The radius of a typical human eardrum is about 4.15 mm. Calculate the energy per second received by an eardrum when it listens to sound that is at the threshold of hearing, assumed to be 1.20E-12 W/m2

Answer:

a.) Speed V = 29.3 m/s

b.) K.E = 1931.6 J

Explanation: Please find the attached files for the solution

Final answer:

The wheel's speed at the bottom of the hill can be found through the conservation of energy equation considering both translational and rotational kinetic energy, while the total kinetic energy at the bottom of the hill is a sum of translational and rotational kinetic energy.

Explanation:

These two questions address the physics concepts of conservation of energy, kinetic energy, and rotational motion. To answer the first question, (a) How fast is the wheel moving when it reaches the bottom of the hill if it rolled without slipping all the way down?, we need to consider the potential energy the wheel has at the top of the hill is completely converted into kinetic energy at the bottom. This includes both translational and rotational kinetic energy. Solving for the final velocity, vf, which would be the speed of the wheel, we get vf = sqrt((2*g*h)/(1+I/(m*r^2))), where g is the acceleration due to gravity, h is the height of the hill, I is the moment of inertia of the wheel, m is the mass of the wheel, and r is the radius of the wheel.

For the second question, (b) How much total kinetic energy does it have when it reaches bottom of the hill?, we use the formula for total kinetic energy at the bottom of the hill, K= 0.5*m*v^2+0.5*I*(v/r)^2. Substituting the value of v found in the first part we find the kinetic energy which we can use the formula provided in the reference information.

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To solve the problem it is necessary to apply the concepts related to thermal expansion of solids. Thermodynamically the expansion is given by

Where,

Original Length of the bar

= Change in temperature

= Coefficient of thermal expansion

On the other hand our values are given as,

Replacing we have,

The width of the expansion of the cracks between the slabs is 0.5832cm

The width of the expansion cracks between the slabs to prevent buckling should be 0.5832cm.

How to calculate width?

According to this question, the following information are given:

• Lo = Original length of the bar
• ∆T = Change in temperature
• α = Coefficient of thermal energy

The values are given as follows:

• Lo = 18m
• T1 = 25°C, T2 = 52°C
• α = 12 × 10-⁶/°C

∆L = Loα (T2 - T1)

∆L = 18 × 12 × 10-⁶ (27)

∆L = 3.24 × 10-⁴ × 18

∆L = 5.832 × 10-³m

Therefore, the width of the expansion of the cracks between the slabs is 0.5832cm.

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Final answer:

To find the new angular momentum of the system if each of the masses were solid spheres, calculate the moment of inertia for each sphere using the formula (2/5) × m × r^2. Multiply the moment of inertia of each sphere by the angular velocity of the system to find the new angular momentum.

Explanation:

The angular momentum of a system can be found by multiplying the moment of inertia of the system with its angular velocity.

If each of the masses were instead a solid sphere 15.0 cm in diameter, we would need to calculate the moment of inertia of each sphere using the formula for the moment of inertia of a solid sphere, I = (2/5) × m × r^2, where m is the mass and r is the radius of the sphere.

Once we have the moment of inertia for each sphere, we can multiply it by the angular velocity of the system to find the new angular momentum.

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Final answer:

The new angular momentum, given the same angular speed, will be 0.9 times the original, as the moment of inertia for the system is replaced with that of solid spheres of given mass and radius.

Explanation:

The question is asking for the new angular momentum of a sphere with a given diameter if we replace each of the masses in a given system with it. To compute the new angular momentum, it's crucial to recognize that angular momentum (L) is given by the product of the moment of inertia (I) and angular velocity (w). The moment of inertia for a solid sphere is given by (2/5)mr^2, where m is the mass and r is the radius of the sphere. Since angular velocity has not been specified in the question, it would be assumed to remain unchanged.

So, for this specific system, each mass is replaced with a solid sphere of mass 20 kg and radius 15 cm (or 0.15 m). Thus using the formula for solid sphere inertia, I = (2/5)*(20 kg)*(0.15 m)^2 = 0.9 kg*m^2. If w remains the same, then the new angular momentum L = I * w will be 0.9 times the original angular momentum. This is because w is the same but the moment of inertia has a new value due to the shape and size of the new masses.

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Answer:

The energy stored is

Explanation:

From the question we are told that  

   The capacitance  is  

    The resistance is  R = 3.00-Ω

    The emf is  

      The power  is  P = 300 W

Generally the total  emf is mathematically represented as

Here   is the emf across that capacitor which is mathematically represented as

and is the emf across the resistor which is mathematically represented as

So  

=>    

Generally the energy stored in a capacitor is mathematically represented as

=>      

=>      

=>      

Final answer:

The energy stored in the capacitor is 0 J.

