Jamaal drove to the mountains to go camping. He drove 300 miles in 5 hours.
What was his average speed?
A. 45 mph
B. 55 mph
C. 50 mph
D. 60 mph

Each of the five friends needs to pay £12 to cover the cost of their own meals and contribute towards the birthday person's meal. Using mean allows us to distribute the cost equally among the friends, ensuring a fair division of expenses for the meal.

To determine how much each of the five friends needs to pay, we can use the concept of averages (mean) and divide the total cost by the number of people paying.

In this scenario, the total cost of the meal for 6 people is £12 per person. Since the other 5 friends have decided to pay for the birthday person's meal, they will collectively cover the cost of their own meals plus the birthday person's meal.

To calculate the total cost covered by the five friends, we can subtract the cost of one person's meal (since the birthday person's meal is being paid by the group) from the total cost. The cost of one person's meal is £12.

Total cost covered by the five friends = Total cost - Cost of one person's meal

= (£12 x 6) - £12

= £72 - £12

= £60

Now, to find out how much each of the five friends needs to pay, we divide the total cost covered by the five friends (£60) by the number of friends (5).

Amount each friend needs to pay = Total cost covered by the five friends / Number of friends

= £60 / 5

= £12

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The following statement is not a scientific hypothesis:

C. Halle Berry is attractive.

A scientific hypothesis is a proposed explanation for an observation or pattern in nature that can be tested through further investigation and experimentation. It should be testable, falsifiable, and based on evidence.

Neon atoms emit red light. This is a scientific hypothesis that can be tested and confirmed by looking at the spectrum of light emitted by neon atoms.

B. There is an attractive force between the earth and moon. This is a scientific hypothesis that can be tested and confirmed by measuring the force of gravity between the earth and moon.

D. Summer days are the hottest of the year. This is a scientific hypothesis that can be tested and confirmed by collecting temperature data during the summer months.

E. The sky is blue. This is a scientific hypothesis that can be tested and confirmed by observing the sky under different atmospheric conditions.

The statement "Halle Berry is attractive" is a subjective opinion that cannot be tested or confirmed through scientific investigation, hence it is not a scientific hypothesis. Attractiveness, as a concept, can vary widely based on personal, cultural, and social factors.

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The energy transferred in Joules by the radio when it has been switched on for 2 minutes would be 6000 Joules.

Power is defined as the rate of energy transfer or the rate at which work is done, and is given by the equation:

Power = Energy transferred / Time

Rearranging the equation to solve for energy transferred, we get:

Energy transferred = Power x Time

We are given:

Power = 50 W

Time = 2 minutes = 120 seconds

Therefore, the energy transferred by the radio when it has been switched on for 2 minutes is:

Energy transferred = Power x Time = 50 W x 120 s = 6000 J

In other words, the energy transferred by the radio is 6000 Joules.

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Answer:

Sound waves travel through the air.

Step-by-step explanation:

As a sound wave travels through a medium, it will often reach the end of the medium to encounter an obstacle or perhaps another medium through which it could travel. In a sound wave, a portion of the energy carried by the sound wave will pass across the boundary and out of the transmission, and a portion of the energy carried by the sound wave will reflect off the boundary, remain in the transmission, and travel in the opposite direction.

It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.

2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.

3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.

4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.

5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.

6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".

7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).

8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).

9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.

10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.

11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).

12. Evaluating the expression, we find: t ≈ 546.

13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

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Answer:

Explanation:

(m1 + m2)*V1 = m2*V2 + m1*Vx

Vx = ((m1 + m2)*V1 -  m2*V2) / m1

Vx = ((82 + 48)*7.4 - 48*8.6) /82 = 6.7 m/s

If the displacement of an object, x, is related to velocity, v, according to the relation .x = Av the dimension of which of the following is time.

An object's position changes if it moves in relation to a reference frame, such as when a passenger moves to the back of an airplane or a lecturer moves to the right in relation to a whiteboard. Displacement describes this shift in location.

A = x/v

since x is displacement and v is velocity

x/v = m/(m/s) = s

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a) The time that the ball is in the air is 0.23 second.

b)  The initial horizontal velocity of the ball is 11.74 m/s.

The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction.

