What is the temperature of an object where it is half as hot as 80°F?​

Hooke's law of elasticity is a principle in physics that states that the force required to extend or compress a spring by some distance is proportional to that distance. It is named after the English physicist Robert Hooke, who first stated the law in 1678. Hooke's law is often written as F = -kx, where F is the force applied to the spring, x is the distance it is stretched or compressed, and k is the spring constant, a measure of the stiffness of the spring.

Answer:

θ = 12.60°

Explanation:

In order to calculate the angle below the horizontal for the velocity of the hockey puck, you need to calculate both x and y component of the velocity of the puck, and also you need to use the following formula:

\(\theta=tan^{-1}(\frac{v_y}{v_x})\)       (1)

θ: angle below he horizontal

vy: y component of the velocity just after the puck hits the ground

vx: x component of the velocity

The x component of the velocity is constant in the complete trajectory and is calculated by using the following formula:

\(v_x=v_o\)

vo: initial velocity = 28.0 m/s

The y component is calculated with the following equation:

\(v_y^2=v_{oy}^2+2gy\)         (2)

voy: vertical component of the initial velocity = 0m/s

g: gravitational acceleration = 9.8 m/s^2

y: height

You solve the equation (2) for vy and replace the values of the parameters:

\(v_y=\sqrt{2gy}=\sqrt{2(9.8m/s^2)(2.00m)}=6.26\frac{m}{s}\)

Finally, you use the equation (1) to find the angle:

\(\theta=tan^{-1}(\frac{6.26m/s}{28.0m/s})=12.60\°\)

The angle below the horizontal is 12.60°

The angle below the horizontal of the velocity of the puck just before it hits the ground is 12.60°.

Given the following data:

To find the angle below the horizontal of the velocity of the puck just before it hits the ground:

First of all, we would determine the horizontal and vertical components of the hockey puck.

For horizontal component:

\(V_y^2 = U_y^2 + 2aS\\\\V_y^2 = 0^2 + 2(9.81)(2)\\\\V_y^2 = 39.24\\\\V_y = \sqrt{39.24} \\\\V_y = 6.26 \; m/s\)

For vertical component:

\(V_x = U_x\\\\V_x = 28.0 \;m/s\)

Now, we can find the angle by using the formula:

\(\Theta = tan^{-1} (\frac{V_y}{V_x} )\)

Substituting the values, we have:

\(\Theta = tan^{-1} (\frac{6.26}{28.0} )\\\\\Theta = tan^{-1} (0.2236)\\\\\Theta = 12.60\)

Angle = 12.60 degrees.

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Answer:

P = 97.2 W

Explanation:

Given that,

Voltage drop, V = 54 V

The resistance of the resistor, R = 20 Ohms

Current, I = 1.8 A

We need to find the power used by the resistor. The formula used to find the power is given by :

P = VI

Putting all the values,

P = 54 V × 1.8 A

P = 97.2 W

So, the power used by the resistor is 97.2 W.

Answer:

29.4 m.s

Explanation:

Vf = vo + at       v o = original velocity = 0 in this case

Vf = at

   = 9.81 m/s^2 * 3 = 29.4 m/s

Answer:

(a) q = 2.357 x 10⁻⁵ C

(b) Φ = 2.66 x 10⁶ N.m²/C

Explanation:

Given;

diameter of the sphere, d = 1.1 m

radius of the sphere, r = 1.1 / 2 = 0.55 m

surface charge density, σ = 6.2 µC/m²

(a)  Net charge on the sphere

q = 4πr²σ

where;

4πr² is surface area of the sphere

q is the net charge on the sphere

σ is the surface charge density

q = 4π(0.55)²(6.2 x 10⁻⁶)

q = 2.357 x 10⁻⁵ C

(b) the total electric flux leaving the surface of the sphere

Φ = q / ε

where;

Φ is the total electric flux leaving the surface of the sphere

ε is the permittivity of free space

Φ = (2.357 x 10⁻⁵) / (8.85 x 10⁻¹²)

Φ = 2.66 x 10⁶ N.m²/C

Using compound interest formula:

Where:

A = Amount

P = Principal = $70

r = Interest rate = 5% = 0.05

n = Number of times interest is compounded per year = 1

t = time = 2

So.

Answer:

$77.18

Energy flows from the Sun to producers, then to primary consumers, secondary consumers, and potentially to tertiary consumers, forming a pyramid-shaped structure that represents the transfer of energy through different trophic levels in an ecosystem.