Explanation:

When a 8.00-μF capacitor that is initially uncharged is connected in series with a 3.00-Ω resistor and an emf source with E = 70.0 V

At the instant when the resistor is dissipating electrical energy at a rate of 300 W, we can calculate the current flowing through the circuit using Ohm's law: I = V/R = 70.0 V / 3.00 Ω = 23.33 A.

The energy stored in a capacitor can be calculated using the formula: E = 1/2 * C * V^2, where C is the capacitance and V is the voltage across the capacitor.

Since the capacitor is initially uncharged, the voltage across it is also zero. So the energy stored in the capacitor is 0.5 * 8.00 x 10^-6 F * (0 V)^2 = 0 J.

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(a) It takes approximately 2.8956 seconds for the camera to reach the ground.

(b) The velocity of the camera just before it lands is approximately -28.375 m/s (downward).

We have,

Given information:

Initialheight (h₀) = 41 m (above the ground)

Descentrate of the hot-air balloon = -2.3 m/s (negative because it's descending)

We can use the kinematicequations to solve for the time it takes for the camera to reach the ground and its velocity just before landing.

(a)

To find the time it takes for the camera to reach the ground, we can use the following kinematic equation:

h = h₀ + (v₀)t + (1/2)at²

Where:

h = final height (0 m, as it reaches the ground)

h₀ = initial height (41 m)

v₀ = initial velocity (0 m/s, as the camera is dropped)

a = acceleration (acceleration due to gravity, approximately -9.8 m/s²)

t = time (what we're solving for)

Plugging in the values:

0 = 41 + (0)t + (1/2)(-9.8)t²

Simplifying:

-4.9t² = 41

Divide by -4.9:

t² = -41 / -4.9

t² = 8.36734694

Taking the square root:

t = √8.36734694

t ≈ 2.8956 seconds

(b)

To find the velocity just before the camera lands, we can use the following kinematic equation:

v = v₀ + at

Where:

v = final velocity (what we're solving for)

v₀ = initial velocity (0 m/s)

a = acceleration (acceleration due to gravity, -9.8 m/s²)

t = time (2.8956 seconds, calculated in part a)

Plugging in the values:

v = 0 + (-9.8)(2.8956)

v ≈ -28.375 m/s

The negativesign indicates that the velocity is directed downward, which is consistent with the descending motion.

Thus,

(a) It takes approximately 2.8956 seconds for the camera to reach the ground.

(b) The velocity of the camera just before it lands is approximately -28.375 m/s (downward).

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Answer:

3.4 x 10^-4 T

Explanation:

A = 1.5 x 10^-3 m^2

N = 50

R = 180 ohm

q = 9.3 x 106-5 c

Let B be the magnetic field.

Initially the normal of coil is parallel to the magnetic field so the magnetic flux is maximum and then it is rotated by 90 degree, it means the normal of the coil makes an angle 90 degree with the magnetic field so the flux is zero .

Let e be the induced emf and i be the induced current

e = rate of change of magnetic flux

e = dФ / dt

i / R = B x A / t

i x t / ( A x R) = B

B = q / ( A x R)

B = (9.3 x 10^-5) / (1.5 x 10^-3 x 180) = 3.4 x 10^-4 T

Final answer:

The magnitude of the magnetic field can be calculated using Faraday's Law of electromagnetic induction, by setting up and solving an equation involving the number of turns in the coil, the area of the coil, and the time it takes for the coil to rotate.

Explanation:

To calculate the magnitude of the magnetic field, we can use Faraday's Law of electromagnetic induction, which can be expressed as E = d(N∙Φ )/dt, where E represents the induced EMF, N is the number of turns, and Φ is the magnetic flux (flux equals the product of the magnetic field B, the area A through which it passes and the cosine of the angle between B and A).

Given the information in the problem, we know that E = Q/R ∙ t. Since the coil is rotated through 90 degrees, it goes from being parallel to being perpendicular to the field, resulting in a change in magnetic flux of BNA. We can set up the equation E = d(NBA)/dt = Q/R ∙ t = [(50 turns) ∙ (1.5 × 10-3 m²) ∙ B)/(t)]

We can solve this equation to determine the magnitude of the magnetic field B. Remember, always double-check your calculations to ensure their accuracy.

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