At sea level, at a latitude where , a pendulum that takes 2.00 s for a complete swing back and forth has a length of 0.993 m. What is the value of g in m/s2 at a location where the length of such a pendulum is 0.970 m

Answer:

a) 3.7 x 10^-3 s

b) 230.41 rad/s

Explanation:

The angular speed N = 2200 rpm (revolution per minute)

==> 2200/60 revolutions per sec = 36.67 rps

The total angle turned in one second = 36.67 x 360° = 13201.2°

if it takes 1 sec to revolve 13201.2°

then it will take t sec to rotate 49.0°

time t = 49/13201.2 = 3.7 x 10^-3 s

conversion to rad/s = 2πN/60 = (2 x 3.142 x 2200)/60 = 230.41 rad/s

Answer:

a) 8.33 x 10^-6 Pa

b) 8.23 x 10^-11 atm

c) 1.67 x 10^-5 Pa

d) 1.65 x 10^-10 atm

Explanation:

Intensity of the light [tex]I[/tex] = 2500 W/m^2

speed of light [tex]c[/tex] = 3 x 10^8 m/s

a) we know that the pressure for for a totally absorbing surface is given as

[tex]P_{abs}[/tex] = [tex]I/c[/tex] = 2500/(3 x 10^8) = 8.33 x 10^-6 Pa

b) 1 atm = 101325 Pa

[tex]P_{abs}[/tex] = (8.33 x 10^-6)/101325 = 8.23 x 10^-11 atm

c) for a totally reflecting surface

[tex]P_{ref}[/tex] = [tex]2I/c[/tex] = twice the value for totally absorbing

[tex]P_{ref}[/tex]  = 2 x 8.33 x 10^-6 = 1.67 x 10^-5 Pa

d)  1 atm = 101325 Pa

[tex]P_{ref}[/tex] = 2 x 8.23 x 10^-11  = 1.65 x 10^-10 atm

Answer:

56°

Explanation:

Brewsters angle can be simply derived from

n1sin theta1= n2sintheta2= n2costheta1

because the reflected light will be 100% polarized if it is reflected at an angle 90o to the refracted light. Hence, Brewsters angle is

Tan theta= n2/n1

1.66/1.11= 1.495

Theta = 56°

Explanation:

Answer:

entropy

Explanation:

Answer:

The magnitude of the magnetic field at the center of the loop is 3.846 x 10⁻⁵ T.

Explanation:

Given;

number of turns of the flat circular loop, N = 18 turns

radius of the loop, R = 15.0 cm = 0.15 m

current through the wire, I = 0.51 A

The magnetic field through the center of the loop is given by;

[tex]B = \frac{N\mu_o I}{2R}[/tex]

Where;

μ₀ is permeability of free space = 4π x 10⁻⁷ m/A

[tex]B = \frac{N\mu_o I}{2R} \\\\B = \frac{18*4\pi*10^{-7} *0.51}{2*0.15} \\\\B = 3.846 *10^{-5} \ T[/tex]

Therefore, the magnitude of the magnetic field at the center of the loop is 3.846 x 10⁻⁵ T.

Answer:

g' = g/9 = 1.09 m/s²

Explanation:

The magnitude of free fall acceleration at the surface of earth is given by the following formula:

g = GM/R²   ----- equation 1

where,

g = free fall acceleration

G = Universal Gravitational Constant

M = Mass of Earth

R = Distance between the center of earth and the object

So, in our case,

R = R + 2 R = 3 R

Therefore,

g' = GM/(3R)²

g' = (1/9) GM/R²

using equation 1:

g' = g/9

g' = (9.8 m/s)/9

g' = 1.09 m/s²

Answer:

Explanation:

Surface of earth,

[tex]g = \frac{GM}{R^2}\\\\g = 9.8m/s^2[/tex]

free fall acceleration at height h,

[tex]g_h = \frac{GM}{(R+h)^2}[/tex]

where

G = gravitational constant

R = Radius of earth

M = mass of earth

therefore,

[tex]\frac{g_h}{g} = \frac{\frac{GM}{(R+h)^2}}{\frac{GM}{R^2}}\\\\ \frac{g_h}{g} = \frac{R^2}{(R+h)^2}\\\\g_h = g\frac{R^2}{(R+h)^2}[/tex]

Where height h = 2R

[tex]g_h = 9.8\frac{R^2}{(R+2R)^2}\\\\g_h = 9.8\frac{R^2}{(3R)^2}\\\\g_h = 9.8\frac{R^2}{(9R^2}\\\\g_h = 1.09m/s^2[/tex]

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Answer:

11.2 Ω

Explanation:

The impedance of a circuit is given by;

Z= √R^2 +(XL-XC)^2

Since

Resistance R= 10 Ω

Inductive reactance XL= 12 Ω

Capacitive reactance XC= 7 Ω

Z= √10^2 + (12-7)^2

Z= √100 + 25

Z= √125

Z= 11.2 Ω

Answer:

81 N

7.1 m/s²

Explanation:

Draw a free body diagram of the sphere.  There are two forces:

Weight force mg pulling straight down,

and tension force T pulling up along the rope.

