You hear 2 beats per second when two sound sources, both at rest, play simultaneously. The beats disappear if source 2 moves toward you while source 1 remains at rest. The frequency of source 1 is 500 Hz. The frequency of source 2 is...


A) 498 Hz.

B) 496 Hz.

C) 502 Hz.

D) 500 Hz.

E) 504 Hz.

Answer:

The speed of the speeder is [tex]8.348x10^6m/s[/tex].

Explanation:

Spectral lines will be shifted to the blue part of the spectrum if the source of the observed light is moving toward the observer, or to the red part of the spectrum when is moving away from the observer (that is known as the Doppler effect).

That shift can be used to find the velocity of the object (in this case the speeder) by means of the Doppler velocity.

[tex]v = c\frac{\Delta \lambda}{\lambda_{0}}[/tex]   (1)

Where [tex]\Delta \lambda[/tex] is the wavelength shift, [tex]\lambda_{0}[/tex] is the wavelength at rest, v is the velocity of the source and c is the speed of light.

[tex]v = c(\frac{\lambda_{0}-\lambda_{measured}}{\lambda_{0}})[/tex]

For this case [tex]\lambda_{measured}[/tex] is equal to 564.2 nm and [tex]\lambda_{0}[/tex] is equal to 575.9 nm.

[tex]v = (3x10^8m/s)(\frac{575.9 nm - 564.2 nm}{564.2 nm)})[/tex]

[tex]v = 8.348x10^6m/s[/tex]

Hence, the speed of the speeder is [tex]8.348x10^6m/s[/tex].

The question involves calculating the speed of a car based on the Doppler shift of light from yellow to green. The formula for Doppler shift of light is utilized to determine the relative velocity, but the practicality of such an effect for a moving car is negligible.

The question relates to the concept of the Doppler Effect for light, where the observed wavelength of light emitted by a source changes due to relative motion between the source and the observer. In this case, to calculate how fast the speeder would have to be traveling for the Doppler shift to change the color of a yellow light (575.9 nm) to green (564.2 nm), we can use the Doppler shift formula for light:

f' = f (c + v) / (c - v), where:

Since frequency is inversely proportional to wavelength (f = c / λ), the formula can be rearranged in terms of wavelength. Solving for v when the source is moving towards the observer gives us the expression:

v = c (λ0 - λ) / λ, where λ0 is the original wavelength and λ is the observed wavelength.

The speed of the car can thus be calculated accordingly. However, the effect of Doppler shift at such speeds is so small that it would not account for the perceptual change from yellow to green in a real-world scenario.

Answer:

[tex]d=2.4\ miles[/tex]

Explanation:

Given:

According to given condition:

[tex]t_w=t_b+\frac{36}{60}[/tex]

where:

[tex]t_w=[/tex] time taken to reach the building by walking

[tex]t_b=[/tex] time taken to reach the building by biking

We know that,

[tex]\rm time=\frac{distance}{speed}[/tex]

so,

[tex]\frac{d}{v_w} =\frac{d}{v_b} +\frac{36}{60}[/tex]

[tex]\frac{d}{3}=\frac{d}{12} +\frac{3}{5}[/tex]

[tex]d=2.4\ miles[/tex]

Answer:

The distance from her apartment to the classroom building is 2.4 miles.

Explanation:

Given that,

Time  = 36 min

Walking average speed of her = 3 m/h

biking average speed of her = 12 m/h

If she takes n minutes to ride, then if the distance is d miles,

We need to calculate the distance

Using formula of time

[tex]t=t_{1}+t_{2}[/tex]

[tex]t=\dfrac{d}{v_{1}}+\dfrac{d}{v_{2}}[/tex]

Put the value into the formula

[tex]\dfrac{36}{60}=\dfrac{d}{3}-\dfrac{d}{12}[/tex]

[tex]d=\dfrac{36\times12}{60\times3}[/tex]

[tex]d=2.4\ miles[/tex]

Hence, The distance from her apartment to the classroom building is 2.4 miles.

Answer:

 v = 0.0147 m / s

Explanation:

For this exercise let's use energy conservation

Starting point. Fully stretched spring

            Em₀ = Ke = ½ k (x-x₀)²

Final point. Unstretched position

          Emf = K = ½ m v²

          Emo = Emf

         ½ k (x- x₀)² = ½ m v²

           v = √m/k    (x-x₀)

Let's calculate

            v = √(0.022 / 0.5)      (0.26-0.19)

            v = 0.0147 m / s

The speed of the mass at the mean position is 0.333 m/s

The potential energy stored in a fully stretched spring

PE = ½ kx²

where x is the stretch of the spring  = 26 -19 = 7 cm = 0.07 m

At the mean position, where x = 0, the PE stored in sprig is zero,

So according to the law of conservation of energy total energy must remain conserved so all the energy is converted into kinetic energy KE of the mass

KE = ½ mv²

where m is the mass and v is the velocity

½ kx² = ½ mv²

where k is the spring constant = 0.5 N/m

and m is the mass = 0.022 kg

[tex]v=\sqrt{\frac{k}{m} } x[/tex]

[tex]v=\sqrt{\frac{0.5}{0.022} } 0.07[/tex]

v = 0.333 m/s

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Answer: The correct option is B (The Young's modulus of women's ACLS is typically smaller than that of men's, resulting in more stress for the same amount of strain)

Explanation:

Anterior cruciate ligament (ACL) is one of the important ligaments found at the knee joint which helps to stabilise the joint. It connects the femur to the tibia bone at the knee joint.