Vertical height of the point = 1.0 meter.

The horizontal distance travelled by the ball = 2.7 m.

a) The time that the ball is in the air is = √(H/2g)

= √(1.0/2×9.8)

= 0.23 second

b) The initial horizontal velocity of the ball is = 2.7 m/0.23 s

= 11.74 m/s

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A) Therefore, the amount of work performed by heart is \($2.9289 \times 10^{-3} \mathrm{~J}\)

b) Therefore, the power require is \($0.013313 \mathrm{~W}\)

c) Therefore, the efficiency of heart is\($0.2219 \%$.\)

A) Calculate the amount of the work performed by the heart during the systole by using the following relation:

\($$\begin{aligned}W & =\frac{1}{2} m_b v^2 \\& =\frac{1}{2}\left(\rho_b A v\right) v^2 \\& =\frac{1}{2} \rho_b A v^3 \\& =\frac{1}{2} \rho_b\left(\frac{\pi}{4} d^2\right) v^3 \\& =\frac{1}{2} \times 1.057 \times 10^3 \times\left(\frac{\pi}{4} \times(0.029)^2\right) \times(0.2032)^3 \\& =2.9289 \times 10^{-2} \mathrm{~J}\end{aligned}$$\)

Therefore, the amount of work performed by heart is \($2.9289 \times 10^{-3} \mathrm{~J}$.\)

b) Calculate the power during systole by using the following relation:

\($$\begin{aligned}P & =\frac{W}{t} \\& =\frac{2.9289 \times 10^{-3}}{0.22} \\& =0.013313 \mathrm{~W}\end{aligned}$$\)

Therefore, the power require is \($0.013313 \mathrm{~W}$.\)

C) Calculate the efficiency of the heart by using the following relation:

\($$\begin{aligned}\eta & =\frac{P_{\text {out }}}{P_{\text {ov }}} \\& =\frac{0.013313}{6} \\& =0.0022188(0.2219 \%)\end{aligned}$$\)

Therefore, the efficiency of heart is\($0.2219 \%$.\)

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Answer:

10.77 m

Explanation:

From the question given above, the following data were obtained:

Initial velocity (u) = 32 m/s

Angle of projection (θ) = 27°

Acceleration due to gravity (g) = 9.8 m/s²

Apogee i.e maximum height (H) =?

Thus, the apogee i.e the maximum height of the pumpkin can be obtained as follow:

H = u² Sine² θ /2g

H = 32² × (Sine 27)² / 2 × 9.8

H = 1024 × (0.454)² / 19.6

H = (1024 × 0.206116) / 19.6

H = 10.77 m

Thus, the apogee i.e the maximum height of the pumpkin is 10.77 m.

1.Unit vector in the direction BA: BA/|BA| = (2/3, 2/3, 1/3)

2.The angular velocity (ω) of the body is given as 3 radians per second.

3.Without the position of point P given, it is not possible to write the position vector of P.

4.Left-handed rotation refers to the direction of rotation where the rotation follows the left-hand rule.

5.Position vector of point A: (4, 1, 1)

Position vector of point B: (2, -1, 0)

The direction vector BA = (-2, -2, -1)

1.To determine the unit vector pointing in the direction BA, we subtract the coordinates of point B from the coordinates of point A and normalize the resulting vector.

The direction vector BA is given by:

BA = (4 - 2, 1 - (-1), 1 - 0) = (2, 2, 1)

To obtain the unit vector in the direction of BA, we divide the direction vector by its magnitude:

|BA| = √(2^2 + 2^2 + 1^2) = √(4 + 4 + 1) = √9 = 3

Unit vector in the direction BA: BA/|BA| = (2/3, 2/3, 1/3)

2.The angular velocity (ω) of the body is given as 3 radians per second.

3.Without the position of point P given, it is not possible to write the position vector of P. Please provide the position of point P to proceed with the calculation.

4.Left-handed rotation refers to the direction of rotation where the rotation follows the left-hand rule. In a left-handed coordinate system, if you curl the fingers of your left hand in the direction of rotation, your thumb will point in the direction of the rotation axis. It is the opposite direction to a right-handed rotation.