Sum of forces in the centripetal direction:

∑F = ma

T − mg sin 45° = m v² / r

T = m (g sin 45° + v² / r)

T = (7 kg) (10 m/s² sin 45° + (3 m/s)² / 2 m)

T = 81 N

Sum of forces in the tangential direction:

mg cos 45° = ma

a = g cos 45°

a = (10 m/s²) cos 45°

a = 7.1 m/s²

Answer:

The magnetic field produced by an electric current is always oriented perpendicular to the direction of the current flow. And.Direction of magnetic field is governed by the 'right hand thumb rule, The right hand rule states that: to determine the direction of the magnetic force on a positive moving charge, ƒ, point the thumb of the right hand in the direction of v, the fingers in the direction of B, and a perpendicular to the palm points in the direction of Force . Similar to the situation with electric field lines, the greater the number of lines (or the closer they are together) in an area the stronger the magnetic field.

Answer:

The induced current in the resistor is I = BLv/R

Explanation:

The induced emf ε in the long bar of length, L in a magnetic field of strength, B moving with a velocity, v is given by

ε = BLv.

Now, the current I in the resistor is given by

I = ε/R where ε = induced emf in circuit and R = resistance of resistor.

So, the current I = ε/R.

substituting the value of ε the induced emf, we have

I = ε/R

I = BLv/R

So, the induced current through the resistor is given by I = BLv/R

Answer:

79.7 days

Explanation:

Half-life equation:

A = A₀ (½)^(t / T)

where A is the final amount,

A₀ is the initial amount,

t is the amount of time,

and T is the half life.

If 90% decays, then 10% is left.

A = A₀ (½)^(t / T)

0.1 A₀ = A₀ (½)^(t / 24)

0.1 = ½^(t / 24)

ln(0.1) = (t / 24) ln(0.5)

t ≈ 79.7 days

Answer:

The time difference is 2.97 sec.

Explanation:

Given that,

Tension = 29 N

Mass per unit length [tex]\mu_{1}=19\ kg/m[/tex]

Mass per unit length [tex]\mu_{2}=45\ kg/m[/tex]

Length of first section = 2.5 m

Length of second section = 2.8 m

We need to total distance of first pulse

Using formula for distance

[tex]d=2.5+2.5[/tex]

[tex]d_{1}=5.0\ m[/tex]

We need to total distance of second pulse

Using formula for distance

[tex]d=2.8+2.8[/tex]

[tex]d_{2}=5.6\ m[/tex]

We need to calculate the speed of pulse in the first string

Using formula of speed

[tex]v_{1}=\sqrt{\dfrac{T}{\mu_{1}}}[/tex]

Put the value into the formula

[tex]v_{1}=\sqrt{\dfrac{29}{19}}[/tex]

[tex]v_{1}=1.24\ m/s[/tex]

We need to calculate the speed of pulse in the second string

Using formula of speed

[tex]v_{2}=\sqrt{\dfrac{T}}{\mu_{2}}}[/tex]

Put the value into the formula

[tex]v_{2}=\sqrt{\dfrac{29}{45}}[/tex]

[tex]v_{2}=0.80\ m/s[/tex]

We need to calculate the time for first pulse

Using formula of time

[tex]t_{1}=\dfrac{d_{1}}{v_{1}}[/tex]

Put the value into the formula

[tex]t_{1}=\dfrac{5.0}{1.24}[/tex]

[tex]t_{1}=4.03\ sec[/tex]

We need to calculate the time for second pulse

Using formula of time

[tex]t_{2}=\dfrac{d_{1}}{v_{1}}[/tex]

Put the value into the formula

[tex]t_{2}=\dfrac{5.6}{0.80}[/tex]

[tex]t_{2}=7\ sec[/tex]

We need to calculate the time difference

Using formula of time difference

[tex]\Delta t=t_{2}-t_{1}[/tex]

Put the value into the formula

[tex]\Delta t=7-4.03[/tex]

[tex]\Delta t=2.97\ sec[/tex]

Hence, The time difference is 2.97 sec.

