2 \)[/tex],

The maximum magnitude of F for which the door will remain at rest is about 265 N

[tex]\texttt{ }[/tex]

Let's recall Moment of Force as follows:

[tex]\boxed{\tau = F d}[/tex]

where:

τ = moment of force ( Nm )

F = magnitude of force ( N )

d = perpendicular distance between force and pivot ( m )

Let us now tackle the problem !

Given:

weight of the door = w = 145 N

direction of the force = θ = 20°

distance between hinge and the applied force = d = 2.50 m

length of the door = L = 3.13 m

Asked:

magnitude of the force = F = ?

Solution:

If the door is in equilibrium position , then :

[tex]\texttt{Total Clockwise Moment at Hinge = Total Anticlockwise Moment at Hinge }[/tex]

[tex]F \times d \times \sin \theta = w \times \frac{1}{2} L[/tex]

[tex]F \times 2.50 \times \sin 20^o = 145 \times \frac{1}{2} (3.13)[/tex]

[tex]\boxed {F \approx 265 \texttt{ N}}[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Physics

Chapter: Moment of Force

Answer:

B broad leaves

Explanation:

Plants in a tropical rainforest usually have large as well as broad leaves. The correct option is B.

Tropical rainforests are rainforests that occur in tropical rainforest climate areas where there is no dry season and all months have an average precipitation of at least 60 mm. They are also known as lowland equatorial evergreen rainforest.

Tropical rainforests are dominated by broad-leaved trees that form a dense upper canopy and contain a diverse array of vegetation and other life. They are one of Earth's largest biomes (major life zones).

Large leaves also allow tropical plants to capture more sunlight energy, which, when combined with a ready supply of water, allows for rapid growth.

Thus, the correct option is B.

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Acceleration is another term for change in motion, referring to changes in velocity due to an applied external force.

Another word for change in motion is acceleration. This term refers to a change in velocity, which includes changes in speed, direction, or both. When an object experiences acceleration, it means there has been a non-zero net external force applied to it, as stated by Newton's first law of motion.

Acceleration is quantified as the rate of change of velocity over time and is observed in everyday phenomena such as the breaking of a car or the circular motion of a rotating wheel.

The coefficient of kinetic friction depends on the materials of the interacting surfaces and their microscopic characteristics, not on the speed of motion. The experimental data in Tables 6.1 and 5.2 indicate this by showing that frictional coefficients are about materials, not speed.

The coefficient of kinetic friction is a factor that determines the amount of frictional force between two objects that are sliding against each other. It depends on the nature of the materials in contact, rather than on the speed of motion. This concept can be demonstrated by the data in Tables 6.1 and 5.1, which show coefficients of kinetic friction that are less than their static counterparts and do not correspond to speed. This indicates that kinetic friction is more about the materials' interactions at the microscopic level.

For instance, through a simple experiment with a cup sliding on a table, the coefficient of kinetic friction can be determined without considering the speed of the cup's motion. Instead, the frictional force is calculated using the normal force, which is based on the weight of the cup plus any added load. Similarly, different surfaces have different coefficients of friction, as shown in Table 5.2, but this is about surface characteristics and not the speed of motion.

To sum up, the coefficient of kinetic friction does not depend on speed. Instead, it's about the materials in contact and their microscopic interactions. The direction of friction is always opposite that of motion, illustrated in Equations 6.1 and 6.2 which showcase the dependence of friction on materials and the normal force.

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Answer: a = (2 v²)/d = 1.9 m/s²

Explanation:

In circular motion, the acceleration is given by:

a = v²/r = v²/(d/2) = (2 v²)/d

where v is the velocity and r is the radius of the circular path in which the vehicle is moving. d is the diameter of the circular path.

It is given that:

v = 28.5 m/s

r = d/2 = 0.85 km /2 = 0.425 km = 425 m

⇒ a = (28.5 m/s)²/425 m = 1.9 m/s²

An expression for the magnitude of the acceleration (a) of the car in terms of the given parameters is: [tex]A_c = \frac{2V^2}{D}[/tex]

Given the following data:

To write an expression for the magnitude of the acceleration (a) of the car in terms of the given parameters:

The acceleration of an object along a circular track is referred to as centripetal acceleration.

Mathematically, the centripetal acceleration of an object is given by the formula:

[tex]A_c = \frac{V^2}{r}[/tex]   .....equation 1

Where:

But, [tex]Radius, \;r = \frac{D}{2}[/tex]  .....equation 2

Substituting the eqn 2 into eqn 1, we have:

[tex]A_c = \frac{V^2}{\frac{D}{2}}[/tex]

Simplifying further, we have:

[tex]A_c = \frac{2V^2}{D}[/tex]

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Final answer:

The outside air temperature is approximately 3375 °C.

Explanation:

The outside air temperature can be calculated using the density altitude and pressure altitude. The formula to calculate the temperature is:

T = T0 + (d × 120)

Where:

T is the outside air temperature

T0 is the temperature at sea level

d is the difference between the pressure altitude and the density altitude, divided by 1,000 (d = (PA - DA) / 1000)

Plugging in the given values, we have:

T = 15 + (28 × 120)

T = 15 + 3360

T = 3375

So, the outside air temperature is approximately 3375 °C.