5.The position vectors of points A and B are:

Position vector of point A: (4, 1, 1)

Position vector of point B: (2, -1, 0)

The direction vector BA can be obtained by subtracting the coordinates of point A from the coordinates of point B:

BA = (2 - 4, -1 - 1, 0 - 1) = (-2, -2, -1)

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Answer:

Explanation:

• Orbital Radius,:

We are already told that the altitude of the satellite is 300,000 meters. Having this information in hand, it is easy to find the radius of orbit using the following relation:

where A is the altitude.

Now we know that A = 300,000 m and earth radius = 6.37 * 10^6 m; therefore, the orbital radius of the satellite is

which is our answer!

• Velocity:

We are told that the velocity of the satellite is given by

where G is the gravitational constant and m_E is the mass of the earth.

Substituting the numerical values for these constants gives

Using a calculator we evaluate the above to be:

which is around 6.5 km per second!

• Orbital Period:

The orbital period T of the satellite is given by

putting in the numerical values for the constants gives

Hence, the period of satellites orbit is only 2.5 hours! This means that we can see the same satellite multiple times in the night sky if it is observable!

• Orbital Path:

The problem with satellites is that since they are travelling so fast, they don't get to observe one location on earth for a long time. One solution to this is to place the satellites into something called the geosynchronous orbit. In such an orbit, the period of the satellite matches the earth's period of rotation. This way, when observed from the earth, the satellite looks stationary, but in fact, it is travelling with the earth in the same orbital period. Such a satellite can be launched to observe locations along the arctic and the antarctic circles to obtain substantial data.

Answer:

To solve this problem, you'll need to break the initial velocity of the seed into its horizontal and vertical components, then use the equations of motion to find the time of flight and horizontal distance.

The initial velocity (v) of the seed is 2.65 m/s. The angle it's launched at (θ) is 30.0 degrees below the horizontal. The height (h) it's launched from is 0.460 m.

First, calculate the horizontal (v_x) and vertical (v_y) components of the velocity. Because the seed is launched downward, the vertical component will be negative:

v_x = v * cos(θ) = 2.65 m/s * cos(30.0) = 2.29 m/s

v_y = v * sin(θ) = -2.65 m/s * sin(30.0) = -1.325 m/s

Next, use the equation of motion to find the time it takes for the seed to hit the ground:

h = v_y * t + 0.5 * g * t^2

Where g is the acceleration due to gravity, which is approximately 9.8 m/s². Solving the equation for t gives:

t = (-v_y - sqrt((v_y)^2 - 4 * 0.5 * g * (-h))) / (2 * 0.5 * g)

Plugging in the values:

t = (1.325 + sqrt((-1.325)^2 - 4 * 0.5 * 9.8 * (-0.460))) / (2 * 0.5 * 9.8)

t = 0.182 seconds

Finally, use the horizontal velocity and time of flight to find the horizontal distance the seed covers:

x = v_x * t = 2.29 m/s * 0.182 s = 0.417 m

So, the seed lands after approximately 0.182 seconds and travels approximately 0.417 meters horizontally.

As per the given scenario, in this case, the coefficient of friction () is half and the coefficient of restitution (e) is zero.

Identify the body's starting velocity:

We may use the equation of motion to get the body's initial velocity (u)

\(v^2 = u^2 + 2as\)

\(0 = u^2 + 2(-9.8)m/s^2 * h\)

\(u^2 = 19.6h\)

u = √(19.6h)

The body's initial velocity (u) and initial relative velocity (u_rel) are the same.

The body's horizontal velocity immediately following the collision, which is zero, is the final relative velocity (v_rel).

\(e = v_{rel }/ u_{rel}\)

e = 0 / u_rel = 0 / u

Now, one can investigate the forces affecting the body: When a body is on an inclined plane.

There are two main forces at work on it: the frictional force that prevents the body from moving and the gravitational force that pulls it downward (mg).

The gravitational force has two components that act perpendicular to and parallel to the inclined plane, respectively: m*g*cos(45°) and m*g*sin(45°).

Determine the conditions for the body to stop:

μ * N = m * g * sin(45°)

μ * (m * g * cos(45°)) = m * g * sin(45°)

μ * cos(45°) = sin(45°)

(1/2) * cos(45°) = sin(45°)

Simplifying further, we have:

√2 / 4 = √2 / 2

Thus, the body will come to rest following the collision if the equation is valid.