Answer:

2.2 ft

Explanation:

0.65 lb / 1 ft = 1.4 lb / x

x ≈ 2.2 ft

Answer:

A simple arrangement by means of which e.m.f,s. are compared is known as?

(a)Voltmeter

(b)Potentiometer

(c)Ammeter

(d)None of the above

Explanation:

Answer:

 cost = $ 243.00

Explanation:

This exercise must assume that it uses a complete table for each piece, we can use a direct ratio of proportions, if 1 table is 0.20 m wide, how many tables will be 3.00 m

                 #_tables = 3 m (1 / 0.20 m)

                #_tables = 15 tables

Let's use another direct ratio, or rule of three, for cost. If a board costs $ 16.20, how much do 15 boards cost?

              Cost = 15 (16.20 / 1)

              cost = $ 243.00

Answer:

Φ = 36.84 × 10^(-20) J

Explanation:

In the photoelectric effect, the energy of the incoming photon is usually used in part to extract the photoelectron from the material (work function) and then the rest is converted into kinetic energy of the photoelectron which is given by the formula;

K_max = hf - Φ

where;

hf represents the energy of the incoming photon

h is the Planck's constant

f is the light frequency

Φ is the work function of the material

K_max is the maximum kinetic energy of the photoelectrons.

From the question, we are told that no current flows unless the wavelength is less than 540 nm. This means that when the wavelength has this value, the maximum kinetic energy of the photoelectrons is zero i.e K_max = 0. Thus the energy of the incoming photons is just enough to extract the photoelectrons from the material.

Thus,

hf - Φ = 0

hf = Φ - - - (1)

We are given the wavelength as;

λ = 540 nm = 540 × 10^(-9) m

Now, let's find the frequency of the light by using the relationship between frequency and wavelength. The equation is;

f = c/λ

Where c is speed of light = 3 × 10^(8) m/s

f = (3 × 10^(8))/(540 × 10^(-9))

f = 5.56 × 10^(14) Hz

Thus, from equation 1,we can now find the work function;

Φ = hf

h is Planck's constant and has a value of 6.626 × 10^(-34) J.s

Thus;

Φ = 6.626 × 10^(-34) × 5.56 × 10^(14)

Φ = 36.84 × 10^(-20) J

Answer:

3x10⁴v

Explanation:

Using

Wavelength= h/ √(2m.Ke)

880nm = 6.6E-34/√ 2.9.1E-31 x me

Ke= 6.6E-34/880nm x 18.2E -31.

5.6E-27/18.2E-31

= 3 x 10⁴ Volts

Answer:

the analog along the diameter of the acceleration of the particle executing simple harmonic motion is the projection along the diameter of the centripetal acceleration of the particle in the circle

Answer:

33.89 m

Explanation:

We must first obtain the acceleration of the car from;

F=ma

Where

F= force= 9500 N

m= mass of the car= 1000kg

a= acceleration

a= F/m= 9500/1000

a= 9.5 m/s^2

From;

V^2=u^2 + 2as

Where;

V= final velocity

u= initial velocity

s= distance covered

a= acceleration

s= v^2 -u^2/2a

s= (30)^2 -(16)^2/2×9.5

s= 900 - 256/19

s= 644/19

s= 33.89 m

The distance is 33.89 m

The first step is to calculate the acceleration

F= ma

force= 9500N

mass= 1000 kg

9500= 1000 × a

a= 9500/1000

= 9.5 m/s

v²= u² + 2as

30²= 16² + 2(9.5)(s)

900= 256 + 19s

900-256= 19s

644= 19s

s= 644/19

s= 33.89 m

Hence the distance traveled by the car is 33.89 m

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Answer:

The direction of the force is towards the East.

Explanation:

Using the right hand rule, the force on the current carrying conductor is east.

In the right hand rule, if the hand is held with the fingers pointed parallel to the palm representing the magnetic field, and the thumb held at right angle to the rest of the fingers representing the direction of the current, then the palm will push in the direction of the force.

In this case, the thumb is pointing downwards, with the fingers pointing north away from the body in the direction of the earth's magnetic field, the palm will push east.

Answer:

I know the answer

Explanation:

We want to choose the film thickness such that destructive interference occurs between the light reflected from the air-film interface (call it wave 1) and from the film-lens interface (call it wave 2). For destructive interference to occur, the phase difference between the two waves must be an odd multiple of half-wavelengths.

You can think of the phases of the two waves as second hands on a clock; as the light travels, the hands tick-tock around the clock. Consider the clocks on the two waves in question. As both waves travel to the air-film interface, their clocks both tick-tock the same time-no phase difference. When wave 1 is reflected from the air-film boundary, its clock is set forward 30 seconds; i.e., if the hand was pointing toward 12, it's now pointing toward 6. It's set forward because the index of refraction of air is smaller than that of the film.

Now wave 1 pauses while wave two goes into and out of the film. The clock on wave 2 continues to tick as it travels in the film-tick, tock, tick, tock.... Clock 2 is set forward 30 seconds when it hits the film-lens interface because the index of refraction of the film is smaller than that of the lens. Then as it travels back through the film, its clock still continues ticking. When wave 2 gets back to the air-film interface, the two waves continue side by side, both their clocks ticking; there is no change in phase as they continue on their merry way.

So, to recap, since both clocks were shifted forward at the two different interfaces, there was no net phase shift due to reflection. There was also no phase shift as the waves travelled into and out from the air-film interface. The only phase shift occured as clock 2 ticked inside the film.

Call the thickness of the film t. Then the total distance travelled by wave 2 inside the film is 2t, if we assume the light entered pretty much normal to the interface. This total distance should equal to half the wavelength of the light in the film (for the minimum condition; it could also be 3/2, 5/2, etc., but that wouldn't be the minimum thickness) since the hand of the clock makes one revolution for each distance of one wavelength the wave travels (right?).

Answer:

Fad = 28.8 kN

Fbd = 16.4 kN

Fcd = 28.1 kN

Explanation:

First, find the length of each cable.

AD = √((2 m)² + (0.5 m)² + (2.5 m)²)

AD = √10.5 m

AD ≈ 3.24 m

BD = √((1.5 m)² + (1 m)² + (2.5 m)²)

BD = √9.5 m

BD ≈ 3.08 m

CD = √((1 m)² + (1 m)² + (2.5 m)²)

CD = √8.25 m

CD ≈ 2.87 m

Next, use similar triangles to find the x, y, and z components of each tension force.

Fadx = 2/3.24 Fad = 0.617 Fad

Fady = 0.5/3.24 Fad = 0.154 Fad

Fadz = 2.5/3.24 Fad = 0.772 Fad

Fbdx = 1.5/3.08 Fbd = 0.487 Fbd

Fbdy = 1/3.08 Fbd = 0.324 Fbd

Fbdz = 2.5 / 3.08 Fbd = 0.811 Fbd

Fcdx = 1/2.87 Fcd = 0.348 Fcd

Fcdy = 1/2.87 Fcd = 0.348 Fcd

Fcdz = 2.5/2.87 Fcd = 0.870 Fcd

Now sum the forces in the x, y, and z directions:

∑Fx = ma

-0.617 Fad + 0.487 Fbd + 0.348 Fcd = 0

∑Fy = ma

-0.154 Fad − 0.324 Fbd + 0.348 Fcd = 0

∑Fz = ma

60 kN − 0.772 Fad − 0.811 Fbd − 0.870 Fcd = 0

To solve this system of equations algebraically, start by subtracting the first two equations, eliminating Fcd.

-0.463 Fad + 0.811 Fbd = 0

0.811 Fbd = 0.463 Fad

Fbd = 0.571 Fad

Substitute into either of the first two equations:

-0.617 Fad + 0.487 (0.571 Fad) + 0.348 Fcd = 0

-0.617 Fad + 0.278 Fad + 0.348 Fcd = 0

-0.339 Fad + 0.348 Fcd = 0

0.348 Fcd = 0.339 Fad

Fcd = 0.975 Fad

Now substituting into the third equation:

60 kN − 0.772 Fad − 0.811 Fbd − 0.870 Fcd = 0

60 kN − 0.772 Fad − 0.811 (0.571 Fad) − 0.870 (0.975 Fad) = 0

60 kN − 0.772 Fad − 0.463 Fad − 0.849 Fad = 0

60 kN − 2.083 Fad = 0

Fad = 28.8 kN

Solving for the other two tension forces:

Fbd = 0.571 Fad = 16.4 kN

Fcd = 0.975 Fad = 28.1 kN

Answer:

Tensions of:

DA = 28.81 KN

DB = 16.45 KN

DC = 28.07 KN

Explanation:

see attached

Answer:

The initial kinetic energy of the bullet is closest to 491.87 J

Explanation:

Given;

mass of bullet, m₁ = 18g = 0.018kg

mass of block, m₂ = 10kg

height moved by the block, h = 9 mm = 0.009 m

time taken for the bullet to travel through the block, t = 0.001s

let the initial velocity of the bullet = v₁

let the final velocity of the bullet = v₂

Apply the principle of conservation of linear momentum;

initial momentum = final momentum

0.018v₁ = v₂(0.018 + 10)

0.018v₁ = 10.018v₂ -----equation (1)

Apply the law of conservation of energy when the bullet lifts the block through 9mm

mgh = ¹/₂mv₂²

gh = ¹/₂v₂²

v₂² = 2gh

v₂ = √2gh

v₂ = √(2 x 9.8 x 0.009)

v₂ = 0.42 m/s

Substitute in v₂ in equation 1, to determine the initial velocity of the bullet;

0.018v₁ = 10.018v₂

0.018v₁  =  10.018(0.42)

0.018v₁  = 4.208

v₁ = 4.208 / 0.018

v₁ = 233.78 m/s

Now, determine the initial kinetic energy of the bullet;

K.E₁ = ¹/₂m₁v₁²

K.E₁ = ¹/₂(0.018)(233.78)²

K.E₁ = 491.87 J

Therefore, the initial kinetic energy of the bullet is closest to 491.87 J

Answer:

0.1 kg or 100 g

Explanation:

The length of the wire = 0.5 m

the field magnitude = 0.98 T

the current through the wire = 2.0 A

magnetic force due to a wire carrying current is

F = [tex]IlB[/tex]

where

F is the force

[tex]I[/tex] is the current = 2 A

[tex]l[/tex] is the length of the wire

B is the magnetic field strength

Substituting, we have

F = 2 x 0.5 x 0.98 = 0.98 N

This force balances the weight of the mass

weight = mg

where m is the mass of the wire

g is acceleration due to gravity = 9.81 m/s^2

therefore, weight = m x 9.81 = 9.81m

equating this weight with the force, we have

0.98 = 9.81m

m = 0.98/9.81 = 0.099 kg ≅ 0.1 kg or 100 g

Answer:

100 g

Explanation:

Answer:

29°

Explanation:

because the refracted ray angle is small than angle of incidence

Answer:

12.2 m

Explanation:

Given:

v₀ = 15.6 m/s

v = 0 m/s

a = -10 m/s²

Find: Δy

v² = v₀² + 2aΔy

(0 m/s)² = (15.6 m/s)² + 2 (-10 m/s²) Δy

Δy = 12.2 m

[tex] \LARGE{ \boxed{ \rm{ \green{Answer:}}}}[/tex]

Given,

Finding the initial kinetic energy,

[tex]\large{ \boxed{ \rm{K.E. = \frac{1}{2}m {v}^{2}}}}[/tex]

⇛ KE = (1/2)mv²

⇛ KE = (1/2)(0.042)(15.6)²

⇛ KE = 5.11 J

|| ⚡By conservation of energy, the potential energy at the highest point will also be 5.11 J, since there is no kinetic energy at the highest point because the ball is not moving (we neglect energy lost due to air resistance, heat, sound, etc.) ⚡||

So, we have:

[tex] \large{ \boxed{ \rm{P.E. = mgh}}}[/tex]

⇛ h = PE/(mg)

⇛ h = 5.11 J /(0.042 × 9.8)

⇛ h = 12.41 m

✏The ball will rise upto a height of 12.41 m

━━━━━━━━━━━━━━━━━━━━

Answer:

The volume will decrease by a factor of 10/51.

Explanation:

Hello,

In this case, since both moles and temperature remain constant, we can use the Boyle's law that relates the volume and pressure as an inversely proportional relationship:

[tex]P_1V_1=P_2V_2[/tex]

Thus, since the pressure increases by a factor of 5.1 (statement), we have:

[tex]P_2=5.1P_1[/tex]

Thus, the final volume is:

[tex]V_2=\frac{P_1V_1}{P_2} =\frac{P_1V_1}{5.1P_1}\\\\V_2=\frac{10}{51}V_1[/tex]

It means that the volume will decrease by a factor of 10/51.

Regards.

Answer:

1.227 m

Explanation:

Given that

Minimum wavelength is 410 nm

Maximum wavelength is 750 nm

Grating is 7800 slits/cm

Distance is 3.2 m

To solve this question, we would use the formula

sin θ = λ/d

sin θ = (410*10^-9) / (0.01/7800)

Sin θ = 410*10^-9 / 1.282*10^-6

Sin θ = 0.32 and θ = 18.67 degrees

For the second wavelength = 750 nm

sin θ = [(0.32x750)/410]

sin θ = (240 / 410)

sin θ = 0.5853 or

θ = 35.8 degrees

And finally, the width of spectrum would be

3.2[tan 35.8 - tan 18.67]

3.2 * 0.3833

= 1.227 m

Answer:

"Endoscope" is the correct answer.

Explanation: