A 12.0-g sample of carbon from living matter decays at the rate of 162.5 decays/minute due to the radioactive 14C in it. What will be the decay rate of this sample in 1000 years? What will be the decay rate of this sample in 50000 years?

Explanation:

(a) The total energy is the elastic potential energy at maximum displacement.

E = ½ kx²

E = ½ (40.0 N/m) (0.0500 m)²

E = 0.05 J

(b) At this displacement, there is both elastic potential energy and kinetic energy.

E = EE + KE

0.05 J = ½ kx² + ½ mv²

0.05 J = ½ (40.0 N/m) (0.0200 m)² + ½ (0.060 kg) v²

v = 1.18 m/s

(c) E = EE + KE

0.05 J = ½ kx² + ½ mv²

0.05 J = ½ (40.0 N/m) (0.0250 m)² + KE

KE = 0.0375 J

(d) EE = ½ kx²

EE = ½ (40.0 N/m) (0.0250 m)²

EE = 0.0125 J

Answer:

Explanation:

Let the volume below water be v . Then

buoyant force = v d g where d is density of water , g is acceleration due to gravity

= v x 1000 x g

weight of wood piece = volume x density of wood x g

= .6 x 600 x g

for equilibrium while floating

buoyant force = weight

= v x 1000 x g  =  .6 x 600 x g

v = .36 m²

volume above water or volume exposed = .6 - .36

= .24 m²

When immersed completely ,

buoyant force = .6 x 1000 x 9.8

= 5880 N

weight of wood

=  .6 x 600 x g

= 3528 N

buoyant force is more than the weight . In order to equalise them for floating with full volume in water

weight required = 5880 - 3528

= 2352 N.

Answer:

B. heat from fire

Explanation:

It is not an example of matter because heat is energy and not matter

Answer:

423v

Explanation:

Using

E= -N ∆န/ ∆ t

= ( -1) X (-83 - 82)/0.39

= 423volts

Answer:

A and B are true C is false

Explanation:

Because it states that if we know everything about where a particle is located (the uncertainty of position is small), we know nothing about its momentum (the uncertainty of momentum is large), and vice versa.

So in A we can know the positions of two objects

In B we can measure the momentum at two different places

While in C we cannot measure both the position and momentum of y accurately

Answer:

Option C, The object cannot be directly observed.

Explanation:The temperature of sun is extremely high due to which it is almost impossible to land on its surface and explore the depth of it. Thus a prototype of it is required to predict its probable internal structure and associated feature which effect our planet "earth".

This prototype/model is based on the deduction arrived after analyzing the  satellite information available in the form of  high resolution images.

Hence, option C is correct

Answer:

The answer is c the object cannot be directly observed.

Explanation:

I took the test and got it right.

Answer: [tex]\frac{K_{A}}{K_{B}}[/tex] = 1

Explanation: Average molecular kinetic energy for monatomic idela gases is given by:

[tex]E=\frac{3}{2}RT[/tex]

where

R is gas constant of ideal gas

T is temperature

Which means kinetic energy depnends only on temperature.

Since gas A and gas B are at the same temperature, kinetic energy will be the same. Therefore:

[tex]\frac{K_{A}}{K_{B}}[/tex] = 1

Ratio of this average molecular kinetic energy is 1.

Answer:

h is 0.27metres without breaking their leg

Explanation:

A body jumping from any heights has potential energy mgh and maximum energy which can be converted by human body from the jump is 200J derived from experiment so using

200J = mgh

h = 200/ 9.8* 75

h= 0.27 m

Explanation:

Answer:

344Hz

Explanation:

First we need to more that the frequency will inky resonate in the portion not containing water. If the total length is 1m and the filled with water up to 75cm, the length of the air column will be 100cm - 75cm = 25cm

Fundamental frequency of a closed pipe fo = V/4L

V is the velocity of sound in air

L is the length of the air column

Given V = 344m/s

L = 25cm = 0.25m

fundamental resonant frequency = 344/4(0.25)

= 344/1

= 344Hz

Explanation:

Kepler's third law gives the relationship between the orbital radius and the orbital period of the planet. Its mathematical form is given by :

[tex]T^2=\dfrac{4\pi ^2}{GM}a^3[/tex]

Here,

G is gravitational constant

M is mass of sun

It means that the mass of Sun is constant for all planets orbiting the sun, assuming circular orbits.

Answer:

v = 6.38 m/s

Explanation:

discharge Q = 500 L / 6.5 min

flow through pipe is 1.6 cm x (1 m/100 cm ) = 0.016 m

using the flow rate formula Q = A * v

where A = area, v = velocity

the speed of water in the pipe = v = Q / A

      500 L        1 m³          1 min           π (0.016 m)²

v = ----------   x  --------  x ------------    ÷  --------------------

      6.5 min       10³ L       60 sec                 4

v = 6.38 m/s

The speed of the water is "12.95 m/s".

According to the question,

Volume,

           = [tex]500\times 10^{-3} \ m^3[/tex]

Time,

          = [tex]3.2\times 60[/tex]

          = [tex]192 \ s[/tex]

Diameter,

           = 0.016 m

As we know,

Area of cross-section of pipe will be:

→ [tex]A = \pi (\frac{d}{2} )^2[/tex]

      [tex]= 3.14\times (\frac{0.016}{2} )^2[/tex]

      [tex]= 2.01\times 10^{-4} \ m^2[/tex]

Flow rate is:

→ [tex]\frac{V}{t} = Av[/tex]

   [tex]v = \frac{V}{At}[/tex]

      [tex]= \frac{500\times 10^{-3}}{2.01\times 10^{-4}\times 192}[/tex]

      [tex]= 12.95 \ m/s[/tex]

Thus the above approach is right.          

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Complete question:

A 40-turn coil has a diameter of 17 cm. The coil is placed in a spatially uniform magnetic field of magnitude 0.40 T so that the face of the coil and the magnetic field are perpendicular. Find the magnitude of the emf induced in the coil (in V) if the magnetic field is reduced to zero uniformly in the following times.  (a) 0.10 s, (b) 1.0 s, and (c) 60 s.

Answer:

(a) E = 3.632 V

(b) E = 0.3632  V

(c) E = 6.053 mV

Explanation:

Given;

number of turn of the coil, N = 40 turn

diameter of the coil, d = 17 cm = 0.17 m

radius of the coil, r = d /2 = 0.17 /2 = 0.085 m

initial magnitude of magnetic field, B₁ = 0.4 T

final magnitude of magnetic field, B₂ = 0

The induced emf in the coil is given by;

[tex]E = -N\frac{dB}{dt} A = \frac{-NA(B_2 - B_1)}{dt} =\frac{NA(B_1-B_2)}{dt} =\frac{NAB_1}{t}[/tex]

A is area of the coil = πr² = π(0.085)² = 0.0227 m²

(a) when the time is 0.1 s

[tex]E= \frac{40*0.0227*0.4}{0.1} = 3.632 \ V[/tex]

(b) when the time is 1 s

[tex]E = \frac{40*0.0227*0.4}{1} \\\\E = 0.3632 \ V[/tex]

(c) when the time is 60 s

[tex]E = \frac{40*0.0227*0.4}{60} \\\\E = 6.053 \ mV[/tex]

Answer:

The angle is  [tex]\theta =21.8 ^o[/tex]

Explanation:

From the question we are told that

   The mass of the crate is  [tex]m_c = 20 \ kg[/tex]

   The coefficient of static friction is  [tex]\mu_s = 0.40[/tex]

   The  coefficient of kinetic friction is  [tex]\mu_k = 0.30[/tex]

Generally  for the the crate not to slip , the static frictional  must be equal to the force driving the truck

   i.e

           [tex]F_f = F[/tex]

Now since we are considering a slope that static frictional force is mathematically represented as

            [tex]F_f = mg * cos(\theta) * \mu_s[/tex]

While the force driving the truck is mathematically represented as

          [tex]F = mg * sin (\theta )[/tex]

Here  mg is the weight of the crate  so

         So

               [tex]mg * cos (\theta ) \mu_s = mg * sin (\theta )[/tex]

=>             [tex]\frac{sin (\theta )}{cos (\theta)} = \mu_s[/tex]

=>          [tex]\theta = tan ^{-1} [\mu_s ][/tex]

=>          [tex]\theta = tan ^{-1} [0.40 ][/tex]

=>          [tex]\theta =21.8 ^o[/tex]

A diagram show an illustration is on the first uploaded image

Answer:

Hey there!

Because you are compressing the spring, these are compressional waves.

Let me know if this helps :)

Answer:

a) the correct answer is 1 , b) x=0   F=0, a=0

x= 0.050    F= -7.5 N,  a= -15 m/s²

x= 0.150     F= 22.5 N,  a=- 45 m/s²

Explanation:

a) In a mass - spring system the force is given by the Hooke force,

          F = - k x

Analyzing this equation we see that the outside is proportional to the elongation from the equilibrium position, therefore the force is zero when the spring is in its equilibrium position

the correct answer is 1

b) we assume that the given values ​​are from the equilibrium position of the spring.

Let's calculate the force

x = 0

      F = 0

x = 0.050

      F = - 150 0.050

      F = - 7.50 N

x = 0.150

      F = - 150 0.150

      F = - 22.5 N

let's use Newton's second law to find the acceleration

      F = m a

      a = F / m

x = 0 m

      a = 0

x = 0.050 m

      a = -7.50 / 0.50

      a = - 15 m / s²

x = 0.150 m

      a = - 22.5 / 0.50

      a = - 45 m/s²

TRASLATE

a) En un sistema masa – resorte  la fuerza es dada por la fuerza de Hoke,  

          F= - k x

analizando esta ecuación vemos que la fuera es proporcional a la elongación desde la posición de equilibrio, por lo tanto la fuerza es cero cuando el resorte esta en su posición de equilibrio

la respuesta correcta es  1

b)suponemos que los valores dados son desde la posición de equilibrio del resorte.

Calculemos la fuerza  

x=0  

              F= 0

x=0.050  

              F = - 150 0.050

              F= - 7.50 N

x= 0.150  

                F= - 150 0.150

                F= - 22.5 N

usemos la segunda ley de Newton para encontrar la aceleración

          F = m a

          a = F/m

x =0  m

        a = 0

x= 0.050 m

         a = -7.50/ 0.50

          a =- 15 m/s²

x= 0.150 m

          a= - 22.5 / 0.50

          a= - 45 m/s²

Answer:

She will speed up because air resistance will decrease and be less than gravity.

Explanation:

While Luz was falling initially, she was experiencing a gravitational force downwards, and air resistance that arise from the drag force on her body

Her gravitational force downwards is constant, and she fall down with a net force of

[tex]F_{net}[/tex] = [tex]F_{g}[/tex] - [tex]F_{d}[/tex]

where [tex]F_{net}[/tex] is the net force on Luz downwards

[tex]F_{g}[/tex] is the gravitational force on Luz

[tex]F_{d}[/tex] is the drag force on Luz

The drag force on on Luz is proportional to her attack surface area.  When Luz changes her body position from her frontal area, parallel to the ground to falling with her feet first, she reduces the area available for drag force from her whole frontal area to just about a little more than the areas of the sole of her feet. This action reduces the drag force due to air resistance on her body.

Answer:

The correct answer to the question is the third statement.

Explanation:

She will speed up because air resistance will decrease and be less than gravity. Changing position during skydiving is one of the factors affecting the speed. Since the cross section area is smaller than the first position, she experiences lesser air resistance, which causes her to speed up.

Answer:

d. 3

Explanation:

x = cos(4377π) + 8 sin(750°)

A full circle is 2π radians or 360°.

x = cos(4377π − 4376π) + 8 sin(750° − 720°)

x = cos(π) + 8 sin(30°)

x = -1 + 8 (1/2)

x = 3

Answer:

The velocity of the particle is 30 m/s.

Explanation:

The velocity can be found using Lorentz force:

[tex] F = q*v \times B [/tex]

Where:

q: is the charge of the particle = 0.002 C

v: is the velocity of the particle

B: is the magnetic field = 0.25 T

F: is the magnetic force = 0.015 N

Since the magnetic field and the particle's velocity are orthogonal, the cross product is equal to the product of the absolutes values of v and B.

We have:

[tex] F = q|v||B| [/tex]

[tex] v = \frac{F}{qB} = \frac{0.015 N}{0.002 C*0.25 T} = 30 m/s [/tex]

Therefore, the velocity of the particle is 30 m/s.

I hope it helps you!        

Answer:

r = 5.08 m

Explanation:

The electric force of attraction or repulsion is given by :

[tex]F=\dfrac{kq_1q_2}{r^2}[/tex]

We need to find how far above the electron would the proton have to be if you wanted to hold up an electron against the force of gravity by the attraction of a fixed proton some distance above it.

So, the force from the proton is balanced by the mass of the electron.

[tex]\dfrac{kq_pq_e}{r^2}=mg[/tex]

r is distance

[tex]r=\sqrt{\dfrac{kq_pq_e}{mg}} \\\\r=\sqrt{\dfrac{9\times 10^9\times (1.6\times 10^{-19})^2}{9.11\times 10^{-31}\times 9.8}} \\\\r=5.08\ m[/tex]

So, proton have to be at a distance of 5.08 meters above the electron.

Answer:

D, both A and B

Explanation:

2168 mV is the SI unit for potential difference and the Voltmeter.

The primary unit is Volt, represented as V. Due to the fact that there can be a much higher reading, or an even much more smaller one, comes the need for variants of the same unit.

10^-3 is called milli and represented as m

10^3 is called killo and represented as k

10^-6 is called micro and represented as µ

10^6 is called mega and represented as M

and even much higher variants of up to 10^12 and 10^-12

As we can see from the aforementioned example, 10^-3 is milli and represented as m

And our question gave us the unit in mV, which stands for millivolts.

Also, if we look at option B, it states, 2.168 volts. This 2.168 volts is also the same thing as A. Take a look at it this way, I said mV is 10^-3, right?

So, 2168*10^-3 is also 2168/100 which is 2.168. The only difference here is, once we make this conversion from mV, we have to drop the milli tag, because we have already made a conversion, and thus, leave it as V.

2168 mV = 2.168V

Hence why we picked option D, Both A & B as the right one

Answer:

The net force on the ball is zero.

Explanation:

Newton's first law of motion states that an object will remain in the same state of motion or at rest unless a resultant force acts on it, and if the net force on an object is zero, then that means that the object will keep moving at the same acceleration or the object stays stationary.

So, the truth about the net forces acting on the ball is that the net force on the ball is zero.

Answer:

The gravitational force is greater than the drag.

Explanation:

I took the quick check and got it wrong when I chose The net force on the ball is zero but I was right the first time with the third answer choice listed in the question.

Answer:

The  compression is  [tex]x = 0.05 \ m[/tex]

Explanation:

From the question we are told that

     The first velocity is  v

     The  compression of the spring is  [tex]d = 1.0 \ cm = 0.01 \ m[/tex]

      The  second velocity is  4v

Generally according to the law of  energy conservation

   The  kinetic energy of the block is equal to the energy stored in the spring that is  

       [tex]\frac{1}{2} * m* v^ 2 = \frac{1}{2} * k * d^2[/tex]

For  first speed

      [tex]m* v^ 2 = k * 0.01^2[/tex]

=>   [tex]m* v^ 2 = k * 0.0001[/tex]

=>  [tex]k = \frac{ m v^2 }{ 0.0001}[/tex]

For second  speed

       [tex]\frac{1}{2} * m* (5v)^ 2 = \frac{1}{2} * k * x^2[/tex]

=>    [tex]12.5mv^2 = 0.5 k x^2[/tex]

substituting for k

=>    [tex]12.5mv^2 = 0.5 (\frac{mv^2}{0.0001} ) x^2[/tex]

=> [tex]12.5 = 5000x^2[/tex]

=>  [tex]x = 0.05 \ m[/tex]

Explanation:

Analog signals :

Digital signals :

Answer:

Analog -

They flow continuously

They may pick up unwanted noise

They copy the original sound

Digital -

They do not flow continuously

They reduce unwanted noise.

They change sound into numbers.

Answer:

7.1 J

Explanation:

From the question,

Work done by the mover  = work done in pushing the crate + work done against friction

W = W'+Wf................. Equation 1

W = mgd+mgμd............ Equation 2

W = mgd(1+μ)................ Equation 3

Where m = mass of the crate, g = acceleration due to gravity, d = distance, μ = coefficient of  friction.

Given: m = 46 kg, d = 10.5 mm = 0.0105 m, μ = 0.5

constant: g = 9.8 m/s²

Substitute these values into equation 3

W = 46×9.8×0.0105(1+0.5)

W = 7.1 J

Explanation:

Use SOH-CAH-TOA.

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

For example, in 2(a), we are given an angle and the hypotenuse.  We want to find the side adjacent to the angle.  Therefore, we should use cosine.

cos 58° = y / 32.3

y = 32.3 cos 58°

y ≈ 17.1

In 3(a), we are given the adjacent side and opposite side.  We want to find the angle.  So use tangent.

tan θ = 3.6 / 6.2

θ = tan⁻¹(3.6/6.2)

θ = 30.1°

In 4(a), we are given an angle and the hypotenuse.  We want to find the side opposite of the angle.  Therefore, we should use sine.

sin 47° = x / 29

x = 29 sin 47°

x ≈ 21.2

Answer:

17047.54 years or 17048 y

Explanation:

From;

0.693/t1/2 = 2.303/t log (Ao/A)

Where;

t1/2=half-life of the carbon-14 =5670 years

t= time elapsed

Ao= activity of living C-14

A= activity if the sample under study

But A= 1/8 Ao

Hence;

0.693/5670= 2.303/t log(Ao/1/8Ao)

1.22×10^-4 = 2.303/t log 8

1.22×10^-4 = 2.0798/t

t= 2.0798/1.22×10^-4

t= 17047.54 years

Answer:

B. T

Explanation:

This is because the mass of the Bob does no relate to the period as given by the relationship

T = 2π(√L/g) so double mass is still T

Answer:

The correct option is (B).

Explanation:

The time period of a pendulum is given by :

[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]

l is the length of the pendulum

g is acceleration due to gravity

It is very clear that the time period is independent of the mass of the bob. If the mass of the bob is doubled, the time period of the pendulum remains the same i.e. T. Hence, the correct option is (B).

Answer:

4 s

Explanation:

Given:

v₀ = 44 m/s

v = 0 m/s

a = -11 m/s²

Find: t

v = at + v₀

0 m/s = (-11 m/s²) t + 44 m/s

t = 4 s

If the boat's initial velocity is 44m/s upstream, the time it takes to stop is found to be 4 seconds.

Acceleration may be defined as the rate of change of velocity with respect to time. It is a vector quantity as it has both magnitude and direction. It is also the second derivative of position and the first derivative of velocity with respect to time.

According to the question,

v₀ = 44 m/s

v = 0 m/s

a = -11 m/s²

Now, you have to calculate the time, t.

So, you calculate the time, t with the help of the following formula:

       0 m/s = (-11 m/s²) t + 44 m/s

        t = 4 s.

Therefore, if the boat's initial velocity is 44m/s upstream, the time it takes to stop is found to be 4 seconds.

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Answer:

a) 3×10^18 Hz

b) The electromagnetic wave is an x-ray

Explanation:

We know that the speed of an electromagnetic wave is given by;

c= λf

Where;

c= speed of electromagnetic waves = 3×10^8 ms-1

f= frequency of electromagnetic waves= the unknown

λ = wavelength of the electromagnetic wave= 1 ×10^-10 m

Hence;

f = c/λ= 3×10^8/ 1×10^-10

f= 3×10^18 Hz

b) The electromagnetic wave is an x-ray.

(a) The frequency of the electromagnetic radiation is [tex]3\times 10^{18} \ Hz[/tex]

(b)  The electromagnetic radiation is ultra violet ray.

The given parameters;

The frequency of the electromagnetic radiation is calculated as follows;

[tex]c =f \lambda \\\\f = \frac{c}{\lambda} \\\\f = \frac{3\times 10^8}{1\times 10^{-10}} \\\\f = 3\times 10^{18} \ Hz[/tex]

The frequency range of ultra violet ray is between 10¹⁴ to 10¹⁸ m.

Thus, the electromagnetic radiation is ultra violet ray.

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