Anterior cruciate ligament tear is one of the common knee joint injury which is seen in individuals( especially females) involved in sports( example soccer and basketball which involves sudden change in direction causing the knee to rotate inwards)

ACL tear occurs through both contact and non contact mechanisms. The contact mechanism of ACL injury occurs when force is directly applied at the lateral part of the knee while in non contact mechanism,tear occurs when the tibia is externally rotated on the planted foot.

Research has proven that women are prone to have ACL tear than men when competing in similar sports. This disparity exists due to structural differences that pose as risk factors. These includes

- the female ACL size is smaller than the male.

- the ACL of female has a lower modulus if elasticity( that is, less stiff) than in males leading to greater joint mobility than in the male.. therefore the option, (The Young's modulus of women's ACLS is typically smaller than that of men's, resulting in more stress for the same amount of strain) is correct.

Answer:

a) Current in wire 1 = 0.132 A

Current in wire 2 = 0.101 A

b) Resistance of wire 1 = R₁ = 0.000376 Ω = (3.76 × 10⁻⁴) Ω = 0.376 mΩ

Resistance of wire 2 = R₂ = 0.000495 Ω = (4.95 × 10⁻⁴) Ω = 0.495 mΩ

Explanation:

Current density, J = (current) × (cross sectional area)

Current density for both wires = J = 2950 A/m²

For wire 1,

Cross sectional Area = πr² = π(0.00378²)

A₁ = 0.00004491 m²

For wire 2,

With the assumption that the strands are well banded together with no spaces in btw.

Cross sectional Area = 19 × πr² = π(0.000756)²

A₂ = 0.00003413 m²

Current in wire 1 = I₁ = J × A₁ = 2950 × 0.00004491 = 0.132 A

Current in wire 2 = I₂ = J × A₂ = 2950 × 0.00003413 = 0.101 A

b) Resistance = ρL/A

ρ = resistivity for both wires = (1.69 x 10⁻⁸) Ω.m

L = length of wire = 1.00 m for each of the two wires

A₁ = 0.00004491 m²

A₂ = 0.00003413 m²

R₁ = ρL/A₁ = (1.69 x 10⁻⁸ × 1)/0.00004491

R₁ = 0.000376 Ω = (3.76 × 10⁻⁴) Ω = 0.376 mΩ

R₂ = ρL/A₂ = (1.69 x 10⁻⁸ × 1)/0.00003413

R₂ = 0.000495 Ω = (4.95 × 10⁻⁴) Ω = 0.495 mΩ

Hope this helps!!

Answer:

[tex]k=13\ m[/tex]

Explanation:

Given:

From the given information by the laws of reflection we can deduce the distance of the first reflection of the back of the head of person in the rear mirror.

Distance of the first reflection of the back of the head in the rear mirror from the object head:

[tex]y'=2\times y[/tex]

[tex]y'=7\ m[/tex] is the distance of the image from the object back head.

Now the total distance of this image from the front mirror:

[tex]z=y'+x[/tex]

[tex]z=7+3[/tex]

[tex]z=10\ m[/tex]

So, the total distance of the image of the back of the head in the front mirror from the person will be:

[tex]k=x+z[/tex]

[tex]k=3+10[/tex]

[tex]k=13\ m[/tex]

Final answer:

The back of the head appears to be 16.00 meters away due to multiple reflections between two parallel mirrors 6.50 meters apart, when your head is positioned 3.00 meters from the nearer mirror.

Explanation:

The question revolves around a flat mirror problem in physics where multiple reflections between two parallel mirrors are considered. When a person looks into a flat mirror, the image of any object (like the back of the head) appears to be the same distance behind the mirror as the object is in front of it. So if your head is 3.00 meters away from the nearer mirror, the first image of the back of your head will appear 3.00 meters behind that mirror.

However, since there are two mirrors, this first image will then act as an object for the second, farther mirror, creating a new image. The additional distance to this second image will be twice the distance between the two mirrors. So, the total apparent distance will be the distance to the first image plus 6.50 meters times 2, which is 16.00 meters (3.00+6.50+6.50 = 16.00 meters). Therefore, the back of your head appears to be 16.00 meters away.

Answer:

V= 3.55 V

Explanation:

         [tex]V_{rint} = I* r_{int}[/tex]

        [tex]V = V_{b} - V_{rint} = 6.00 V - 0.207A* r_{int}[/tex]

        [tex]r_{int} = \frac{V_{b} - V}{I} = \frac{6.00 V - 5.03V}{0.207A} = 4.7 \Omega[/tex]

         [tex]V = V_{b} - V_{rint} = 6.00 V - 0.523A* 4.7 \Omega = 3.55 V[/tex]

Answer:

[tex]v=12.65\ m.s^{-1}[/tex]

Explanation:

Given:

During the turn to prevent the skidding of the vehicle its centripetal force must be equal to the opposite balancing frictional force:

[tex]m.\frac{v^2}{r} =\mu.N[/tex]

where:

[tex]\mu=[/tex] coefficient of friction

[tex]N=[/tex] normal reaction force due to weight of the car

[tex]v=[/tex] velocity of the car

[tex]1350\times \frac{v^2}{71} =0.23\times (1350\times 9.8)[/tex]

[tex]v=12.65\ m.s^{-1}[/tex] is the maximum velocity at which the vehicle can turn without skidding.

Final answer:

The maximum speed at which a car can safely make a turn on a flat road, given the mass of the car, the turn's radius of curvature, and the coefficient of friction, is approximately 25 m/s. This calculation demonstrates that the car's load does not influence its ability to negotiate the turn safely on a flat surface.

Explanation:

The student is asking how to calculate the maximum speed at which a car can safely make a turn on a flat road, given the car's mass, the turn's radius of curvature, and the coefficient of friction between the tires and the road. First, let's denote the mass of the car as m, gravitational acceleration as g, the radius of curvature as R, and the coefficient of friction as μ. To find the maximum speed v, we use the fact that the centripetal force needed to make the turn must be less than or equal to the maximum static friction force, which is μmg. This gives the condition mv²/R ≤ μmg. Solving for v, we find v = √(μgR).

By plugging in the numbers: m = 1350 kg, R = 71 m, g = 9.8 m/s², and μ = 0.23, we get v = √(0.23 * 9.8 * 71) which calculates to be approximately 25 m/s. Note, because coefficients of friction are approximate, the answer is given to only two digits.

This result is quite significant as it shows that the maximum safe speed is independent of the car's mass due to the proportional relationship between friction and normal force, which in turn is proportional to mass. This implies that how heavily loaded the car is does not affect its ability to negotiate the turn, assuming a flat surface.

Since there is a meeting of the cables at their midpoints, it is therefore understood that the force on them is the same but in the opposite direction, this to maintain the static balance between the two.

This can also be corroborated by applying the right hand rule for the force, at which depends of the magnetic field. The net force is zero because the cable segment to the left of the vertical cable feels an opposite force in the direction of the cable segment to the right.

Then the forces cancel.

Therefore the correct answer is C. Therefore the net force on each wire is zero

Answer:

[tex]v=177.95m/s[/tex]

Explanation:

First, determine circle's radius  between Earth's pole and the location. This can be calculated as:

[tex]r=R_e_a_r_t_hCos(90\frac{3}{4})\\R_e_a_r_t_h=6.37\times10^6m\\r=6.37\times10^6\times Cos67.5\textdegree\\r=2,437,693.46m\\[/tex]

The angular speed of earth is constant and is :

[tex]w=\frac{2\pi}{T}=\frac{2\pi}{24\times 3600}\\=7.3\times10^{-5}rad/s[/tex]

Velocity is:

[tex]v=wr\\=7.3\times10^{-5}\times 2,437,693.46\\v=177.95m/s[/tex]

Answer:

8.46 N/C

Explanation:

Using Gauss law

[tex]E=\frac {kQ}{r^{2}}[/tex]

Gauss's Law states that the electric flux through a surface is proportional to the net charge in the surface, and that the electric field E of a point charge Q at a distance r from the charge

Here, K is Coulomb's constant whose value is [tex]9\times 10^{9} Nm^{2}/C^{2}[/tex]

r = 0.43 + 0.106 = 0.536 m

[tex]E=\frac {9\times 10^{9}\times 0.270\times 10^{-9}}{0.536^{2}}=8.4581755402094007\approx 8.46 N/C[/tex]

The magnitude of the electric field at a point 0.106 m outside a solid metal sphere with a radius of 0.430 m and a net charge of 0.270 nC is approximately 892 N/C, to three significant figures.

The subject of your question is Physics, specifically focussing on electrostatics and the calculation of the electric field outside a charged sphere. The formula for the electric field (E) due to a point charge is given by Coulomb's Law, which is E = kQ/r^2, where 'Q' is the charge, 'r' is the distance from the charge, and 'k' is Coulomb's constant, approximately 8.99 x 10^9 N.m^2/C^2. Since the electric field due to a uniformly distributed spherical charge behaves as if all the charge is concentrated at the center, you can use this formula for the magnitude of the electric field outside the sphere.

Substituting the provided values (converted to appropriate units), we find E = (8.99 x 10^9 N.m^2/C^2 x 0.270 x 10^-9 C)/(0.536 m)^2, which gives E approximately equal to 892 N/C to three significant figures.

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Answer:

The direction of the electric field vector is horizontal and pointing north.

Option (C) is correct option.

Explanation:

Given :

The direction of wave propagation is toward the west.

The direction of magnetic field vector is vertically upward.

According to the theory of electromagnetic wave propagation, the electric field and magnetic field is perpendicular to each other and the direction of propagation is also perpendicular to both electric and magnetic field vector.

⇒   [tex]\vec{E} + \vec{B} = \vec {k}[/tex]

From right hand rule, the fingers goes towards horizontal and pointing north and curl the finger goes towards  vertically upward and thumb will give you the direction of wave propagation toward west.

Hence, the direction of electric field vector is horizontal and pointing north.

The correct direction of the electric field vector in an electromagnetic wave propagating to the west with an upward magnetic field is horizontal and pointing north, following the right-hand rule for perpendicularity and direction of electromagnetic waves.

The subject of this question is the direction of the electric field vector in an electromagnetic wave that is propagating towards the west, with a magnetic field vector that points vertically upward. According to the properties of electromagnetic waves, the electric field (E) and magnetic field (B) are perpendicular to each other and to the direction of wave propagation. Therefore, if the magnetic field is pointing upward and the wave is moving west, the electric field must be pointing horizontally. Since the right-hand rule dictates that E x B gives the direction of wave propagation, and the wave is moving west, the electric field cannot be pointing east or west as it would not satisfy the right-hand rule. Thus, the electric field is either pointing north or south. To determine the correct direction between north and south, we rely on the right-hand rule: the fingers of the right hand point in the direction of E, the curled fingers point towards B, and the thumb points in the direction of the wave propagation (west in this case). If the magnetic field points up, and propagation is to the west, the electric field must be directed to the north. Therefore, the correct answer is C. horizontal and pointing north.

Answer:

Analyte⇒ one of analgesics

stationery phase⇒ silica

mobile phase⇒ solvent

Explanation:

during the thin layer chromatography non volatile mixtures are separated.The technique is performed on the plastic or aluminum foil that is coated with a thin layer.

Answer:

a) 201

b) 0

Explanation:

note:

solution is attached in word form due to error in mathematical equation. furthermore i also attach Screenshot of solution in word due to different version of MS Office please find the attachment

For the time interval from 0 to 2, sine wave reaches to zero for 201 times. Hence the current equals to zero for 201 times.

No charge transported through the light in the first second.

Given that, the current flowing through the bulb is [tex]I(t)=114 sin (100\pi t) \;\rm A[/tex].

The general equation of the current is,

[tex]I(t) =Asin(2\pi ft)[/tex]

So the frequency can be calculated as,

[tex]2\times \pi\times f\times t = 100\times \pi[/tex]

[tex]f =50 \;\rm Hz[/tex]

Hence the frequency of the sine wave is 50 Hz.

For the time interval from 0 to 2, the number of zero for the sine wave is,

[tex]No.\;of\; zero = (2\times50\times2 )+1[/tex]

[tex]No.\;of\;zero=201[/tex]

So, For the time interval from 0 to 2, sine wave reaches to zero for 201 times. Hence the current equals to zero for 201 times.

The charge can be calculated  by the formula given below.

[tex]Q(t) = \int\limits^{t_1}_{t_2} {I(t)} \ dt[/tex]

[tex]Q(t)=\int\limits^1_0 {114sin(100\pi t)} \ dt[/tex]

[tex]Q(t) = \dfrac {-114cos(100\pi t)}{100\pi}[/tex]

[tex]Q(t) = \dfrac {-114cos(100\pi \times 1)}{100\pi}-\dfrac {-114cos(100\pi \times0)}{100\pi}[/tex]

[tex]Q(t)=0[/tex]

Hence, no charge transported through the light in the first second.

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Answer:

[tex]9.198\times 10^6 m/s[/tex]

Explanation:

We are given that

Magnetic field, B=1.2 T

Radius of circular path, r=0.080 m

[tex]q_p=1.6\times 10^{-19} C[/tex]

[tex]m_p=1.67\times 10^{-27} kg[/tex]

[tex]\theta=90^{\circ}[/tex]

We have to find the speed of proton.

We know that

Magnetic force, F=[tex]qvBsin\theta[/tex]

According to question

Magnetic force=Centripetal force

[tex]q_pvBsin90^{\circ}=\frac{m_pv^2}{r}[/tex]

[tex]1.6\times 10^{-19}\times 1.2=\frac{1.67\times 10^{-27}v}{0.08}[/tex]

[tex]v=\frac{1.6\times 10^{-19}\times 1.2\times 0.08}{1.67\times 10^{-27}}[/tex]

[tex]v=9.198\times 10^6 m/s[/tex]

Answer:

ΔS = - 3.74 × 10⁻²³ J/K = - 3.7 × 10⁻²³ to 2 s.f

Explanation:

The change in entropy for a system with changing allowable Microsystems is given as

ΔS = K In (W/W₀)

K = Boltzmann's constant = 1.381 × 10⁻²³ J/K

W₀ = initial number of microstates

To calculate this, how many ways can 2 atoms occupy 16 available microstates with order important?

That is, ¹⁶P₂ = 16!/(16 - 2)! = 16 × 15 = 240 microstates.

W = the number of microstates for Chlorine atom when Bromine atom desorps = 16 microstates.

ΔS = K In (W/W₀)

ΔS = (1.381 × 10⁻²³) In (16/240)

ΔS = (1.381 × 10⁻²³) × 2.7081

ΔS = - 3.74 × 10⁻²³ J/K

Entropy change is positive when an atom desorbs from a surface and drifts away, allowing for more freedom of movement and increasing the system's entropy.

Entropy change is a measure of disorder in a system. When an atom desorbs from a surface and drifts away, the change in entropy is positive as it increases the freedom of movement of the atom. This occurs because there are more possible locations for the atom to occupy, leading to an increase in entropy.