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The root-mean-square speed of an oxygen molecule at a pressure of 3.9 x 10^4 Pa and a density of 1.3 kg/m^3 is approximately 6.13 x 10^-9 m/s.

The root-mean-square (rms) speed of an oxygen molecule can be calculated using the ideal gas law and the definition of density.

The ideal gas law states:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

Rearranging the ideal gas law to solve for the rms speed (v) gives:

v = sqrt(3 * P / (density * N))

where P is the pressure, density is the density of the gas, and N is Avogadro's number (6.022 x 10^23 molecules/mol).

Given:

Pressure (P) = 3.9 x 10^4 Pa

Density = 1.3 kg/m^3

We can substitute these values into the formula to calculate the rms speed of an oxygen molecule.

v = sqrt(3 * (3.9 x 10^4) / (1.3 * (6.022 x 10^23)))

v = sqrt(3.77 x 10^-18 m^2/s^2)

v ≈ 6.13 x 10^-9 m/s

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The time will be the same for both horizontal and vertical component. The initial speed is 10.7 m/s

Speed is a distance travel per time taken. It is a scalar quantity and it is measured in m/s

Given that a person standing at the edge of a seaside cliff kicks a rock horizontally of the cliff from a height of 52 m and it lands a distance of 35 m from the base of the cliff.

The rock will move vertically downward with initial velocity = 0. The time taken will be constant. That is, same horizontally.

Let us first calculate the time by using the formula

h = ut + 1/2gt²

Where

Substitute all the necessary parameters into the formula

52 = 0 + 1/2 × 9.8 × t²

52 = 4.9t²

t² = 52/4.9

t² = 10.6

t = √10.6

t = 3.26 s

The speed at which the rock was initially kicked can be found by

R = Ut

35 = U × 3.26

U = 35/3.26

U = 10.7 m/s

Therefore, rock was initially kicked at a speed of 10.7 m/s

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Answer:

The power output of this engine is  \(P = 17.5 W\)

The  the maximum (Carnot) efficiency is  \(\eta_c = 0.7424\)

The  actual efficiency of this engine is  \(\eta _a = 0.46\)

Explanation:

From the question we are told that

    The temperature of the hot reservoir is  \(T_h = 1250 \ K\)

      The temperature of the cold reservoir  is  \(T_c = 322 \ K\)

     The energy absorbed from the hot reservoir is \(E_h = 1.37 *10^{5} \ J\)

       The energy exhausts into  cold reservoir is  \(E_c = 7.4 *10^{4} J\)

The power output is mathematically represented as

      \(P = \frac{W}{t}\)

Where t is the time taken which we will assume to be 1 hour =  3600 s  

W is the workdone which is mathematically represented as

      \(W = E_h -E_c\)

substituting values

       \(W = 63000 J\)

So

    \(P = \frac{63000}{3600}\)

    \(P = 17.5 W\)

The Carnot efficiency is mathematically represented as

          \(\eta_c = 1 - \frac{T_c}{T_h}\)

         \(\eta_c = 1 - \frac{322}{1250}\)

         \(\eta_c = 0.7424\)

The actual efficiency is mathematically represented as

        \(\eta _a = \frac{W}{E_h}\)

substituting values

         \(\eta _a = \frac{63000}{1.37*10^{5}}\)

         \(\eta _a = 0.46\)

Answer:

pupil is the correct answer ... explanation : pupil is the opening that allows light to enter our eyes and iris controls the amount of light entering our eyes by controlling the size of pupil

Answer:

No, it is not a good assumption

Explanation:

From the given information:

The work Jessie did was quite more than the work done by the force of gravity. This is because the gravity of the force on her body is perpendicular to its motion and the work done by Jessie is due to the muscular force of her body. Hence, the total power she produced is more than the calculated amount.

Explanation:

The satement that can be made about sound wave A and sound wave B is, they will slow down.

Relationship between sound wave and temperature

The relationship between sound waves and temperature is given by the following formula;

v= √γRT

The speed of sound wave increases with increase in temperature, and vice versa.

Speed of sound wave in liquid and gaseous medium

Sound wave is mechanical wave, because it requires material medium for its propagation. Sound will travel faster in liquid medium than gaseous medium because of number of molecules per unit volume.

Thus, the satement that can be made about sound wave A and sound wave B is, they will slow down.

Answer:

a. 282.84 cm/s b. 100 cm/s c. 400 cm/s d. 200 cm/s

Explanation:

The speed of the wave v = √(T/μ) where T = tension and μ = mass per unit length = m/l where m = mass of string and l = length of string.

So, v = √(T/μ)

v = √(T/m/l)

v = √(Tl/m)

a. The string's tension is doubled?

If the tension is doubled, T' = 2T the new speed is

v' = √(T'l/m)

v' = √(2Tl/m)

v' = √2(√Tl/m)

v' = √2v

v' = √2 × 200 cm/s

v' = 282.84 cm/s

b. The string's mass is quadrupled (but its length is unchanged)?

If the mass is quadrupled, m' = 4m the new speed is

v' = √(Tl/m')

v' = √(Tl/4m)

v' = (1/√4)(√Tl/m)

v' = v/2

v' = 200/2 cm/s

v' = 100 cm/s

c. The string's length is quadrupled (but its mass is unchanged)?

If the length is quadrupled, l' = 4l the new speed is

v' = √(Tl'/m)

v' = √(T(4l)/m)

v' = √4)(√Tl/m)

v' = 2v

v' = 200 × 2 cm/s

v' = 400 cm/s

d. The string's mass and length are both quadrupled?

If the length is quadrupled, l' = 4l and mass quadrupled, m' = 4m, the new speed is

v' = √(Tl'/m')

v' = √(T(4l)/4m)

v' = √(Tl/m)

v' = v

v' = 200 cm/s

Considering the definition of precision and accuracy, the mass readings of the digital balance are accurate but not precise.

Precision as the proximity between the indications or measured values ​​of the same measurand, obtained in repeated measurements, under specified conditions.

Accuracy is defined as the closeness between the measured value and the "true" value of the measurand.

In other words, accuracy is how close a measurement is to the true value, while precision is how close the values ​​of several measurements are to a point.

Precision and accuracy are independent of each other. Thus, the results in the values ​​of a measurement can be precise and not exact (and vice versa).

A set of 500-g masses is placed one at a time on a digital balance during quality control testing. The mass readings are 397 g, 401 g, and 403 g.

In this case, the measurement is accurate, since the results of each individual measurement are quite similar. But the measurements are not exact (not precise) because the results are far from the real value.

In summary, the mass readings of the digital balance are accurate but not precise.

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The function of the power supply is to provide electrical energy to the device or system that needs it. The power supply converts the incoming voltage from the power source into a form that is usable by the device, such as DC voltage.

The readout is a device or component that displays data or information to the user. The readout could be a simple LED display or a complex graphical display.

A peripheral is a device or component that connects to a computer or other electronic device to provide additional functionality. Examples of peripherals include printers, scanners, and external hard drives.

A microcomputer is a type of computer that is designed to fit on a single microchip. Microcomputers are found in a wide range of devices, including smart phones, tablets, and embedded systems.

A transducer is a device that converts one form of energy to another. In electronics, transducers are commonly used to convert electrical energy into mechanical energy, or vice versa.

The processor is the central component of a computer or electronic device. The processor is responsible for executing instructions and controlling the other components of the system. The performance and capabilities of a device are largely determined by the speed and power of the processor.

Answer:

it has constant angular velocity

Explanation:

an object moving in a uniform circular motion moves with constant angular velocity about a point

The original velocity is \(5.71 m/s\)

What do you know about momentum?

The conservation of momentum principle states that, in a closed system, the overall momentum before and after a collision is equal.

