Testing shows that a sample of wood from an artifact contains 50% of the original amount of carbon-14. Given that the half-life of carbon-14 is 5730
years, how old is the artifact?
A. 22,920 years
B. 11,460 years
C. 5730 years
D. 2865 years

Answer:

λ = 1.90 10⁻⁶ m

Explanation:

The interference pattern for the two-slit case is

          d sin θ = m λ

let's use trigonometry

         tan θ = y / L

interference experiments angles are small

        tan θ = sin θ /cos θ = sin θ

        sin θ = y / L

we substitute

       d y / L = m λ

       λ = [tex]\frac{ d \ y}{m \ L}[/tex]

we calculate

       λ = 0.2000 10⁻³ 9.49 10⁻³ / (1  1.00)

       λ = 1.898 10⁻⁶ m

       λ = 1.90 10⁻⁶ m

The wavelength of the light after calculation is find out to be λ = 1.90 *10⁻⁶ m

The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.

The interference pattern for the two-slit case is

d sin θ = m λ

let's use trigonometry

[tex]tan\theta=\dfrac{y}{L}[/tex]

interference experiments angles are small

[tex]sin\theta=\dfrac{y}{L}[/tex]

we substitute

[tex]\dfrac{dy}{L}=m\lambda[/tex]    

[tex]\lambda=\dfrac{dy}{mL}[/tex]

we calculate

[tex]\lambda=\dfrac{0.2\times 10^{-3}\times 9.49\times 10^{-3}}{1\times 1}[/tex]  

[tex]\lambda=1.90\times 10^{-6}\ m[/tex]    

Hence the wavelength of the light after calculation is find out to be λ = 1.90 *10⁻⁶ m

To know more about wavelength follow

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Answer:

The correct option is D.

Explanation:

The wavelength of the photon can be calculated with the following equation:

[tex] E = h\frac{c}{\lambda} [/tex]

Where:

E: is the energy of the photon = 2.90 eV

h: is the Planck's constant = 6.62x10⁻³⁴ J.s

c: is the speed of light = 3x10⁸ m/s

λ: is the wavelength

Hence, the photon's wavelength is:

[tex] \lambda = \frac{hc}{E} = \frac{6.62 \cdot 10^{-34} J*s*3.0 \cdot 10^{8} m/s}{2. 90 eV*\frac{1.6 \cdot 10^{-19} J}{1 eV}} = 428 nm [/tex]

Therefore, the correct option is D.

I hope it helps you!

Answer:

the answer is option B because opposit sides of the magnets attract each other

Answer:

9 joules of heat energy was produced

Explanation: there is no acceleration therefore its not a kinetic energy

Energy= force × distance

= 3×3

=9

The question is incomplete. The complete question is :

Assume that the energy lost was entirely due to friction and that the total length of the PVC pipe is 1 meter. Use this length to compute the average force of friction (for this calculation, you may neglect uncertainties).

Mass of the ball :  16.3 g

Predicted range :  0.3503 m

Actual range : 1.09 m

Solution :

Given that :

The predicted range is 0.3503 m

Time of the fall is :

[tex]$t=\sqrt{\frac{2H}{g}}$[/tex]

[tex]v_1t= 0.35[/tex]  ...........(i)

[tex]v_0t= 1.09[/tex]  ...........(ii)

Dividing the equation (ii) by (i)

[tex]$\frac{v_0t}{v_1t}=\frac{1.09}{035} = 3.11$[/tex]

∴ [tex]v_0=3.11 \ v_1[/tex]

Now loss of energy  = change in the kinetic energy

[tex]$W=\frac{1}{2} m [v_0^2-v_1^2]$[/tex]

[tex]$W=\frac{1}{2} \times (16.3 \times 10^{-3}) \times [v_0^2-\left(\frac{v_0}{3.11}\right)^2]$[/tex]

[tex]$W=7.307\times 10^{-3} \ v_0^2$[/tex]

If f is average friction force, then

(f)(L) = W

(f) (1) = [tex]$7.307\times 10^{-3} \ v_0^2$[/tex]

(f)  = [tex]$7.307\times 10^{-3} \ v_0^2$[/tex]

The Average force of friction is ( F )  = 7.307 * 10⁻³ v₀²

Given data:

Predicted range ( v₁t ) = 0.3503 m

Actual range ( v₀t ) = 1.09 m

mass = 16.3 g

First step : Determine the value of  V₀

[tex]t = \sqrt{\frac{2H}{g} }[/tex]    ,    v₁t  =  0.3503 ,    ( v₀t ) = 1.09 m

To obtain the value of  V₀  

Divide ( v₀t ) by ( v₁t )  =  1.09 / 0.3503 = 3.11 v₁

∴ V₀ = 3.11 v₁

Next step : Determine the average force of friction ( f )

given that loss of energy results in a change in kinetic energy

W = [tex]\frac{1}{2} m ( vo^{2} - v1^{2} )[/tex]

    = 1/2 * 16.3 * 10⁻³ * [ v₀² - [tex](\frac{v_{0} }{3.11} )^{2}[/tex] ]

∴ W = 7.307 * 10⁻³ v₀²

Average force of friction = W / Actual length

                                         = 7.307 * 10⁻³ v₀² / 1  

∴ Average force of friction ( F )  = 7.307 * 10⁻³ v₀²

Hence we can conclude that the average force of friction is 7.307 * 10⁻³ v₀²

Learn more about average force of friction : https://brainly.com/question/16207943

Your question has some missing data below are the missing data related to your question

Mass of the ball :  16.3 g

Predicted range :  0.3503 m

Actual range : 1.09 m

Answer:

a) 65.83 km

b) 52.664 km/h

Explanation:

Different speed values :

Initial speed : 50 km/h  for 15 mins

                       80 km/h  for 25 mins

stops for 55 mins

40 km/h for 30 minutes

a) Determine total distance covered

Speed = distance covered / time

∴ Total distance = ∑speed * time

                           = ( 50 * 15/60 ) + ( 80*25/60) + ( 40 * 30/60 )

                           = 65.83 km

b) Average speed

Total distance / time taken

= 65.83 / ( 15 + 25 + 30 ) / 60

= 65.83 / ( 75/60)

= 52.664 km/h

Answer:

c.

Explanation:

Given that:

The initial speed of the projective v = 13.2 m/s

The angle θ = 37.0°

At the highest point, the particle will comprise only the horizontal component of the speed because the vertical component will be zero.

So,

the horizontal component [tex]v_x = vcos \theta[/tex]

[tex]v_x = 13.2 \ m/s (cos 37^0)[/tex]

[tex]\mathsf{v_x = 10.5 \ m/s}[/tex]

Answer:

The average speed is 1 m/s

The average velocity is 0

Explanation:

Given;

length of the pool, L = 50 m

time taken for the motion, t = 100 s

The total distance = 50 m + 50 m

The total distance = 100 m

The average speed = total distance / total time

                                  = 100 / 100

                                  = 1 m/s

The average velocity = change in displacement / change in time

change in displacement = 50 m - 50 m = 0

The average velocity = 0 / 100

The average velocity = 0

Binary code is the answer

Answer:

binary code is the answer of blank

Answer:

1. Power = 5000 Watts

2. Workdone = 11185.5 Joules

Explanation:

Given the following data;

1. Distance = 18 m

Energy = 100 KJ = 100,000 Joules

Time = 20 seconds

To find the average power of the elevator;

Power = energy/time

Power = 100000/20

Power = 5000 Watts

2. Power = 0.4 HP

Time = 15 seconds

Conversion:

1 horsepower = 745.7 Watts

0.4 horsepower = 0.4 * 745.7 = 298.28 Watts

To find the amount of work done by the electric mixer;

Work done = power * time

Workdone = 745.7 * 15

Workdone = 11185.5 Joules

Answer:

No of proton is 13 and nucleus is 13

Answer:

43994

Explanation:

Hope this helps!

Answer:

Option A

Explanation:

Water posses hydraulic force and hence it carries off all the particles that lie in its way of flow.

The canyon route have rocks and soil which are first broken down by river velocity and turbulence and then carried away from their base location there by clearing way for the canyon to widen further

Hence, option A is correct

Answer:

According to " The second law of thermodynamics", the randomness of the universe is constantly increasing?

Explanation:

So answer option C. Have a great summer.

Answer:

50 N-m

Explanation:

5 N-m x 10 N-m = 50 N-m

Answer:

50 n-m

Explanation:

Answer:

The speed of the bus is 40 km/hr so this means the bus is travelling at a speed of 40 km per hour.

Answer:

The slope of the position time graph gives the velocity.

Explanation:

The slope of the position time graph gives the value of velocity.

In first graph,

The slope is constant in both the parts but positive . So the velocity is also constant and positive for both the parts.  and more than the second part, so the initial velocity is more than the final velocity.

In the second graph,

The slope is constant in both the parts but negative. So, the velocity is constant but negative for both the parts. Initial velocity is more negative than the final velocity.

Answer:

the magnitude of momentum is √2≈ b

Explanation:

hope that helped

Answer:

5156.37 ft

Explanation:

Given data:

weight ( W ) = 243,000 Ib

Motion of shuttle ; from 189 mi/hr to 101 mi/hr

dv/dt = -0.0002 V^2

I/v * dv/dt = -0.0002 ds

Convert mi/hr to ft/s ( 1 mi/hr = 1.467 ft/s)

189 mi/hr = 277.263 ft/s

101 mi/hr = 148.167 ft/s

After Integrating

In ( 148.167 / 277.263 ) = -0.0002 ( S1 - S2 )

S1 - S2 = -0.627 / -0.0002

S1 - S2 = 3135 ft/s

Now from 101 mi/hr to 35 mi/hr

dv/dt = ( - 0.0002 V^2 + 3.5 )

ds =  V*dv / ( -0.0002 v^2 - 3.5 )

given :  35 mi/hr = 51.345 ft/s

             101 mi/hr = 148.167 ft/s

Integrate

S3 - S2 = - In( 0.0002 v^2 + 3.5 ) / 0.0002 * 2 ]

            = 1644.75 ft/s

S4 - S3 = 376.62 ft/s

attached below is the remaining part of the solution

Total distance travelled = 3135 + 1644.75 + 376.62 = 5156.37 ft

Answer:

0.32 m.

Explanation:

To solve this problem, we must recognise that:

1. At the maximum height, the velocity of the ball is zero.

2. When the velocity of the ball is 2.5 m/s above the ground, it is assumed that the potential energy and kinetic energy of the ball are the same.

With the above information in mind, we shall determine the height of the ball when it has a speed of 2.5 m/s. This can be obtained as follow:

Mass (m) = constant

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

Velocity (v) = 2.5 m/s

Height (h) =?

PE = KE

Recall:

PE = mgh

KE = ½mv²

Thus,

PE = KE

mgh = ½mv²

Cancel m from both side

gh = ½v²

9.8 × h = ½ × 2.5²

9.8 × h = ½ × 6.25

9.8 × h = 3.125

Divide both side by 9.8

h = 3.125 / 9.8

h = 0.32 m

Thus, the height of the ball when it has a speed of 2.5 m/s is 0.32 m.

Answer:

ΔD = 2.29 10⁻⁵ m

Explanation:

This is a problem of thermal expansion, if the temperature changes are not very large we can use the relation

          ΔA = 2α A ΔT

the area is

         A = π r² = π D² / 4

we substitute

         ΔA = 2α π D² ΔT/4

as they do not indicate the initial temperature, we assume that ΔT = 75ºC

    α = 1.7 10⁻⁵ ºC⁻¹

we calculate

          ΔA = 2 1.7 10⁻⁵ pi (1.8 10⁻²) ² 75/4

          ΔA = 6.49 10⁻⁷ m²

by definition

           ΔA = A_f- A₀

           A_f = ΔA + A₀

           A_f = 6.49 10⁻⁷ + π (1.8 10⁻²)² / 4

           A_f = 6.49 10⁻⁷ + 2.544 10⁻⁴

           A_f = 2,551 10⁻⁴ m²

the area is

           A_f = π D_f² / 4

           A_f = [tex]\sqrt{4 A_f /\pi }[/tex]

           D_f = [tex]\sqrt{4 \ 2.551 10^{-4} /\pi }[/tex]

           D_f = 1.80229 10⁻² m

the change in diameter is

           ΔD = D_f - D₀

           ΔD = (1.80229 - 1.8) 10⁻² m

           ΔD = 0.00229 10⁻² m

           ΔD = 2.29 10⁻⁵ m

Answer:

We can also prove the conservation of mechanical energy of a freely falling body by the work-energy theorem, which states that change in kinetic energy of a body is equal to work done on it. i.e. W=ΔK. And ΔE=ΔK+ΔU. Hence the mechanical energy of the body is conserved

Explanation:

Answer:

The average power per day is 1008 kW.

Explanation:

Solar constant = 1.4 kW/m2

efficiency = 20 %

area, a = 1 square meter

time = 6 hours

Energy falling on the panel in 6 hours = 1.4 x 6 x 3600 kJ

The output is

= 20 % of 1.4 x 6 x 3600

= 0.2 x 1.4 x 6 x 3600

= 6048 kJ

Average power per day is

= 6048/6 = 1008 kW

Answer:

The total momentum of the cars before the collision is 61,000 kg.m/s

The total momentum of the cars after the collision is 61,000 kg.m/s

The velocity of the cars after the collision is 27.727 m/s

Explanation:

Given;

mass of the first car, m₁ = 1000 kg

initial velocity of the car, u₁ = 25 m/s

mass of the second car, m₂ = 1200 kg

initial velocity of the second car, u₂ = 30 m/s

The common velocity of the cars after collision = v

The total momentum of the cars before collision is calculated as;

P₁ = m₁u₁  +  m₂u₂

P₁ = (1000 x 25)  +  (1200 x 30)

P₁ = 61,000 kg.m/s

The total momentum of the cars after collision is calculated as;

P₂ = m₁v + m₂v

where;

v    is the common velocities of the cars after collision since they stick together.

P₂ = v(m₁ + m₂)

To determine "v" apply the principle of conservation of linear momentum for inelastic collision.

m₁u₁  +  m₂u₂  = v(m₁  + m₂)

(1000 x 25)  +  (1200 x 30) = v(1000 + 1200)

61,000 = 2,200v

v = 61,000/2,200

v = 27.727 m/s

The total momentum after collsion = v(m₁ + m₂)

                                                         = 27.727(1000 + 1200)

                                                          = 61,000 kg.m/s

Thus, momentum before and after collsion are equal.

Answer:

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector. ... In its simplest form, average velocity is calculated by dividing change in position (Δr) by change in time (Δt).

Explanation:

Answer:

a. 1.56 × 10¹⁸ electrons per second

b. The electrons in wire 3 flow into the junction.

Explanation:

Here is the complete question

Three wires meet at a junction. Wire 1 has a current of 0.40 A into the junction. The current of wire 2 is 0.65 A out of the junction. (a) How many electrons per second move past a point in wire 3? (b) In which direction do the electrons move in wire 3 -- into or out of the junction?

Solution

(a) How many electrons per second move past a point in wire 3?

Using Kirchhoff's current law, at the junction, i₁ + i₂ + i₃ = 0 where i₁ = current in wire 1 = 0.40 A, i₂ = current in wire 2 = 0.65 A and  i₃ = = current in wire 3,

So, i₃ = -(i₁ + i₂)

taking current flowing into the junction as positive and those leaving as negative, i₁ = + 0.40 A and i₂ = -0.65 A

So, i₃ = -(i₁ + i₂)

i₃ = -(0.40 A + (-0.65 A))

i₃ = -(0.40 A - 0.65 A)

i₃ = -(-0.25 A)

i₃ = 0.25 A

Since i₃ = 0.25 C/s and we have e = 1.602 × 10⁻¹⁹ C per electron, then the number of electrons flowing in wire 3 per second is i₃/e = 0.25 C/s ÷ 1.602 × 10⁻¹⁹ C per electron = 0.1561  × 10¹⁹ electrons per second = 1.561  × 10¹⁸ electrons per second ≅ 1.56 × 10¹⁸ electrons per second

(b) In which direction do the electrons move -- into or out of the junction?

Given that i₃ = + 0.25 A and that positive flows into the junction, thus, the electrons in wire 3 flow into the junction.

Answer:

The magnitude of the force is 64.634 newtons.

Explanation:

According to the statement, the crate is a constant mass system, whose upward force is described by the following expression:

[tex]F(t) = m\cdot \ddot{y} (t)[/tex] (1)

Where:

[tex]F(t)[/tex] - Force, in newtons.

[tex]m[/tex] - Mass, in kilograms.

[tex]\ddot {y}(t)[/tex] - Acceleration, in meters per square second.

The function acceleration is obtained by deriving the function position twice in time:

[tex]\dot y (t) = 2.80 + 1.83\cdot t^{2}[/tex] (2)

[tex]\ddot y(t) = 3.66\cdot t[/tex] (3)

And we expand (1) by applying (3):

[tex]F(t) = 3.66\cdot m \cdot t[/tex]

Where [tex]t[/tex] is the time, in seconds.

If we know that [tex]m = 4.76\,kg[/tex] and [tex]t = 3.71\,s[/tex], then the magnitude of the force is:

[tex]F = 3.66\cdot (4.76)\cdot (3.71)[/tex]

[tex]F = 64.634\,N[/tex]

The magnitude of the force is 64.634 newtons.

Answer:

Explanation:

Hope this helps... pls vote as brainliest

Answer:

a) F = [tex]\frac{\pi d^2B^2lv}{16p}[/tex]  

b) attached below

c) 0.037 m/s

Explanation:

a) Determine the magnetic "drag" force acting  at the moment

speed = v

first step: determine current in the loop

I = [tex]\frac{\pi d^2}{16pl} B lv[/tex]   ----- ( 1 )

given that the current will induce force on the three sides of the loop found in the magnetic field

forces on vertical sides = + opposite

we will cancel out

hence equation 1 becomes

F = [tex]\frac{\pi d^2B^2lv}{16p}[/tex]   ( according to Lenz law we can say that the direction of force is upwards and this force will slow down the decrease in flux )

b) Determine the formula for Vt

attached below

c) Find Vt

given :

B = 0.80 T

density of copper = 8.9 * 10^3 kg/m^3

resistivity of copper = 1.68 * 10^-8 Ωm

∴ Vt = 16 ( 8.9 * 10^3 kg/m^3 ) ( 1.68 * 10^-8 Ωm ) ( 9.8 m/s^2 ) / ( 0.08 T)^2

       = 0.037 m/s