Explanation:

Below is an attachment containing the solution .

Answer:

a) 2 m/s

b) i) [tex]K.E = 50 (1.5t^2 + 2) ^2\\[/tex]

ii) [tex]F = 3tm[/tex]

Explanation:

The function for distance is [tex]x = 0.5t ^3 + 2t[/tex]

We know that:

Velocity = [tex]v= \frac{d}{dt} x[/tex]

Acceleration = [tex]a= \frac{d}{dt}v[/tex]

To find speed at time t = 0, we derivate the distance function:

[tex]x = 0.5 t^3 + 2t\\v= x' = 1.5t^2 + 2[/tex]

Substitute t = 0 in velocity function:

[tex]v = 1.5t^2 + 2\\v(0) = 1.5 (0) + 2\\v(0) = 2[/tex]

Velocity at t = 0 will be 2 m/s.

To find the function for Kinetic Energy of the box at any time, t.

[tex]Kinetic \ Energy = \frac{1}{2} mv^2\\\\K.E = \frac{1}{2} \times 100 \times (1.5t^2 + 2) ^2\\\\K.E = 50 (1.5t^2 + 2) ^2\\[/tex]

We know that [tex]Force = mass \times acceleration[/tex]

[tex]a = v'(t) = 1.5t^2 + 2\\a = 3t[/tex]

[tex]F = m \times a\\F= m \times 3t\\F = 3tm[/tex]

The speed of the box at time t=0 is 0 m/s. The acceleration, displacement, and velocity functions of the box as a function of time are a(t) = 3t, x(t) = .5t^3 + 2t and v(t) = 1.5t^2 + 2 respectively.

For part (a), the speed of the box at time t=0 can be found by taking the derivative of the position function x(t), which gives us the velocity function v(t). Therefore, v(t) = 1.5t^2 + 2 and v(0) = 0. Thus, the speed of the box at t=0 is 0 m/s.

For part (b), the box's acceleration at any time t can be found by taking the derivative of the velocity function v(t), which gives us the acceleration function a(t). Therefore, a(t) = 3t, the displacement function as a function of time is the original function x(t) = .5t^3 + 2t and the velocity function is as mentioned above, v(t) = 1.5t^2 + 2.

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Answer:

Atomic Size and Mass:

convert given density to kg/m^3 = 8900kg/m^3 2) convert to moles/m^3 (kg/m^3 * mol/kg) = 150847 mol/m^3 (not rounding in my actual calculations) 3) convert to atoms/m^3 (6.022^23 atoms/mol) = 9.084e28 atoms/m^3 4) take the cube root to get the number of atoms per meter, = 4495309334 atoms/m 5) take the reciprocal to get the diameter of an atom, = 2.2245e-10 m/atom 6) find the mass of one atom (kg/mol * mol/atoms) = 9.7974e-26 kg/atom Young's Modulus: Y=(F/A)/(dL/L) 1) F=mg = (45kg)(9.8N/kg) = 441 N 2) A = (0.0018m)^2 = 3.5344e-6 m^2 3) dL = 0.0016m 4) L = 2.44m 5) Y = 1.834e11 N/m^2 Interatomic Spring Stiffness: Ks,i = dY 1) From above, diameter of one atom = 2.2245e-10 m 2) From above, Y = 1.834e11 N/m^2 3) Ks,i = 40.799 N/m (not rounding in my actual calculations) Speed of Sound: v = ωd 1) ω = √(Ks,i / m,a) 2) From above, Ks,i = 40.799 N/m 3) From above, m,a = 9.7974e-26 kg 4) ω=2.0406e13 N/m*kg 5) From above, d=2.2245e-10 m 6) v=ωd = 4539 m/s (not rounding in actual calculations) Time Elapsed: 1) length sound traveled = L+dL = 2.44166 m 2) From above, speed of sound = 4539 m/s 3) T = (L+dL)/v = 0.000537505 s

Answer: 5cm

Explanation: Since the radius of curvature is 10cm, the focal length of the mirror (f) is

f = r/2

Where r is the radius of curvature.

Since r = 10cm, f = 10/2 = 5cm.

To produce a parallel light rays of a flash light, it means the the image will be at infinity this making the image distance to be infinite.

From the mirror formulae

1/u + 1/v = 1/f

Where u = object distance =?, v = image distance = infinity and f = focal length = 5cm.

Let us substitute the parameters, we have that

1/u + 1/∞ = 1/5

1/∞ = 0

Hence 1/u = 1/5

u = 5cm.

Hence the object needs to be placed nearly 5cm to the mirror

Final answer:

The light bulb should be placed at the focal length of the concave mirror, which is 5 cm, to produce near-parallel light rays in a flashlight.

Explanation:

The distance between the light bulb and a concave mirror to produce a beam of near-parallel light rays in a flashlight is most nearly the focal length of the mirror. Since the mirror's radius of curvature (R) is 10 cm, using the formula R = 2f, we can calculate the focal length (f). Dividing the radius of curvature by 2, we get f = R/2 = 10 cm / 2 = 5 cm. Therefore, the light bulb should be placed approximately 5 cm from the mirror to achieve near-parallel rays.

Answer:

See the answers and the explanation below.

Explanation:

To solve this problem we must make a free body diagram with the forces applied as well as the direction. In the attached images we can see the nomenclature of the direction of the forces and the free body diagram.

a)

Sum of forces in y-axis

Fy = 140 - (220*sin(10))

Fy = 101.8 [N]

Sum of forces in x-axis

Fx = - (220*cos(10))

Fx = - 216.65 [N]

b)

For the above result, for there to be balance we realize that we need one equal to the resulting y-axis but in the opposite direction and another opposite force in direction but equal in magnitude on the x-axis.

Fy = - 101.8 [N]

Fx =   216.65 [N]

c )

Now we need to use the Pythagorean theorem to find the result of these forces.

[tex]F = \sqrt{(101.8)^{2} +(216.65)^{2} } \\F=239.4[N][/tex]

And the direction will be as follows.

α = tan^(-1) (101.8 / 216.65)

α = 25.16° (south to the east)

F = 216.65 i - 101.8 j [N]

Explanation:

According to the law of conservation of energy, work done by the force is as follows.

        [tex]W_{F} = F Cos (30^{o}) \times 1.5[/tex]

                   = 64.95 J

Now, gain in potential energy is as follows.

                P.E = mgh

                      = [tex]2 \times 9.8 \times 1.5[/tex]

                      = 29.4 J

Gain in potential energy will be as follows.

           = [tex]\frac{1}{2}kx^{2}_{2} - \frac{1}{2}kx^{2}_{1}[/tex]

           = [tex]\frac{1}{2} \times 30 N/m \times [(2.5 - 1.5)^{2} - (2 - 1.5)^{2}][/tex]

           = 11.25

As,

          [tex]W_{f} = u_{1} + u_{2} + \frac{1}{2}mv^{2}[/tex]

          [tex]\frac{1}{2}mv^{2} = W_{f} - u_{1} - u_{2}[/tex]  

                   = 64.95 J - 29.4 - 11.25

                   = 24.3

              [tex]v^{2} = \frac{24.3 \times 2}{2}[/tex]

                  v = 4.92 m/s

Therefore, we can conclude that relative velocity at point B is 4.92 m/s.  

To calculate the velocity of the collar as it passes position B, we need to consider the forces acting on the collar and use Newton's second law of motion. The collar is attached to a light spring, so the force exerted by the spring can be calculated using Hooke's law. The net force acting on the collar is the sum of the force exerted by the spring and the constant 50-N force.

To calculate the velocity of the collar as it passes position B, we need to consider the forces acting on the collar and use Newton's second law of motion. The collar is attached to a light spring, so the force exerted by the spring can be calculated using Hooke's law. The net force acting on the collar is the sum of the force exerted by the spring and the constant 50-N force. We can equate this net force to the mass of the collar times its acceleration. Solving for the acceleration gives us the magnitude of the velocity as it passes position B.

Using Hooke's law, the force exerted by the spring can be calculated as:

F = k * x

where F is the force, k is the stiffness of the spring, and x is the displacement of the collar from its equilibrium position. Since the collar is attached to a light spring, we can assume that the displacement of the spring is negligible. Therefore, the force exerted by the spring is zero.

The net force is then equal to the constant 50-N force:

Net force = 50 N

Applying Newton's second law, we have:

Net force = mass * acceleration

Solving for acceleration gives us:

Acceleration = Net force / mass = 50 N / 2 kg = 25 m/s^2

Since velocity is the derivative of displacement, we can integrate the acceleration with respect to time to find the velocity:

v = a * t

where v is the velocity, a is the acceleration, and t is the time.

Since the collar is released from rest at position A, the time taken to reach position B can be determined using the equation of motion:

s = u*t + (1/2)*a*t^2

where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.

Since the collar starts from rest, the initial velocity is zero. Solving for t gives us:

t = sqrt((2*s) / a) = sqrt((2*1.5 m) / 25 m/s^2) = 0.7746 s

Finally, substituting the values of acceleration and time into the equation for velocity gives us:

v = a * t = 25 m/s^2 * 0.7746 s = 19.365 m/s

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Complete Question:

A volley ball is hit directly toward the ceiling in a gymnasium with a ceiling height of 10 m. If the initial vertical velocity is 13 m/s and the release height is 1.8 m will the ball hit the ceiling?

Answer:

The ball will hit the ceiling

Explanation:

Given;

Initial vertical Velocity U = 13 m/s

Height of the ceiling = 10 m

Released height of the volley ball = 1.8 m

Height traveled by the volley ball, is calculated as follows;

[tex]V^2 =U^2 -2gH[/tex]

where;

V is final vertical velocity

[tex]2gH =U^2\\\\H = \frac{U^2}{2g} = \frac{(13)^2}{2(9.8)} = 8.62 m[/tex]

Remember this ball was released from 1.8 m height and it traveled 8.62 m.

Total distance traveled = 1.8 + 8.62 = 10.42 m

Therefore, the ball will hit the ceiling

Answer:

The distance is 709.5 m.

Explanation:

Given that,

Speed = 150 m/s

Distance = 110 m

Suppose, How far short of the target should it drop the package?