We know of momentum conservation,

\(MU+mu=MV +mv\)

where \(M\) is the mass of the bowling ball, \(m\) is the mass of the pin, \(U\) is the bowling ball's starting velocity, \(u\) is the pin's initial velocity, \(V\) is the bowling ball's final velocity, and \(v\) is the pin's final velocity

Given

\(M= 7 kg, m=2kg, u = 0 m/s, v = 6 m/s, V= 4 m/s\)

\(MU+mu=MV +mv\)

\(7(U) + 2(0) = 7(4) +2(6)\\7U = 28 +12\\7U = 40\\U = 5.71 m/s\)

Hence the velocity will be \(5.71 m/s\)

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Answer:

f = 7.57 Hz

Explanation:

To find the frequency of the damping oscillator, you first use the following formula for the angular frequency:

\(\omega=\sqrt{\omega_o-(\frac{b}{2m})^2}=\sqrt{\frac{k}{m}-(\frac{b}{2m})^2}\\\\\)   (1)

k: spring constant = 2.65*10^4 N/m

m:  mass = 11.7 kg

b: damping coefficient = 4.50 Ns/m

You replace the values of k, m and b in the equation (1):

\(\omega=\sqrt{\frac{2.65*10^4N/m}{11.7kg}-(\frac{4.50Ns/m}{2(11.7kg)})^2}\\\\\omega=47.59\frac{rad}{s}\)

Finally, you calculate the frequency:

\(f=\frac{\omega}{2\pi}=\frac{47.59}{2\pi}Hz=7.57\ Hz\)

hence, the frequency of the oscillator is 7.57 Hz

The magnitude of the magnetic field B must change at a rate of approximately -2.6675 T/s to induce a current of 0.1 A in the windings of the coil.

To find the rate at which the magnitude of the magnetic field B must change, we can use Faraday's law of electromagnetic induction. The formula is:

EMF = -N * (ΔΦ/Δt)

where EMF is the induced electromotive force, N is the number of turns in the coil, ΔΦ is the change in magnetic flux, and Δt is the change in time.

We know that EMF = I * R, where I is the induced current and R is the resistance. In this case, I = 0.1 A and R = 8 Ω, so:

EMF = 0.1 A * 8 Ω = 0.8 V

Now we can find the change in magnetic flux (ΔΦ). The magnetic flux (Φ) through a rectangular coil is given by:

Φ = B * A

where A is the area of the coil. The area of the rectangular coil is 5 cm * 8 cm = 40 cm², or 0.004 m² when converted to square meters.

Since we want to find ΔΦ/Δt, we can rearrange Faraday's law:

ΔΦ/Δt = -EMF / N

Plugging in the values, we get:

ΔΦ/Δt = -0.8 V / 75 turns = -0.01067 Vs/turn

Now we can find the rate of change of the magnetic field (ΔB/Δt):

ΔB/Δt = (ΔΦ/Δt) / A

ΔB/Δt = -0.01067 Vs/turn / 0.004 m² = -2.6675 T/s

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Hey again!

Ok..

Now... The melting Point of this solid is 90°C.

Meaning That as soon as it gets to this temp... It STARTS Melting.

So at that temp... It still has some solid parts in it.

You can say its a Solid Liquid Mixture.

Additional Heat being applied at that point is not raising the temperature;rather its used in breaking the bonds in the solid. This is the Fusion stage.

After Fusion...It'd then Be a Pure Liquid with no solids in it.

So

Q'=MC∆0----- This is the heat needed to take the solid's temp from 30°c - 90°c

Q"=ml ----- This is the heat used in breaking the bonds holding the solids in the solid-liquid phase.

So

Q= Q' + Q"

Q= mc∆0 + ml

∆0 = 90°c - 30°c = 60°c

Q= 2.5(390)(60) + (2.5)(4000)

Q=6.9 x 10⁴Joules

The heat required to change 2.5 kg of the solid at 30.0C to a liquid is 6.9 x 10⁴J.

The specific heat is the amount of heat energy required to change the temperature of 1kg of object by 1°C.

The heat needed to change the solid's temperature from 30°C - 90°C is

Q' = mC∆T

The heat used to change the phase solid-liquid phase .i.e.

Q'' =mL where L =latent heat of fusion

The total heat required is

Q= Q' + Q"

Q= mc∆T + ml

Q= 2.5(390)(90 - 30) + (2.5)(4000)

Q=6.9 x 10⁴Joules

Thus, the heat required to change the solid to liquid is 6.9 x 10⁴J.

Learn more about  specific heat

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