Energy flows in a specific order through various components of an ecosystem, starting with the Sun and progressing through producers and consumers. This flow of energy is known as the energy pyramid or trophic levels.

At the base of the energy pyramid is the Sun, which is the ultimate source of energy for most ecosystems on Earth. Sunlight provides the energy needed for photosynthesis, a process carried out by plants, algae, and some bacteria, collectively known as producers. These organisms convert solar energy into chemical energy through photosynthesis, using carbon dioxide and water to produce glucose and oxygen. This process captures and stores energy in the form of organic compounds.

The next level in the energy pyramid consists of primary consumers, also known as herbivores. These are animals that feed directly on producers, such as grazing animals or insects that consume plants. Herbivores obtain energy by consuming plant material and breaking down the organic compounds present in the plants into simpler forms, such as sugars and amino acids, through digestion.

Above the primary consumers are the secondary consumers, which are carnivores or omnivores that feed on herbivores. They obtain energy by consuming primary consumers and breaking down the organic compounds in their prey through digestion. This energy transfer continues up the trophic levels, with each level consuming the one below it.

At the top of the energy pyramid are tertiary consumers, which are typically apex predators. They are carnivores that consume other carnivores. Tertiary consumers obtain energy by consuming secondary consumers and breaking down the organic compounds in their prey.

It's important to note that energy is not efficiently transferred between trophic levels. Only a fraction of the energy consumed at each level is converted into biomass and passed on to the next level. This inefficiency is due to processes such as respiration, heat loss, and incomplete digestion.

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The speed of the running shaft driving the machine, given that the main shaft to drive the machine has a pulley of diameter 140 mm is 111.4 rev/min

First, we shall list out the given parameters from the question. Details below:

The speed of the running shaft can be obtain as shown below:

S₁D₁ = S₂D₂

183 × 140 = S₂ × 230

183 × 140 = S₂ × 230

25620 = S₂ × 230

Divide both sides by 230

S₂ = 25620 / 230

S₂ = 111.4 rev/min

Thus, we can conclude that the speed of the running shaft driving the machine is 111.4 rev/min

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In a DC generator, the generated electromotive force (emf) is directly proportional to the rotational speed of the generator's armature and the strength of the magnetic field within the generator.

This relationship is described by the equation for the generated emf in a DC generator:

Emf = Φ * N * A * Z / 60

Where:

Emf is the generated electromotive force (in volts),

Φ is the magnetic flux density (in Weber/meter^2\(meter^2\) or Tesla),

N is the number of turns in the armature winding,

A is the effective area of the armature coil (in square meters),

Z is the total number of armature conductors, and

60 is a constant representing the conversion from seconds to minutes.

From this equation, we can see that the generated emf is directly proportional to the magnetic flux density (Φ) and the product of the number of turns (N), effective area (A), and the total number of armature conductors (Z). This means that increasing any of these factors will result in a higher generated emf.

The magnetic flux density (Φ) can be increased by using stronger permanent magnets or increasing the strength of the field windings in the generator.

The number of turns (N) and the effective area (A) are design parameters and can be optimized for a specific generator. Increasing the number of turns or the effective area will result in a higher generated emf.

Similarly, the total number of armature conductors (Z) can be increased to enhance the generated emf.

By controlling and optimizing these factors, the generated emf in a DC generator can be increased, resulting in higher electrical output. However, it is important to note that there are practical limits to these factors based on the design and construction of the generator.

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The skater's final angular velocity is approximately 9.86 rad/s.

The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Initially, the skater has an angular momentum of:

L_initial = I_initial * ω_initial

Substituting the given values:

L_initial = 2.12 kg m² * 3.25 rad/s

The skater's final angular momentum remains the same, as angular momentum is conserved:

L_final = L_initial

The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:

L_final = I_final * ω_final

0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s

Solving for ω_final:

ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²

Hence, the skater's final angular velocity is approximately 9.86 rad/s.

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According to Gauss' equation, the total flux of an electric field in a confined surface is directly proportional to the charge enclosed.

1)To determine the outward electric flux through the rounded "side" of the cylinder, we can use Gauss's law. We choose a cylindrical Gaussian surface with radius r and length L, centered at the origin (where the charged sphere is located). The electric field due to the sphere is spherically symmetric, so the electric field lines are parallel to the cylinder's axis and perpendicular to its sides.

E = (1/4πϵ0) (Q/r^2)

where r is the distance from the origin (center of the sphere) to the point on the Gaussian surface.

The area element of the Gaussian surface is dA = 2πRdz, where dz is an element of length along the cylinder's axis. The electric flux through the top and bottom surfaces of the Gaussian surface is then given by:

Φ = ∫E⋅dA = E ∫dA = E(2πR)L

Substituting the expression for the electric field, we have:

Φ = (Q/2ϵ0r^2)(2πRL)

Therefore, the outward electric flux through the rounded "side" of the cylinder is:

Φ = (Q/ϵ0)(R/Lr^2)

2)To determine the electric flux upward through the circular cap at the top of the cylinder, we use a flat Gaussian surface with radius R and height r, centered at the top of the cylinder. The electric field due to the charged sphere is perpendicular to the Gaussian surface, so the electric flux through the top cap is simply the flux through the flat Gaussian surface. The electric field at any point on the Gaussian surface is given by Coulomb's law as:

E = (1/4πϵ0) (Q/R^2)

The area element of the Gaussian surface is dA = πR^2, so the electric flux through the top cap is given by:

Φ = ∫E⋅dA = E ∫dA = EπR^2

Substituting the expression for the electric field, we have:

Φ = (Q/ϵ0)(R/r^2)

3)To determine the electric flux downward through the circular cap at the bottom of the cylinder, we use a similar flat Gaussian surface with radius R and height r, centered at the bottom of the cylinder. The electric flux through the bottom cap is also given by:

Φ = (Q/ϵ0)(R/r^2)

4)Adding the results from parts 1-3, we have the total outward electric flux through the closed cylinder as:

Φ_total = Φ_side + Φ_top + Φ_bottom

= (Q/ϵ0)(R/Lr^2) + 2(Q/ϵ0)(R/r^2)

Simplifying this expression, we have:

Φ_total = (Q/ϵ0) [(2R/r^2) + (R/Lr^2)]

5)According to Gauss's law, the total outward electric flux through a closed surface is proportional to the total charge enclosed within that surface. In this case, the closed surface is the cylindrical Gaussian surface with radius r and length L, centered at the origin (where the charged sphere is located). The charge enclosed within this surface is simply the charge of the sphere, which is +Q. Therefore, we expect the total outward electric flux through the closed cylinder to be:

Φ_total = Q/

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According to the question, the work done by a car is calculated as 144Nm.

Force may be defined as a process of pushing or pulling on an object that significantly produces acceleration in the body on which it acts. It is an external agent capable of changing a body's state of rest or motion. It has a magnitude and a direction.

According to the question,

The force applied on a car = 18 N

The displacement made by a car = 8m.

Now, the work done is calculated with the help of the given formula:

                           = 18 N × 8m = 144Nm.

Therefore, the work done by a car is calculated as 144Nm.

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The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².

To calculate the average acceleration of the motorcycle, we can use the formula:

Average acceleration = (final velocity - initial velocity) / time

First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.

Converting the final velocity:

Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s

Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:

Average acceleration = (21.67 m/s - 0 m/s) / time

To find the time taken to reach this velocity, we need to use the formula for average speed:

Average speed = total distance/time

Rearranging the formula:

time = total distance / average speed

Plugging in the values:

time = 50 m / 21.67 m/s ≈ 2.31 seconds

Now we can calculate the average acceleration:

Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²

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A 7 kg mass moving across the table at an acceleration of 25 m\(/s^2\)requires a force of 175 N.

To determine the force required to cause the acceleration of a 7 kg mass moving across the table at 25\(m/s^2\), we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.

Given:

Mass (m) = 7 kg

Acceleration (a) = 25 \(m/s^2\)

We can substitute these values into the equation:

Force (F) = mass (m) * acceleration (a)

F = 7 kg * 25 \(m/s^2\)

F = 175 kg·\(m/s^2\)

Therefore, the force required to cause the acceleration of the 7 kg mass is 175 kg·\(m/s^2\).

To understand the calculation, we need to know that force is a measure of how much an object accelerates when a certain amount of mass is acted upon by that force. In this case, the mass of the object is 7 kg, and it is experiencing an acceleration of 25\(m/s^2\).

By multiplying the mass and acceleration together, we find that the force required is 175 kg·\(m/s^2\). This unit, also known as a Newton (N), represents the force required to accelerate a 1 kg mass at a rate of 1 \(m/s^2\)

In summary, the force required to cause the acceleration of the 7 kg mass across the table at 25 \(m/s^2\) is determined to be 175 kg·\(m/s^2\). This calculation follows Newton's second law of motion and shows the relationship between mass, acceleration, and force.

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The mass of the the object, given that the same force acted upon it to accelerate at 2 m/s² is 34 Kg

First, we shall determine the force. This can be obtained as follow:

Force (F) = mass (m) × acceleration (a)

Force = 4 × 17

Force = 68 N

Finally, we shall determine the mass of the object that will accelerate at 2 m/s² when the force of 68 N is applied to it. Details below:

Force = mass × acceleration

68 = mass × 2

Divide both sides by 2

Mass = 68 / 2

Mass = 34 Kg

Thus, from the above calculation, we can conclude that the mass is 34 Kg

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The amount of water affects the mass and the height of the plants.

The correct conclusion is the conclusion which the data obtained supports.

Plants need both water and sunlight to grow.

The variation the amount of water or sunlight that a plant receives will affect the growth rate of the plant.

Based on the data obtained from the experiment where Pots A and B both have plain soil, bean seeds, and the same amount of light, while Pot B receives more water, the amount of water affects the mass and the height of the plants.

In conclusion, plants need both water and sunlight for growth.

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Answer:

Explanation:

Given:

To Find:

Solution:

Here, we have a formula

Substituting the values

\(\implies\:\:F = \dfrac{G(1)(4)}{2^{2}}\)

\(\implies\:\:F = \dfrac{4G}{4}\)

\(\implies\:\:F = \dfrac{\cancel{4}G}{\cancel{4}}\)

\(\implies\:\:\red{F = G}\)

Know More:

The applied formula for the above solution is

\({\boxed{F_{G}=\dfrac{G.M_{1}.M_{2}}{r^{2}}}}\)

where,

Answer:

A)  a_c = 1.75 10⁴ m / s², B) a = 4.43 10³ m / s²

Explanation:

Part A) The relation of the test tube is centripetal

               a_c = v² / r

the angular and linear variables are related

              v = w r

we substitute

               a_c = w² r

let's reduce the magnitudes to the SI system

              w = 4000 rpm (2pi rad / 1 rev) (1 min / 60s) = 418.88 rad / s

               r = 1 cm (1 m / 100 cm) = 0.10 m

let's calculate

              a_c = 418.88² 0.1

               a_c = 1.75 10⁴ m / s²

part B) for this part let's use kinematics relations, let's start looking for the velocity just when we hit the floor

as part of rest the initial velocity is zero and on the floor the height is zero

                v² = v₀² - 2g (y- y₀)

                v² = 0 - 2 9.8 (0 + 1)

                v =√19.6

                v = -4.427 m / s

now let's look for the applied steel to stop the test tube

                v_f = v + a t

                0 = v + at

                a = -v / t

                a = 4.427 / 0.001

                a = 4.43 10³ m / s²

Therefore, of the three options given, the electromagnet with more coils around the metal rod is the most powerful if all other factors such as current and core material are kept constant.

What is the very short response to an electromagnet?

An electromagnet is a temporary magnet made by winding a wire around an iron core. When current flows through the coil, iron becomes a magnet, and when the current is cut off, it loses its magnetic properties.

What is Electromagnetism?

Electromagnetism is the branch of physics that deals with the electromagnetic forces that occur between charged particles. Electromagnetic force is one of the four basic forces and describes the electromagnetic field.

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Answer: The answer is B

Explanation:

45º angle will result in the trebuchet’s furthest thrown projectile.

It is acceptable to infer from the results shown in the demonstration on Interactive Physics that as the weight of a counterweight on a trebuchet rises, so too should the projectile's range. Except for the fact that the distance did not rise linearly but rather more quadratically, the results support the theory. The results showed that the distance rose as the weight of the trebuchet's counterweight was increased in steps of 5 kilograms, starting at 20 kilograms and ending at 200 kilograms.

Each time, the projectiles were launched from the trebuchet at a 45-degree angle, and their distances typically followed the equation -8.1551E-4x2 +.304388x + 8.12756 (where x is the mass of the counterweight). The graph was thought to be more quadratic than linear because gravity has more time to work against the projectile and pull it down to the earth the longer it is in the air. Therefore, as additional mass is applied and the projectile is in the air for a longer period of time, the projectile distances would not grow as quickly. These findings back up Newton's Third Law of Motion as well as earlier, historical investigations.