We need to calculate the time

Using equation of motion

[tex]s=ut+\dfrac{1}{2}gt^2[/tex]

[tex]t^2=\dfrac{2s}{g}[/tex]

Where, g = acceleration due to gravity

t = time

Put the value into the formula

[tex]t=\sqrt{\dfrac{2\times110}{9.8}}[/tex]

[tex]t=4.73\ sec[/tex]

We need to calculate the distance

Using formula of distance

[tex]d= vt[/tex]

Put the value into the formula

[tex]d=150\times4.73[/tex]

[tex]d=709.5\ m[/tex]

Hence, The distance is 709.5 m.

Answer:

(1)

The velocity of the center of mas of the system is= 0.801 m/s

(2)

Initial velocity of car 1 in the center of mass reference frame is =4.099 m/s

(3)

The final velocity of car 1 in the center of mass reference frame is

 - 4.099 m/s

(4)

The final velocity of car 1 in the ground (original ) reference frame is = -3.298 m/s

(5)

The final velocity of car 2 in the ground (original) reference frame is = 7.166  m/s

Explanation:

Given

m₁ = 109 kg

v₁= 4.9 m/s

m₂= 83 kg

v₂= -3.6 m/s

The two cars have an elastic collision.

(1)

The velocity of the center of mas of the system is

[tex]V_{cm}=\frac{m_1v_1+m_2v_2}{m_1+m_2}[/tex]

       [tex]= \frac{109.4.9+83(-3.4)}{109+83}[/tex] m/s

      = 0.801 m/s

(2)

Initial velocity of car 1 in the center of mass reference frame is

[tex]V_{1,i}[/tex] = initial velocity - [tex]V_{cm}[/tex]

    = (4.9 - 0.801) m/s

    =4.099 m/s

(3)

Since the collision is elastic, the car 1 will bounce of opposite direction.

The final velocity of car 1 in the center of mass reference frame is

 [tex]V_{1,f}[/tex] = - 4.099 m/s

(4)

The final velocity of car 1 in the ground (original ) reference frame

[tex]V'_{1,f}[/tex]  =  [tex]V_{cm}+V_{1,f}[/tex]

      =(0.801- 4.099) m/s

      = - 3.298 m/s

(5)

The momentum is conserved,

[tex]m_1v_1+m_2v_2=m_1v'_1+m_2v'_2[/tex]

[tex]\Rightarrow v'_2=\frac{m_1}{m_2}(v_1-v'_1) +v_2[/tex]  

Here [tex]v'_1= V'_{1,f}[/tex] =  - 3.298 m/s

[tex]\Rightarrow v'_2=\frac{109}{83}[4.9-(-3.298)]+(-3.6)[/tex]

      =7.166 m/s

The final velocity of car 2 in the ground (original) reference frame is = 7.166  m/s

Final answer:

The velocity of the center of mass of the bumper car system is 1.225 m/s. Car 1 has an initial velocity of 3.675 m/s in the center-of-mass reference frame. After the elastic collision, car 1's final velocity is -2.45 m/s, and car 2's final velocity is 4.825 m/s in the ground reference frame.

Explanation:

Velocity of the Center of Mass, Velocities in Reference Frames, and Final Velocities After an Elastic Collision

The velocity of the center of mass (V cm) of a system in one dimension is given by the formula:

V cm = (m1 * v1 + m2 * v2) / (m1 + m2)

In this case, we have m1 = 109 kg moving at v1 = 4.9 m/s and m2 = 83 kg moving at v2 = -3.6 m/s. The velocity of the center of mass is therefore:

V cm = (109 kg * 4.9 m/s + 83 kg * (-3.6 m/s)) / (109 kg + 83 kg)

Calculating this we get:

V cm = (534.1 kg*m/s - 298.8 kg*m/s) / 192 kg = 235.3 kg*m/s / 192 kg = 1.225 m/s (rounded to three significant figures)

The initial velocity of car 1 in the center-of-mass reference frame is given by:

u1 = v1 - V cm

Substituting the known values:

u1 = 4.9 m/s - 1.225 m/s = 3.675 m/s

In an elastic collision, velocities in the center-of-mass reference frame are mirrored. Thus, the final velocity of car 1 in the center-of-mass reference frame remains the same but in the opposite direction:

u1' = -u1 = -3.675 m/s

To find the final velocity of car 1 in the ground reference frame, we add the velocity of the center of mass:

v1' = u1' + V cm = -3.675 m/s + 1.225 m/s = -2.45 m/s

For car 2, the same principle applies. The final velocity in the center-of-mass reference frame will be the opposite of the initial, and thus:

v2' = -v2 + V cm = 3.6 m/s + 1.225 m/s = 4.825 m/s

Answer:

The scale reading at the top = 565.8N

The scale reading at the bottom = 610.44N

Explanation:

We are given:

t = 32seconds

R = 9.7meters

mass (m) = 60Kg

We take g as gravitational field = 9.8

Therefore, to find the scale reading (N) at the top, let's use the formula:

[tex] N_t = m (g - w^2 R) [/tex]

Where w = 2π/t

w = 2π/32 = 0.197

Substituting the figures into the equation, we have

[tex] N = 60 (9.8 - 0.197^2 * 9.7) [/tex]

N = 60 (9.8 - 0.37)

N = 60 * 9.43

Na = 565.8N

To find scalar reading at the bottom, we use;

[tex] N_b = m(g + w^2 R) [/tex]

= 60 (9.8 + 0.37)

= 60 * 10.17

[tex] N_b = 610.44 [/tex]

Answer:

The scale reading at the top is [tex]z_{top} = 565.6\mu N[/tex]

The scale reading at the bottom is [tex]z_{bottom} = 610.356\ N[/tex]

Explanation:

From the question

       The radius is [tex]r = 9.7 m[/tex]

       The period is [tex]T = 32sec[/tex]

      The mass is [tex]m =60kg[/tex]

Generally the mathematical representation for angular velocity of the wheel is

                  [tex]\omega = \frac{2 \pi}{T}[/tex]

                    [tex]= \frac{2*3.142}{32}[/tex]

                    [tex]= 0.196 \ rad/sec[/tex]

The velocity at which the point scale move can be obtained as

                     [tex]v = r\omega[/tex]

                        [tex]= 9.7* 0.196[/tex]

                       [tex]= 1.9 m/s[/tex]

Considering the motion of the 60kg mass as shown on the first and second uploaded image

Let the z represent the reading on the scale which is equivalent to the normal force acting on the mass.

          Now at the topmost the reading of the scale would be

                       [tex]mg - z_{top} =\frac{mv^2}{r} =m\omega^2r[/tex]

Where mg is the gravitational force acting on the mass and [tex]\frac{mv^2}{r}[/tex] is the centripetal force keeping the mass from spiraling out of the circle

Now making z the subject of the formula

                    [tex]z_{top} = mg - \frac{mv^2}{r}[/tex]

                       [tex]= m(g- \frac{v^2}{r})[/tex]

                       [tex]= 60(9.8 - \frac{1.9^2}{9.7} )[/tex]

                      [tex]= 565.6\mu N[/tex]

Now at the bottom the scale would be

                      [tex]z_{bottom}-mg = \frac{mv^2}{r} = m \omega^2r[/tex]

This is because in order for the net force to be in the positive y-axis (i.e for the mass to keep moving in the Ferris wheel) the Normal force must be greater than the gravitational force.  

Making  z the subject

                  [tex]z_{bottom}= mg +m\omega^2r[/tex]

                  [tex]z =m(g+\omega^2r)[/tex]

                  [tex]z= 60(9.8 + (0.196)^2 *(9.7))[/tex]

                     [tex]= 610.356\ N[/tex]

4.45 * 10¹⁴ J is transferred to get this mass of aluminum from 20°C to its melting point, 660⁰C.

The quantity of heat required to change the temperature of a substance is given by:

Q = mcΔT

Where Q is the heat, m is the mass of the substance, ΔT is the temperature change = final temperature - initial temperature. c is the specific heat capacity

m = 1.7 billion pounds = 77 * 10⁷ kg, ΔT = 660 - 20 = 640°C, c = 903 J/kg•K

Hence:

Q = 77 * 10⁷ kg *  903 J/kg•K * 640°C

Q = 4.45 * 10¹⁴ J

4.45 * 10¹⁴ J is transferred to get this mass of aluminum from 20°C to its melting point, 660⁰C.

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The energy required to heat 1.7 billion pounds of aluminum from 20 degrees Celsius to 660 degrees Celsius is approximately 4.398 × 10^17 Joules.

The thermal energy transferred, or heat, to raise the temperature of a substance is given by the formula q=mcΔT where 'm' is the mass, 'c' is the specific heat capacity, and 'ΔT' is the change in temperature. For aluminum, the specific heat capacity is 0.897 Joules per gram per degree Celsius (J/g°C).

First, we need to convert 1.7 billion pounds of aluminum into grams since the specific heat value is in grams. There are about 453,592.37 grams in a pound, so this gives us about 7.711 × 10^14 grams of aluminum.

The change in temperature (ΔT) is the final temperature minus the initial temperature, or 660 degrees Celsius - 20 degrees Celsius, which equals 640 degrees Celsius.

So, to find the total energy required, we use the formula and substitute the known values: q=(7.711 × 10^14 g)*(0.897 J/g°C)*(640°C), which equals approximately 4.398 × 10^17 Joules.

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Answer:

[tex]c. 5cm \times 8cm[/tex]

Explanation:

The dimensions [tex]5cm\times 8cm[/tex] have the highest cross-sectional area combination of [tex]40cm^2[/tex].

-Resistance reduces with an increase in cross sectional area.

-[tex]Reason-[/tex]Electrons have alarger area to flow through.

Answer:

Please find attached file for complete answer solution and explanation of same question.

Explanation:

Answer:

B = (4.76 × 10⁻⁷) T

Explanation:

From Biot Savart's law, the magnetic field formula is given as

B = (μ₀I)/(2πr)

B = magnetic field = ?

I = current = 238 mA = 0.238 A

μ₀ = magnetic constant = (4π × 10⁻⁷) H/m

r = 10 cm = 0.1 m

B = [4π × 10⁻⁷ × 0.238)/(2π×0.1)]

B = (4.76 × 10⁻⁷) T

The direction of the magnetic field is in the clockwise direction wrapped around the current-carrying wire.

Hope this Helps!!!