By equation of equilibrium and friction:

Fb = Kx = 15(0.175) = 2.625 kN.

The wedge is on the verge of moving right then slipping will have to occur at both contact surfaces.

Fa = usNa = 0.35Na

Fb = 0.35Nb

Nb = 2.625 = 0; Nb = 2.625 kN

Nacos10 – 0.35Na sin 10 = 2.625 = 0

Na = 2.841 kN

P – (0.35 * 2.625) – 0.35 (2.841) cos 10 – 2.841 sin 10 = 0

P = 2.39 kN

The minimum force required to move wedge A can be approximated as slightly higher than the force of static friction, which can be calculated using the coefficient of static friction and the force exerted by the spring at its compressed state.

To calculate the minimum applied force required to move the wedge A to the right, we first need to obtain the force of static friction, (μs) which resists motion. The force of static friction (F_s) can be calculated using the relation F_s = μs * N, where N is the normal force.

In this case, the normal force can be determined from the compression of the spring which follows Hooke's Law, stating that the force (F) exerted by a spring is proportional to its compression (x), i.e., F = kx, where k is the spring constant. Although k is not provided here, we can assume the spring force equals the normal force due to the system's equilibrium, which occurs before moving A.

Thus, the minimum applied force (p) to make A move would be slightly higher than the force of static friction, i.e., p > F_s. To get an exact value, we need additional data such as the spring constant (k).

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Gravity is not a direct force causing plate motion in the context of plate tectonics; instead, key forces include ridge push, slab pull, and basal drag, with slab pull being the predominant mechanism.

The question pertains to the forces that are responsible for plate tectonics and plate motion. It is a common misconception that gravity is a direct force causing plate motion; however, in the context of tectonic plates, gravity is not a force that directly initiates their movement. In tectonic plate motion, the key driving forces are ridge push, slab pull, and basal drag. Ridge push occurs at mid-ocean ridges, where newly formed lithosphere pushes plates apart. Slab pull is the force exerted by a subducting plate that pulls the rest of the plate after it as it descends into the mantle due to its higher density. Basal drag is the force exerted by the mantle's convection currents on the base of the tectonic plates.

Gravity, while essential in providing the overall setting by influencing the density and buoyancy of rocks, does not directly move the plates on its own. Rather, gravity contributes indirectly to gravitational sliding, which pulls lithospheric plates down from the elevated mid-ocean ridges due to the height difference. However, current evidence supports slab pull as the predominant mechanism over ridge push and gravitational sliding.

Final answer:

The rate at which the length of the person's shadow is growing is \(\frac{{48}}{{5}}\) feet per second.

Explanation:

In this problem, we can use similar triangles to determine the rate at which the length of the person's shadow is growing. Let's consider the situation at a particular moment when the person is a certain distance away from the pole. At this moment, the length of the person's shadow is the distance from the pole to the person multiplied by the ratio of the height of the pole to the height of the person. Let's call this length S. The rate of change of S, which represents the speed at which the length of the person's shadow is growing, can be determined using derivatives. To find this rate, we need to differentiate the expression for S with respect to time (t), since the person is moving and therefore the distance from the pole is changing over time.

The length of the person's shadow (S) can be expressed as:

S = \(\frac{{12}}{{5}}x\)

where x is the distance from the pole to the person at a particular moment.

To find the rate of change of S with respect to time (\(\frac{{dS}}{{dt}}\)), we differentiate the expression for S:

\(\frac{{dS}}{{dt}} = \frac{{12}}{{5}}\frac{{dx}}{{dt}}\)

Since the person is moving away from the pole at a rate of 4 feet per second, \(\frac{{dx}}{{dt}} = 4\). Plugging this value into the equation, we can calculate the rate at which the length of the person's shadow is growing:

\(\frac{{dS}}{{dt}} = \frac{{12}}{{5}} \cdot 4 = \frac{{48}}{{5}}\) feet per second

By using similar triangles and differentiating with respect to time, we find that the length of the person's shadow is growing at a rate of approximately 2.86 feet per second.

The question involves calculating the rate at which the length of a person's shadow grows as they walk away from a street light. To start, we can use similar triangles to relate the heights and shadows of the pole and the person. Given:

Let the distance of the person from the pole be x, and the length of the shadow be s. By similar triangles, we have:

(Height of the pole)/(Total distance from the pole to the tip of the shadow) = (Height of the person)/(Length of the shadow)

This converts to:

12/(x + s) = 5/s

Cross multiplying gives us:

12s = 5(x + s)

Which simplifies to:

12s = 5x + 5s

Rearranging terms gives us:

7s = 5x

So,  s = (5/7)x

Next, we differentiate both sides of this equation with respect to time (t), noting that both s and x are functions of time:

ds/dt = (5/7)dx/dt

Given that the rate at which the person walks (dx/dt) is 4 feet per second, we find:

ds/dt = (5/7) * 4 = 20/7 ≈ 2.86 feet per second

Thus, the length of the person's shadow is growing at a rate of approximately 2.86 feet per second.