As a 5.00-kg sample of liquid mercury is cooled into a solid, it liberates 157 kJ of energy. What is the original temperature of the mercury? For mercury, the melting point is 234 K, the heat of fusion is 11.3 kJ/kg,
and the specific heat is 140 J/kg . K.

378 K
690 K
157 K
410 K

The value of  the missing resistance, R₃ = 10.35 ohms.

The value of the missing voltages, V₁ = 6 V, V ₃ = 24 V.

The value of the missing currents, I₁ = 3 A, I₃ = 2.32 A.

The values of the missing component of the circuit is calculated by applying the following formula.

The total resistance of the circuit;

For R₂, R₃, 1/R = 1/R₂ + 1/R₃

1/R = 1/12 +  1/R₃

1/R = (R₃ + 1)/(12R₃)

R = 12R₃ / (R₃ + 1)

For, R₁, R₂ and R₃, total resistance;

R = 12R₃ / (R₃ + 1) + R₁

R = [12R₃ / (R₃ + 1)] + 2

R = (12R₃ + 2(R₃ + 1) ) / (R₃ + 1)

R = (12R₃ + 2R₃ + 2 ) / (R₃ + 1)

R = (14R₃ + 2 ) / (R₃ + 1)

The total current in circuit is calculated as;

I = V/R

I = 30 / R

I = ( 30 ) / (14R₃ + 2 ) / (R₃ + 1)

I = (30R₃ + 30) / (14R₃ + 2) ------- (1)

The voltage in parallel circuit is the same

V₂ = V₃ = 24 V

V₃ = IR₃

24 = IR₃

I = 24/R₃  --------- (2)

Solve (1) and (2) together as follows;

24/R₃ = (30R₃ + 30) / (14R₃ + 2)

30R₃² - 306R - 48 = 0

Solve the quadratic equation, using formula method.

R₃ = 10.35 ohms

I₃ = V₃/R₃

I₃ = 24 V / 10.35

I₃ = 2.32 A

If the voltage drop at R₂ and R₃ = 24 V, the voltage drop at R₁ = 30V - 24 V = 6 V

The current in R₁ = V₁/R₁ = 6 V / 2 V = 3 A

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Baseball, neutrons, and protons are all perfect spheres.

Circumference of the baseball, \($L_{\text {ball }}=23 \mathrm{~cm}$\).

mass of the proton or neutron, \($m_{\mathrm{p}}=10^{-27} \mathrm{~kg}$\)

diameter of the proton or neutron, \($r_{0}=10^{-15} \mathrm{~m}$\)

Mass per unit volume is the definition of a material's density. The density equation is

\($$\rho=\frac{M}{V} .$$\)

Here, M is the mass of the material, V is the volume, and \($\rho$\) is the density of the material.

We know that formula for the volume of a sphere having diameter d is \(V=\frac{\pi d^{3}}{6}$.\)

You may obtain this result by plugging this number into the proton/neutron density equation:

\($$\rho_{0}=\frac{m_{0}}{\left(\frac{\pi d_{0}^{3}}{6}\right)}$$\)

By replacing the variables in the aforementioned equation with their values, you will obtain

\($$\begin{aligned}\rho_{\circ} &=\frac{10^{-27}}{\left(\frac{\pi\left(10^{-15}\right)^{3}}{6}\right)} \\&=1.91 \times 10^{18} \mathrm{kgm}^{-3}\end{aligned}$$\)

The formula for calculating a circle's circumference with diameter d is \(L=\pi d$.\)

Using this, you get the diameter of the baseball:

\($$\begin{aligned}d_{\text {ball }} &=\frac{L_{\text {ball }}}{\pi} \\&=\frac{23}{\pi} \\&=7.32 \mathrm{~cm} \\&=0.0732 \mathrm{~m}\end{aligned}$$\)

The volume of the baseball may be calculated using the formula for the volume of a sphere:

\($$\begin{aligned}V_{\text {ball }} &=\frac{\pi d_{\text {ball }}^{3}}{6} \\&=\frac{\pi \times(0.0732)^{3}}{6} \\&=2.054 \times 10^{-4} \mathrm{~m}^{3}\end{aligned}$$\)

The mass of the baseball is determined by the concept of density if you suppose that its density is equal to that of a proton or neutron.

\($m_{\text {ball }}=\rho_{\circ} \cdot V_{\text {ball }}$\)

Here, \($\rho_{\circ}$\) is the density of the proton/neutron.

By replacing the variables in the aforementioned equation with their values, you will obtain

\($$\begin{aligned}m_{\text {ball }} &=\left(1.91 \times 10^{18}\right) \cdot\left(2.054 \times 10^{-4}\right) \\&=3.92 \times 10^{14} \mathrm{~kg}\end{aligned}$$\)

Therefore, if the density of the baseball was equal to that of the neutron/proton, then its mass would be \(3.92 \times 10^{14} \mathrm{~kg}$.\)

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The absolute pressure at an ocean depth of 1.0 x 10^3 m is 1.002 x 10^8 Pa.

Hydrostatic pressure is the pressure that a fluid exerts on a surface due to the weight of the fluid above it. It is the result of the force of gravity acting on a column of fluid, and it is directly proportional to the height of the column of fluid and the density of the fluid.

The absolute pressure at an ocean depth of 1.0 x 10^3 m can be calculated using the hydrostatic pressure equation:

P = ρgh + Po

where:

P is the absolute pressure at the given depth

ρ is the density of the water

g is the acceleration due to gravity (assumed to be 9.81 m/s²)

h is the depth of the ocean

Po is the atmospheric pressure at the surface (assumed to be 1.01 x 10^5 Pa)

Substituting the given values, we get:

P = (1.025 x 10^3 kg/m³) x (9.81 m/s²) x (1.0 x 10^3 m) + 1.01 x 10^5 Pa

P = 1.025 x 9.81 x 10^6 Pa + 1.01 x 10^5 Pa

P = 1.002 x 10^8 Pa.

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The power of the hot rod of mass 2000 kg is 580645.16 W.

Power is the rate at which work is done.

To caculate the power output of the hot rod, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Hence, the power is 580645.16 W.

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Answer:

\(\theta_c = 36.78^o\)

Explanation:

The relationship between the refractive index and the critical angle is given as follows:

\(\eta = \frac{1}{Sin\ \theta_c} \\\\Sin\ \theta_c = \frac{1}{\eta}\\\\\theta_c = Sin^{-1}(\frac{1}{\eta} )\)

where,

η = refractive index = 1.67

θc = critical angle =?

Therefore,

\(\theta_c = Sin^{-1}(\frac{1}{1.67} )\)

\(\theta_c = 36.78^o\)

The two sentences that best state the central ideas of Wiesel's speech are:

Elie Wiesel's speech focuses primarily on the Holocaust and the atrocities that were committed during that time, particularly at Auschwitz. The central ideas of his speech are:

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Answer:

The deepest part of earth or oceans. They are most commonly found in oceans however

Explanation:

The uncertainty of the heavy object if the scale remains constant is 0.24 lbs.

The percent uncertainty in measuring the light weight object is calculated as follows;

\(= \frac{0.034}{11} \times 100\%\\\\= 0.309\%\)

The uncertainty of the heavy object if the scale remains constant is calculated as follows;

\(= \frac{0.309}{100} \times 78.0 \ lbs\\\\= 0.24 \ lbs\)

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(a) The change in the length of the bar is 0.012 m.

(b) The new length of the bar is 10.012 m.

The change in the length of the bar is calculated by applying the following formula.

ΔL = αLΔθ

where;

ΔL = ( 24 x 10⁻⁶ x 10) x ( 40 - -10)

ΔL =  ( 24 x 10⁻⁶ x 10) x ( 50)

ΔL = 0.012 m

The new length of the bar is calculated as follows;

L₁ = L + ΔL

L₁ = 10 m + 0.012 m

L₁ = 10.012 m

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Answer:

the dual nature of light

Explanation:

Answer:

The temperature the plants are grown in

The amount of water the sunflowers get

The amount of light the sunflowers get

Explanation:

They want to know if increasing the acidity of the soil makes the plants flower sooner. So, they need to hold constant all the other variables in that area not the acidity of the soil or the day the plants begin to flower.

Therefore, the answers are

The temperature the plants are grown in

The amount of water the sunflowers get

The amount of light the sunflowers get

Answer:

x = 0.9 m

Explanation:

For this exercise we must use the rotational equilibrium relation, we will assume that the counterclockwise rotations are positive

          ∑ τ = 0

          60 1.5 - 78 1.5 + 30 x = 0

where x is measured from the left side of the fulcrum

           90 - 117 + 30 x = 0

           x = 27/30

           x = 0.9 m       

In summary the center of mass is on the side of the lightest weight x = 0.9 m

Answer:

First scenario,

From 2nd Newton's law

F = ma

from the above eqn, it's evident

a = F/m

that is to say, acceleration is inversely proportional to mass

The greater the mass, the smaller the acceleration and the higher the acceleration, the smaller the mass.

Thus, You was in the wagon when it had the greatest acceleration because You has the smaller mass and thus the acceleration will be greater.

Second scenario,

Since Sara pulls with greater force and Force is directly proportional to acceleration according to the second Newton's law,

F = ma

then, when You is in the wagon it had greater acceleration since they have the same mass.

All the best!

Answer:

2

Explanation:

İf system ideal ( no frictional force )

Fnet=m.a

20=10.a

a=2m/s2

The acceleration of the wagon pulled by the girl is 2m/s².

Given the data in the question;

Acceleration of wagon; \(a =\ ?\)

To determine the acceleration of the wagon, we use the expression from the Newton's Second law of motion:

\(F = m * a\)

Where m is mass and a is acceleration

We substitute our given values into the equation and solve for "a"

\(20N = 10kg * a\\\\20kg.m/s^2 = 10kg * a\\\\a = \frac{20kg.m/s^2}{10kg}\\\\a = 2m/s^2\)

Therefore, the acceleration of the wagon pulled by the girl is 2m/s².

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The force actually being used to push the mower along the ground is 191 N.

When the physics student exerts a force of 250 N along the handle of the push mower, it's important to consider the components of this force that contribute to the actual force used to push the mower along the ground.

To determine the force used to push the mower along the ground, we need to find the horizontal component of the applied force. The angle of 40° indicates that the applied force can be broken down into two components: the horizontal component and the vertical component. The vertical component of the force is perpendicular to the direction of motion and does not contribute to pushing the mower forward.

To find the horizontal component, we can use trigonometry. The horizontal component is given by the formula:

Horizontal component = Applied force * cos(angle)

Plugging in the values, we get:

Horizontal component = 250 N * cos(40°)

Calculating this value, we find that the horizontal component of the applied force is approximately 191 N.

Therefore, the force actually being used to push the mower along the ground is 191 N. This is the component of the applied force that contributes to the forward motion of the mower, while the remaining vertical component is directed perpendicular to the ground and does not assist in pushing the mower forward.

By exerting a force of 250 N along the handle at a 40° angle, the student effectively applies 191 N of force to push the mower along the ground, ensuring efficient use of their effort while considering the environmental impact.

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Answer: Economists measure the gross domestic product to see how much economic activity there is in a particular country.

Explanation:

The image only shows the path of the ball and its different positions at different times during the flight.

To determine the speed of the ball at each position, additional information such as the time elapsed between each position and the distance traveled would be needed. Only with this information would it be possible to calculate the speed at each position and determine where the ball is traveling the fastest.

Speed is the measure of the distance traveled by an object over a specified period. It is a scalar quantity and is typically expressed in units of distance per unit of time, such as miles per hour, kilometers per hour, or meters per second. Speed can be calculated as the ratio of the distance covered by an object to the time taken to cover that distance. It is an important concept in physics and plays a critical role in determining the motion of objects, particularly in the field of mechanics.

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Image is missing, so i have attached it

Answer:

Tension in back wire = 24.5 N

Explanation:

let the tension in the back wire be Tₒ

let the tension in the front wire be T

Applying static equilibrium in the vertical direction, we have:

T + Tₒ = (5 × 9.8) + (2.5 × 9.8)

T + Tₒ = 73.5

Where Tₒ = (2.5 × 9.8) = 24.5 N

Thus, Tension in back wire = 24.5 N

The tension in the back wire equals 24.5 N.

We can arrive at this answer with the static equilibrium formula, for that, let's consider that the tension in the back wire is represented by the letter "t," while the tension in the front wire is represented by the letter "T."

Therefore, we can use the following formula:

\(t= W*g\\t= 2,5*9.8\\t= 24.5 N\)

In this case, the letter "W" refers to the tool weight, while the letter "g" refers to gravity.

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The approximate heat transfer through 1.65 cm of air with a temperature difference of 23.0 °C is approximately 24.4 J/s.

To approximate the heat transfer through the air layer in the double-paned window, we can assume that the glass layers have a negligible impact on the heat flow. The heat transfer can be calculated using Fourier's Law of Heat Conduction, which states that the heat flow (Q) is proportional to the temperature difference (ΔT) and inversely proportional to the thickness (L) and thermal conductivity (k) of the material.

First, we need to calculate the effective thermal conductivity of the air layer due to its thickness and the thermal conductivity ratio between air and glass. Let's denote the thermal conductivity of air as k_air and the thermal conductivity of glass as k_glass. Since glass has a thermal conductivity roughly 36 times greater than air, we have k_glass = 36 * k_air.

Next, we calculate the effective thermal conductivity of the air layer as:

k_eff = (k_air * L_air) / (L_air + k_glass)

Substituting the given values, we have:

k_eff = (k_air * 0.0165 m) / (0.0165 m + 0.005 m) = 0.01309 * k_air

Now, we can calculate the heat flow per second through the air layer using the formula:

Q = (k_eff * A * ΔT) / L_air

Substituting the given values, we get:

Q = (0.01309 * k_air * 0.760 m^2 * 23.0 K) / 0.0165 m = 24.4 J/s

Therefore, the approximate heat transfer through 1.65 cm of air with a temperature difference of 23.0 °C is approximately 24.4 J/s.

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The speed of the roller coaster at the bottom of the hill if the track was frictionless is 34.04 m/s.

Given that the weight of the roller coaster is 2000 kg and the initial vertical drop of the ride is 59.3 m. We are to find the speed of the roller coaster at the bottom of the hill if the track was frictionless.We know that the roller coaster will lose potential energy due to the vertical drop. Assuming there is no friction, the potential energy will be converted into kinetic energy at the bottom of the hill.Considering the conservation of energy between the potential and kinetic energy, we can set the initial potential energy equal to the final kinetic energy. We can use the formula to calculate potential energy, which is PE = mgh where m = 2000 kg, g = 9.8 m/s², and h = 59.3 m. Therefore,PE = 2000 kg × 9.8 m/s² × 59.3 m = 1,157,924 JWe can use the formula to calculate kinetic energy, which is KE = 1/2mv² where m = 2000 kg and v is the final velocity. Therefore,KE = 1/2 × 2000 kg × v².The total energy remains constant as we know there is no friction. Therefore the final kinetic energy will be equal to the initial potential energy,1,157,924 J = 1/2 × 2000 kg × v²v² = (2 × 1,157,924 J) / 2000 kgv² = 1157.924v = √1157.924v = 34.04 m/s.

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Answer:

3 maybe 4 seconds

Explanation:

Vessel Mass Acting Downward (mg)

Bayonet Force Acting Above Vessel (Fb)

This force is called buoyancy. Buoyancy pushes objects up. Gravity exerts a downward force on an object determined by the object's mass. Therefore, if the downward force exerted by gravity on an object is less than the buoyant force the object floats.

Since the buoyant force on the body and the weight of the body are equal and opposite, the net force on the body is zero, giving the body a net force to levitate. The wind force acting on a sail moving a boat is an example of Newton's third law of motion. That is, every action has an equal and opposite reaction. But the relationship between force and motion is not as simple as the wind blowing just behind the sails propels the ship forward.

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Given, two 0.4 kg masses with initial velocities of 2 m/s experience a moment of 0.6 N·m. The formula for moment of inertia can be expressed as:I = (m × r²)Where I = moment of inertia, m = mass, and r = radius. The speed of blocks A and B when t = 3 s is 22.5 m/s.

Substituting the values, we get:I = (0.4 kg × (0.1 m)²) + (0.4 kg × (0.1 m)²)I = 0.008 kg m²Next, we need to find the angular acceleration. The formula for angular acceleration is given by:α = τ / I . Where α = angular acceleration, τ = torque, and I = moment of inertia.

Substituting the values, we get:α = (0.6 N m) / (0.008 kg m²)α = 75 rad/s²Using the formula for angular velocity, we get:ω = αt Where ω = angular velocity, α = angular acceleration, and t = time. Substituting the values, we get:ω = (75 rad/s²) × (3 s)ω = 225 rad/s

Finally, using the formula for tangential velocity, we get:v = rωWhere v = tangential velocity, r = radius, and ω = angular velocity. Substituting the values, we get:v = (0.1 m) × (225 rad/s)v = 22.5 m/s

Therefore, the speed of blocks A and B when t = 3 s is 22.5 m/s.

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An electromagnet consists of a conductive wire wrapped around a magnetic core, creating a magnetic field when an electrical current is passed through it.

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Answer:

b. has mass and takes up space.

Explanation:

Matter, in physics and chemistry, is defined as any substance that has mass and takes up space by having volume. The rest of the following options do not match this definition.

hope this helps!

Answer:

B and D

Explanation:

Answer:

It is B. inherits all the traits from its parent

And D. is identical to the parent's structure

Explanation:

Hope this helped have an amazing day!

Explanation:

A machine is useful because it can perform tasks or processes more efficiently, accurately, and consistently than humans. Machines are designed to automate or augment various functions, ranging from simple to complex, across numerous industries and domains. Here are some key reasons why machines are valuable:

1. Efficiency: Machines can complete tasks at a much faster pace than humans, significantly improving productivity. They operate without fatigue, breaks, or distractions, ensuring continuous and uninterrupted performance.

2. Accuracy: Machines are built to execute tasks with precision and minimal errors. They can follow programmed instructions or algorithms meticulously, reducing the chances of mistakes and increasing overall quality and reliability.

3. Repetitive or labor-intensive tasks: Machines excel at handling repetitive or physically demanding tasks that may be monotonous or hazardous for humans. By automating such tasks, machines free up human resources to focus on more complex and creative endeavors.

4. Scalability: Machines offer scalability, allowing businesses and industries to handle larger workloads or increasing demands. They can be easily replicated or scaled up to meet production requirements without compromising performance.

5. Data processing and analysis: Machines possess the capability to process and analyze vast amounts of data quickly, extracting valuable insights and patterns that would be time-consuming for humans to perform manually. This is especially crucial in fields like data science, finance, and scientific research.

6. Precision and consistency: Machines can achieve a high level of precision and maintain consistency in their output, ensuring that tasks are completed with a predefined level of accuracy. This is particularly advantageous in manufacturing, engineering, and medical applications.

7. Risk reduction: Machines can be utilized in hazardous or risky environments where human safety might be compromised. They can perform tasks in extreme temperatures, toxic conditions, or dangerous settings, minimizing human exposure to potential harm.

8. Enhancing human capabilities: Machines can augment human abilities by providing advanced tools, equipment, or robotic assistance. They can enhance human productivity, accuracy, and effectiveness, resulting in improved outcomes in various fields.

9. Increased productivity and cost-effectiveness: By streamlining processes and minimizing manual labor, machines contribute to enhanced productivity and reduced costs. They can optimize resource utilization, decrease waste, and optimize production efficiency.

10. Innovation and exploration: Machines facilitate innovation and exploration by enabling complex simulations, modeling, and experimentation. They support scientific discoveries, technological advancements, and the development of new products or services.

It's important to note that while machines offer numerous benefits, they are not meant to replace humans entirely. Instead, they work alongside humans, complementing their skills and expertise to create a powerful partnership that drives progress and efficiency in various industries.

Answer:

Explanation:

Answer:

100

Explanation:

F = m * a

Given that the mass (m) of the toy car is 20 grams (or 0.02 kilograms, since 1 kilogram = 1000 grams) and the acceleration (a) is 5 m/s^2, we can plug these values into the formula to calculate the force (F):

F = 0.02 kg * 5 m/s^2 = 0.1 N

So, the amount of force required to accelerate the 20 gram toy car at 5 m/s^2 is 0.1 N, which is equivalent to 100 N when rounded to the nearest whole number. Therefore, the correct answer is 100 N.

Answer:

\( \boxed{\sf Kinetic \ energy \ (KE) = 48 \ J} \)

Given:

Mass (m) = 6 kg

Speed (v) = 4 m/s

To Find:

Kinetic energy (KE)

Explanation:

Formula:

\( \boxed{ \bold{\sf KE = \frac{1}{2} m {v}^{2} }}\)

Substituting values of m & v in the equation:

\( \sf \implies KE = \frac{1}{2} \times 6 \times {4}^{2} \)

\( \sf \implies KE = \frac{1}{ \cancel{2}} \times \cancel{2} \times 3 \times 16\)

\( \sf \implies KE =3 \times 16\)

\( \sf \implies KE = 48 \: J\)