Thus, Thomas should launch the trebuchet at a 45º angle to get the farthest thrown projectile.

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Answer:

W = 181.26 J

Explanation:

Given that,

The force acting on the cart, F = 20 N

It is at an angle of 25 degrees above the horizontal to  move a crate a distance of 10m across the floor.

We need to find work done by the student. The work done by the student is given by :

\(W=Fd\cos\theta\\\\W=20\times 10\times \cos25\\W=181.26\ J\)

So, the required work done is 181.26 J.

The change in surface area of Gaussian surface with radius (r) is 8πr.

The electric field experienced by a charge is calculated as follows;

\(E = \frac{Q}{4\pi \varepsilon_o r^2}\)

where;

The electric field reduces by a factor of \(\frac{1}{r^2}\)

The surface area of a sphere is given as;

\(A = 4\pi r^2\)

\(\frac{dA}{dr} = 8\pi r\)

Thus, the change in surface area of Gaussian surface with radius (r) is 8πr.

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The region a represents the distance of the electron from the nucleus.

According to the wave mechanical model of the atom, the probability of finding an electron within a given volume element (representing the atom) is the square of the wave function psi.

Since a is the region in space where there is the greatest probability of finding the electron in the atom, it follows that distance of the electron form the atom is always a.

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Answer:

equilibrium because its equal force on the ball.

Explanation:

Answer:

good

Explanation:

Answer: Eclipses do not happen at every new moon, of course. This is because the moon's orbit is tilted just over 5 degrees relative to Earth's orbit around the sun. For this reason, the moon's shadow usually passes either above or below Earth, so a solar eclipse doesn't occur.

Explanation:   :>

Answer:

D

Explanation:

I'm not sure but I think so haha

Answer:

\(p = {i}^{2} r\)

\(i = \sqrt{ \frac{p}{r} } \)

P= VI

V= IR

Substitute eqn 1 into eqn 2

P= (IR) I

\(p = {i}^{2} r\)

\( \frac{p}{r} = \frac{ {i}^{2}r }{r} \)

\( {i}^{2} = \frac{p}{r} \)

\(i = \sqrt{ \frac{p}{r} } \)

ANSWERS

a. f₁ = 380 Hz; f₂ = 760 Hz; f₃ = 1140 Hz

b. f₁ = 190 Hz; f₃ = 570 Hz; f₅ = 950 Hz

EXPLANATION

a. For a pipe of length L open at both ends, the frequencies of the first three harmonics are:

Assuming that the speed of the wave is the speed of sound: 343 m/s and knowing that the length of the pipe is L = 45.132 cm = 0.45132 m we can find the frequencies of the first three harmonics:

b. For a pipe of length L closed at one end and open at the other, the frequencies of the first three harmonics are:

In a closed pipe, there can only be odd harmonics (1, 3, 5...). Therefore, the second harmonic does not exist and the "third harmonic" would be the 5th,

Again, the length of the pipe is 45.132 cm = 0.45132 m, so the first three harmonics are:

The mattress of a water bed is 2.0m wide and 30.0cm deep. When the water bed is in its normal condition, the area in contact with the floor with 4.0 m², then the weight of the water in the mattress would be 11772 N.

It can be defined as the mass of any object or body per unit volume of the particular object or body. Generally, it is expressed as in gram per cm³ or kilogram per meter³.

As given in the problem The mattress of a water bed is 2.0m wide and 30.0cm deep.When the water bed is in its normal condition, the area in contact with the floor with 4.0 m².

At normal pressure and temperature, the density of the water is 1000 kg/m³

The mass of the mattress of water

mass = density×volume

= 1000 ×4 ×0.3

= 1200 kg

The weight of the mattress of water

W = mg

= 1200×9.81

=11772 N

Thus, the weight of the mattress of the water would be 11772 N

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The question seems incomplete, the complete question is

The mattress of a water bed is 2.0m wide and 30.0cm deep. When the water bed is in its normal condition, the area in contact with the floor with 4.0 m², Find the weight of the mattress of the water

Answer:

The slope intercept form is probably the most frequently used way to express equation of a line. To be able to use slope intercept form, all that you need to be able to do is 1) find the slope of a line and 2) find the y-intercept of a line.

Explanation:

Answer:You plot the numbers and divide

Explanation: