The half-life of cobalt-60 is 5.26 years. If 50 g are left after 15.8 years, how many
grams were in the original sample?

Answer:

         v₃ = - (3 i ^ + 4 j ^) m / s

v₃ = 5 m / s,  θ = 233º

Explanation:

This is a momentum problem. Let us form a system formed by the three objects so that the forces during the collisions have been internal and the moment is conserved.

Let's start working with the first two objects.  As each object moves in a different direction let's work with the components in an xy coordinate system

X axis

initial instant. Before the shock

       p₀ₓ = m₁ v₁₀ + 0

final instant. After the crash

      p_{fx} = (m1 + m2) vₓ

the moment is preserved

       p₀ₓ = p_{fx}

       m₁ v₀₁ = (m₁ + m₂) vₓ

       vₓ = [tex]\frac{m_1}{m_1+m_2} \ v_{o1}[/tex]

Y axis  

initial instant

       p_{oy} = 0 + m₂ v₀₂

final moment

       p_{fy} = (m₁ + m₂) v_y

the moment is preserved

      p_{oy} = p_{fy}

      m₂ v₀₂ = (m₁ + m₂) v_y

      v_y = [tex]\frac{m_2}{m_1 +m_2 } \ v_{o2}[/tex]

We already have the speed of the set of these two cars, now let's work on this set and vehicle 3

X axis    

initial instant

      p₀ₓ = (m₁ + m₂) vₓ + m₃ v₃ₓ

final instant

      p_{fx} = 0

      p₀ₓ = p_{fx}

      (m₁ + m₂) vₓ + m₃ v₃ₓ = 0

       v₃ₓ = [tex]- \frac{m_1+m_2 }{m_3} \ v_x[/tex]

Y Axis

initial instant

        p_{oy} = (m₁ + m₂) v_y + m₃ v_{3y}

final moment

        p_{fy} = 0

        p_{oy} = p_{fy}

        (m₁ + m₂) v_y + m₃ v_{3y} = 0

        v_{3y} = [tex]- \frac{m_1+m_2}{m_3} \ v_y[/tex]

now we substitute the values ​​of the speeds

       v₃ₓ = [tex]- \frac{m_1+m_2}{m_3} \ \frac{m_1}{m_1+m_2} \ v_{o1}[/tex]  

       v₃ₓ = [tex]- \frac{m_1}{m_3} \ v_{o1}[/tex]

       v_{3y} = [tex]- \frac{m_1+m_2}{m_3} \ \frac{m_2}{m_1+m_2} \ v_{o2}[/tex]

       v_{3y} = [tex]- \frac{m_2}{m_3} \ v_{o2}[/tex]

let's calculate

         v₃ₓ = - ⅓ 9

         v₃ₓ = - 3 m / s

         v_{3y} = - ⅔ 6

         v_{3y} = - 4 m / s

therefore the speed of vehicle 3 is

         v₃ = - (3 i ^ + 4 j ^) m / s

It can also be given in the form of modulus and angles using the Pythagorean theorem

         v₃ = [tex]\sqrt{v_{3x}^2 + v_{3y}^2}[/tex]

          v₃ = [tex]\sqrt{3^2+4^2}[/tex]

          v₃ = 5 m / s

let's use trigonometry for the angle

          tan θ' = [tex]\frac{v_{3y}}{v_{3x}}[/tex]

          θ' = tan⁻¹ (\frac{v_{3y}}{v_{3x}})

          θ' = tan⁻¹ (4/3)

          θ'  = 53º

That the two speeds are negative so this angle is in the third quadrant, measured from the positive side of the x axis

          θ = 180 + θ'

          θ = 180 +53

          θ = 233º

Answer:

a) Longest wavelength is: [tex]\lambda_{1}=2*0.75=1.5\: m[/tex]

b) The frequency associated with this longest wavelength is: [tex]f=86.7\: Hz[/tex]

Explanation:

a)

The wavelength equation of a standing wave is given by:

[tex]\lambda_{n}=\frac{2}{n}L[/tex]

Where:

We use n=1 to find the longest possible wavelength, so we will have:

[tex]\lambda_{1}=2L[/tex]

[tex]\lambda_{1}=2*0.75=1.5\: m[/tex]

b)

The speed of the wave is given by:

[tex]v=f\lambda[/tex]

So we just need to find the f (frequency).

[tex]f=\frac{v}{\lambda}[/tex]

[tex]f=\frac{130}{1.5}[/tex]

[tex]f=86.7\: Hz[/tex]

I hope it helps you!

Answer:

E = K Q / R^2     by Gauss' Law where Q is the  charge enclosed by the surface of revolution and R is the distance from the enclosed charge

Since Q = d 4 pi r^2   where d is the charge density and r the radius of the inner sphere

E = K / R^2 * (4 d pi r^2) = 4 K pi d (r / R)^2 = 4 K pi d * 1/4

E =  9 * 10E9 * 3.14 * 40 * 10E-12 = 1.13 N / C

Answer:

The new velocity of the string is 100 centimeters per second (1 meter per second).

Explanation:

The speed of a wave through a string ([tex]v[/tex]), in meters per second, is defined by the following formula:

[tex]v = \sqrt{\frac{T\cdot L}{m} }[/tex] (1)

Where:

[tex]T[/tex] - Tension, in newtons.

[tex]L[/tex] - Length of the string, in meters.

[tex]m[/tex] - Mass of the string, in kilograms.

The expression for initial and final speeds of the wave are:

Initial speed

[tex]v_{o} = \sqrt{\frac{T_{o}\cdot L_{o}}{m_{o}} }[/tex] (2)

Final speed

[tex]v = \sqrt{\frac{(4\cdot T_{o})\cdot (0.5\cdot L_{o})}{2\cdot m_{o}} }[/tex]

[tex]v = \sqrt{\frac{T_{o}\cdot L_{o}}{m_{o}} }[/tex] (3)

By (2), we conclude that:

[tex]v =v_{o}[/tex]

If we know that [tex]v_{o} = 1\,\frac{m}{s}[/tex], then the new speed of the wave in the string is [tex]v = 1\,\frac{m}{s}[/tex].

Answer:C

Explanation:

I think its c im pretty sure

Answer:

0.525 m

Explanation:

From the question,

In an open pipe,

v = λf................... Equation 1

Where v = speed of sound in the pipe, f = frequency, λ = wave length.

But,

λ = 2l................ Equation 2

Where l = length of the pipe

Substitute equation 2 into equation 1

v = 2lf.............. Equation 3

make l the subject of the equation

l = v/2f............. Equation 4

Given:

v ≈ (331+0.60T) m/s at T = 26°C

v ≈ (331+0.60×26) ≈ 346.6 m/s

f = 330 Hz.

Substitute these values into equation 4

l = 346.6/(2×330)

l = 346.6/660

l = 0.525 m

Hence the length of the pipe is 0.525 m

Answer:

D.

Explanation:

Viscosity is a measure of a fluid resistance to flow. It describes the internal friction of a moving fluid. A fluid with large viscosity resists motion because its molecules makeup gives it a lot of internal friction.

Answer:

B.Volcanism

Explanation:

Cause every time the current wave moves is causes and eruption

Unlike the five big mass extinctions in the geological record, the current wave of extinctions is caused by the Volcanism. Thus, the correct option is B.

A mass extinction event is also known as biotic crisis. It is a widespread and rapid decrease in the biodiversity on the Earth which could be due to various reasons. Such an extinction event is identified by a sharp change or decrease in the diversity and abundance of multicellular organisms in an area.

Past mass extinctions on this planet were caused due to extreme temperature changes, rise or fall in the sea levels and catastrophic events, one-off events like a huge volcano erupting or an asteroid hitting the Earth. The current wave of extinctions is caused by volcanism.

Therefore, the correct option is B.

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Answer:

0.00221 N

Explanation:

Given that,

The charge on the particle, [tex]q=34\mu C[/tex]

The speed of the particle, v = 65.8 m/s (+x direction)

Magnetic field, B = 0.545 T (in +y direction) and 0.828 T in the positive z direction.

The magnetic force is given by the formula as follows :

[tex]F=q(v\times B)[/tex]

Substitute all the values,

[tex]F=34\times 10^{-6}\times (65.8i\times (0.545j+0.828 k))\\\\=34\times 10^{-6}\times (65.8i\times 0.545j +65.8i\times 0.828 k)\\\\=34\times 10^{-6}\times(35.86k +(-54.48j))\\\\=34\times 10^{-6}\times \sqrt{35.86^2+54.48^2} \\\\=0.00221\ N[/tex]

So, the magnitude of the magnetic force on the particle is equal to 0.00221 N.

Answer:

dorsiflexion

Explanation:

To decrease the angle between the anterior surface of the foot and anterior surface of the lower leg is described as: dorsiflexion

Answer:

dorsiflexion

Explanation:

Hope this helps

Answer:

a. I = 30 A

b. E = 1080000 J = 1080 KJ

c. ΔT = 12.86°C

d. Cost = $ 4.32  

Explanation:

a.

The current in the coil is given by Ohm's Law:

[tex]V = IR\\I = \frac{V}{R}[/tex]

where,

I = current = ?

V = Voltage = 120 V

R = Resistance = 4 Ω

Therefore,

[tex]I = \frac{120\ V}{4 \Omega}\\[/tex]

I = 30 A

b.

The energy can be calculated as:

[tex]E = VIt\\E = (120\ V)(30\ A)(5\ min)(\frac{60\ s}{1\ min})\\[/tex]

E = 1080000 J = 1080 KJ

c.

For the increase in the temperature of water:

[tex]E = mC\Delta T\\[/tex]

where,

m = mass of water = 20 kg

C = specific heat of water = 4.2 KJ/kg.°C

Therefore,

[tex]1080\ KJ = (20\ kg)(4.2\ KJ/kg.^oC)\Delta T[/tex]

ΔT = 12.86°C

d.

First, we will calculate the total energy consumed:

[tex]E=(Power)(Time)\\E=VI(Time)\\E = (120\ V)(30\ A)(0.5\ h/d)(30\ d)\\E = 54000\ Wh\\E = 54 KWh[/tex]

Now, for the cost:

[tex]Cost = (Unit\ Cost)(Energy)\\Cost = (\$ 0.08\KWh)(54\ KWh)[/tex]

Cost = $ 4.32

Answer:

tbh i think hes right

Explanation:

The femur would be shortened by 0.0434 cm by a load of 600N.

The total applied force per unit of area is known as the pressure.

The pressure depends both on externally applied force as well the area on which it is applied.

The mathematical expression for the pressure

Pressure = Force /Area

As given in the problem assume the femur has a diameter of 3.0cm and a hollow center of 0.8cm diameter and a length of 50cm.if it is supporting a load of 600N,

The stress in the femur = force /area

                                       =600 / π(.004²-.0015²)

                                        = 13.89 ×10⁶ Pa

The length reduced by the load = PL/AE

                                                      = 13.89 ×10⁶ ×50/ 16 × 10⁹ cm

                                                       =0.0434 cm

The femur would be shortened by 0.0434 cm by a load of 600N.

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Answer:

In a third class lever, the effort is located between the load and the fulcrum. ... If the fulcrum is closer to the effort, then the load will move a greater distance. A pair of tweezers, swinging a baseball bat or using your arm to lift something are examples of third class levers.

Explanation:

Answer:

Semi-centrifugal clutches are used in high powered race cars, to reduce the driver effort. Working is just like semi-centrifugal clutch.

The clutch action is purely under centrifugal force.

At low engine rpm the centrifugal force is low, so there is slip, as engine rpm increases, so does the centrifugal force.

Explanation:

a hot toothbrush. ......lol

Answer:

Potential energy only occurs when an object is in motion.

Explanation:

Energy can be defined as the ability (capacity) to do work. The two (2) main types of energy are;

a. Kinetic energy (K.E): it is an energy possessed by an object or body due to its motion.

Mathematically, kinetic energy is given by the formula;

[tex] K.E = \frac{1}{2}MV^{2}[/tex]

Where;

K.E represents kinetic energy measured in Joules.

M represents mass measured in kilograms.

V represents velocity measured in metres per seconds square.

b. Potential energy (P.E): it is an energy possessed by an object or body due to its position above the earth.

Mathematically, potential energy is given by the formula;

[tex] P.E = mgh[/tex]

Where,

P.E represents potential energy measured in Joules.

m represents the mass of an object.

g represents acceleration due to gravity measured in meters per seconds square.

h represents the height measured in meters.

Additionally, the mechanical energy of a physical object or body is the sum of the potential energy and kinetic energy possessed by the object or body.

Mathematically, it is given by the formula;

Mechanical energy = P.E + K.E

Answer:

The angular speed of the blade is of 166.67 rad/min

If a radial saw has a blade with a 9-in. radius. Suppose that the blade spins at 1000 rpm then the angular speed of the blade would be 104.72 rad/seconds.

The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object. The unit of speed is a meter/second. The generally considered unit for speed is a meter per second.

The mathematical expression for speed is given by

speed = total distance /Total time

As given in the problem If a radial saw has a blade with a 9-in. radius. Suppose that the blade spins at 1000 rpm then we have to find the angular speed of the blade,

the angular speed of the blade (ω) = 2πN/60

                                                          =2×π×1000/60

                                                          = 104.72 rad/seconds

Thus, the angular speed of the radial saw would be 104.72 rad/seconds

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Answer:

I1 = ε/R1

I2 = ε/R2

I3 = ε/R3

Explanation:

From the image, we see that the resistors are connected in parallel. This means that the voltage passing through them is the same.

Now, formula for current is; I = V/R

In this case, V which is voltage is denoted by ε.

Thus;

I1 = ε/R1

I2 = ε/R2

I3 = ε/R3

An electron particle needs to be added to this equation to show that the total number of neutrons and protons is not changed by the reaction.

Tritium has nearly the same chemical characteristics as regular hydrogen. It produces helium-3 by releasing a beta particle and decaying with a half-life of 12 years.

Tritium breaks down into helium by producing a beta particle. The discharge of radiation during this decay process raises questions regarding tritium's and other radioactive compounds' safety.

The radiation produced by tritium decay is in the form of low-energy beta particles.

The chemical equation representation during the tritium decay is;

₁H³→₂He³+₋₁e⁰

The particle needs to be added to this equation to show that the total number of neutrons and protons are not changed by the reaction will be an electron.

Hence option D is correct.

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Answer: long pipe is used to increase torque and reduce force needed.

Explanation: A torque is needed to open bolt. torque = F·r, if

R increases, Force F needed to open bold is smaller.

Problem is a worn bolt may break down. It sometimes I send useful to heat bolt instead using too much power.

Answer:

It's important

Explanation:

Mental wellness is critical to overall physical health. Participating in recreational activities helps manage stress. Taking time to nurture oneself provides a sense of balance and self-esteem, which can directly reduce anxiety and depression.

Answer:

Mental wellness is critical to overall physical health. Participating in recreational activities helps manage stress. Taking time to nurture oneself provides a sense of balance and self-esteem, which can directly reduce anxiety and depression.

Explanation:

Answer:

Explanation:

It is better to say “It is correct.” The word THIS is a demonstrative pronoun. The word THIS should be used to point out or to indicate the things. The word CORRECT is an abstract noun therefore it can not be pointed out this is why it is better to say IT IS CORRECT.

Answer:

The correct answer is "3899.92 N".

Explanation:

The given values are:

Force,

[tex]F_{app}=58 N[/tex]

Ratio,

[tex]\frac{R_2}{R_1}=8.2[/tex]

As we know,

Area, [tex]A=\pi r^2[/tex]

or,

⇒  [tex]\frac{F_2}{F_1} =\frac{A_2}{A_1}[/tex]

On substituting the value of "A", we get

⇒  [tex]\frac{F_2}{F_1} =\frac{\pi r_2^2}{\pi r_1^2}[/tex]

⇒  [tex]\frac{F_2}{F_1} =\frac{r_2^2}{r_1^2}[/tex]

On applying cross-multiplication, we get

⇒  [tex]F_2=F_1\times (\frac{r_2}{r_1} )^2[/tex]

On substituting the given values, we get

⇒       [tex]=58\times (8.2)^2[/tex]

⇒       [tex]=58\times 67.2[/tex]

⇒       [tex]=3899.92 \ N[/tex]