Describe an experiment to find the density of copper turning using a density bottle and kerosene

Answer:

C. 2666W

Explanation:

m =200kg

h =20m

t =15s

g =10ms^-2

p = mgt/t

=200×20×10/15

=40,000/15

=2666.6

≈2666W

Answer:

a camera employs camera lens to firm some images.

Explanation:

hope this helps.

Answer:

  r = 2,026 10⁹ m  and   T = 2.027 10⁴ s

Explanation:

For this exercise let's use Newton's second law

        F = m a

where the force is electric

        F = [tex]k \frac{q_1q_2}{r^2}[/tex]

Acceleration is centripetal

        a = v² / r

we substitute

        [tex]k \frac{q_1q_2}{r^2} = m \frac{v^2}{r}[/tex]

        r = [tex]k \frac{q_1q_2}{m \ v^2}[/tex]          (1)

let's look for the charge in the insulating sphere

          ρ = q₂ / V

          q₂ = ρ V

the volume of the sphere is

         v = 4/3 π r³

we substitute

        q₂ = ρ [tex]\frac{4}{3}[/tex] π r³

        q₂ = 3 10⁻⁹ [tex]\frac{4}{3}[/tex] π 4³

        q₂ = 8.04 10⁻⁷ C

let's calculate the radius with equation 1

        r = 9 10⁹  1.6 10⁻¹⁹  8.04 10⁻⁷ /(9.1  10⁻³¹ 628 10³)

        r = 2,026 10⁹ m

this is the radius of the electron orbit around the charged sphere.

Since the orbit is circulating, the speed (speed modulus) is constant, we can use the uniform motion ratio

        v = x / t

the distance traveled in a circle is

        x = 2π r

In this case, time is the period

        v = 2π r /T

        T = 2π r /v

let's calculate

        T = 2π 2,026 10⁹/628 103

        T = 2.027 10⁴ s

Answer:

B) (80m/s/s)(70kg)=5600N + Fg = 5600N+(70kg)(9.8N/kg)~5600N+700N=6300N

Explanation:

The total force by the chair is given by the following formula:

[tex]F = m(g+a)[/tex]

where,

F = Force = ?

m = mass of person = 70 kg

g = value of acceleration dueto gravity = 9.81 m/s²

a = acceleration of ejection seat = 8g = 80 m/s²

Therefore,

[tex]F = mg+ma \\F = (70\ kg)(9.8\ m/s^2)+(70\ kg)(80\ m/s^2)\\F = 6300 N[/tex]

Therefore, the correct option is:

B) (80m/s/s)(70kg)=5600N + Fg = 5600N+(70kg (9.8N/kg)~5600N+700N=6300N

Answer:

the electric potential difference between the point at the center of the ring and a point on its axis ΔV is [tex]( 0.8356 )[/tex][tex]\frac{kQ}{R}[/tex]

Explanation:

Given the data in the question;

electric potential at the center of the ring V₀ = kQ / R

electric potential on the axis point Vr = kQ / √( R² + x² )

at a distance 6R from the center,

point at x = 6R

so distance circumference r = √( R² + (6R)² )

so

electric potential on the axis point Vr = kQ / √( R² + (6R)² )

Vr = kQ / R√37

Now

ΔV = V₀ - Vr

we substitute

ΔV = ( kQ / R) - ( kQ / R√37 )

ΔV =  kQ/R( 1 - 1/√37 )

ΔV =  kQ/R( 1 - 0.164398987 )

ΔV =  kQ/R( 0.8356 )

ΔV = [tex]( 0.8356 )[/tex][tex]\frac{kQ}{R}[/tex]       { where k = [tex]\frac{1}{4\pi e_0}[/tex] }

Therefore, the electric potential difference between the point at the center of the ring and a point on its axis ΔV is [tex]( 0.8356 )[/tex][tex]\frac{kQ}{R}[/tex]

Answer:

C. while the magnet is moving

Explanation:

Electromagnetic induction implies the production of electric current by mere movement of a magnet with respect to a coil or wire.

In the given question, current would be induced in the wire only when the magnet moves. That is either when the magnet is pushed into a wire, or when pulled out. But no current would flow through the wire when the magnet is left there for a while.

The current is induced because of the motion involved. Thus, the appropriate option is C.

Answer:

a. keeps its speed for a short while, then slows and stops. slows steadily until it stops.

Explanation:

Since the tension in the rope, t is greater than the kinetic friction fk, the box is moving forward because there is a net force on it. That is, t - fk = f = ma.

Since there is a net force, there is an acceleration and thus an increasing velocity.

When the rope breaks, the tension, t = 0. So, t - fk = 0 - fk = -fk = ma'.

Now, the net force acting on the box is friction in the opposite direction. This force tends to slow the box down from its initial velocity at acceleration, 'a' until its velocity is zero, where it stops. Since the frictional force is constant, the acceleration, a' on the box is thus constant and the box undergoes uniform deceleration until its velocity is zero.

So, the box keeps its speed for a short while, then slows and stops. slows steadily until it stops.

So, the answer is a.

Answer:

the horizontal component of the force is 50 N

Explanation:

Given;

force applied by the man, F = 100 N

angle of inclination of the force, θ = 60⁰

mass of the dog, m = 20 kg

The horizontal component of the force is calculated as;

[tex]F_x = F\times cos(\theta)\\\\F_x = 100 \ N \times cos(60^0)\\\\F_x = 100\ N \times 0.5\\\\F_x = 50 \ N[/tex]

Therefore, the horizontal component of the force is 50 N

Answer:

C) 1.4W

Explanation:

Given;

energy of the battery, E = 10,000 J

duration of the battery, t = 2 hours

The power consumption of the battery is calculated as;

[tex]Power = \frac{Energy}{time} \\\\Power = \frac{10,000}{2 \times 3600 } \\\\Power = 1.4 \ J/s = 1.4 \ W[/tex]

Therefore, the power consumption of the battery is 1.4 W

Answer:

T = 20.84°C

Explanation:

From the law of conservation of energy:

Heat Lost by Copper Block = Heat Gained by Aluminum Calorimeter + Heat Gained by Water

[tex]m_cC_c\Delta T_c = m_wC_w\Delta T_w + m_aC_a\Delta T_a[/tex]

where,

[tex]m_c[/tex] = mass of copper = 227 g

[tex]m_w[/tex] = mass of water = 844 g

[tex]m_a[/tex] = mass of aluminum = 155 g

[tex]C_c[/tex] = specific heat capacity of calorimeter = 385 J/kg.°C

[tex]C_w[/tex] = specific heat capacity of water = 4200 J/kg.°C

[tex]C_a[/tex] = specific heat capacity of aluminum = 890 J/kg.°C

[tex]\Delta T_c[/tex] = change in temperature of copper = 283°C - T

[tex]\Delta T_w[/tex] = change in temperature of water = T - 14.6°C

[tex]\Delta T_a[/tex] = change in temperature of aluminum = T - 14.6°C

T = equilibrium temperature = ?

Therefore,

[tex](227\ g)(385\ J/kg.^oC)(283^oC-T)=(844\ g)(4200\ J/kg.^oC)(T-14.6^oC)+(155\ g)(890\ J/kg.^oC)(T-14.6^oC)\\\\24732785\ J - (87395\ J/^oC) T = (3544800\ J/^oC) T - 51754080\ J+ (137950\ J/^oC) T-2014070\ J\\\\24732785\ J +51754080\ J+2014070\ J = (3544800\ J/^oC) T+(137950\ J/^oC+(87395\ J/^oC) T\\\\78560935\ J = (3770145\ J/^oC) T\\\\T = \frac{78560935\ J}{3770145\ J/^oC}[/tex]

T = 20.84°C

Answer:

NO, 1. is stocks

2. is also stocks

bouquit GARNI IS NUMBER 3

NUMBER 4 IS ACID PRODUCTS

number 5 is brown stock

Explanation:

stocks are bones

Answer:

the electric field is  3.91 x 10⁶ N/C

Explanation:

Given the data in the question;

Electric field at a point due to point charge is;

E = kq/r²

where k is the constant, r is the distance from centre of terminal to point where electric field is, q is the excess charge placed on the centre of terminal of Van de Graff,a generator

Now, given that r = 3.9 m, k = 9.0 x 10⁹ Nm²/C², q = 6.60 mC = 6.60 x 10⁻³ C

so we substitute into the formula

E = [(9.0 x 10⁹ Nm²/C²)( 6.60 x 10⁻³ C)] / ( 3.9 )²

E = 59400000 / 15.21

E = 3.91 x 10⁶ N/C

Therefore, the electric field is  3.91 x 10⁶ N/C

Answer:

22.36 rad

Explanation:

Applying,

ω = θ/t.............. Equation 1

Where ω  = angular velocity, θ = angular displacement of the baseball, t = time

make θ the subject of the equation

θ = ωt............... Equation 2

From the question,

Given: ω = 350 rev/min = 350(0.10472) = 36.652 rad/s, t = 0.61 s

Substitute these values into equation 1

θ = 0.61(36.652)

θ = 22.36 rad

Hence the angular displacement of the baseball is  22.36 rad

Answer:

7.51

Explanation:

The mass of the bat is given to us as:

m = 0.277  kg

,

and its initial velocity is:

v

i  = 4.25  m/s

When the velocity is doubled, the new value becomes:

v f = 4.25 m/s × 2 = 8.5   m/s

.

The formula for kinetic energy is:

K

=

1

2

m

v

2

.

The change in kinetic energy is:

Δ K = 1 /2( m ) ( v2 f − v 2 i ) = 1 2 ( 0.277)

10-2.5=7.5J

7.51  J

.

The bat gained 7.51 joules.

Answer:

a. El peso = 686 Newton

b. El peso = 113.4 Newton

Explanation:

Dados los siguientes datos;

Masa = 70 kg

Aceleración debida a la gravedad en la luna = 1,62 m/s² una.

a. Para encontrar la fuerza-peso en la Tierra;

Sabemos que la aceleración debida a la gravedad es igual a 9,8 m/s² en el planeta Tierra.

El peso se puede definir como la fuerza que actúa sobre un cuerpo o un objeto como resultado de la gravedad.

Matemáticamente, el peso de un objeto viene dado por la fórmula;

[tex] Peso = mg [/tex]

Dónde;

m es la masa del objeto.

g es la aceleración debida a la gravedad.

Substituting into the formula, we have;

El peso = 70 * 9.8

El peso = 686 Newton

b. To find weight on moon;

Weight = mass * acceleration due to gravity on moon

Weight = 70 * 1.62

Weight = 113.4 Newton

Answer:

157n is the correct answer

Answer:

The net field will be the sum of the fields created by each charge.

where the charge Q in a position r' is given by:

E(r) = k*Q/(r - r')^2

Where k is a constant, and r is the point where we are calculating the electric field.

Then for the charge 3q, in the position r₁ = (-d, 0, 0) the electric field will be:

E₁(r) = k*3q/(r - r₁)^2

While for the other charge of -2q in the position r₂ = (d, 0, 0)

The electric field is:

E₂(r) = -k*2*q/(r - r₂)^2

Then the net field at the point r is:

E(r) = E₁(r) + E₂(r) = k*3q/(r - r₁)^2 + -k*2*q/(r - r₂)^2

E(r) = k*q*( 3/(r - r₁)^2 - 2/(r - r₂)^2)

Then if the we want to find the points r = (x, y, z) such that:

E(r) = 0 = k*q*( 3/(r - r₁)^2 - -k*2*q/(r - r₂)^2)

Then we must have:

0 = ( 3/(r - r₁)^2 - 2/(r - r₂)^2)

Also remember that the distance between two points:

(x, y, z) and (x', y', z') is given by:

D = √( (x - x')^2 + (y - y)^2 + (z -z')^2)

Then we can rewrite:

r - r₁ = √( (x - (-d))^2 + (y - 0 )^2 + (z -0)^2)

       = √( (x + d))^2 + y^2 + z^2)

and

r - r₂ =  √( (x - d)^2 + (y - 0 )^2 + (z -0)^2)

       = √( (x - d))^2 + y^2 + z^2)

Replacing that in our equation we get:

0 = ( 3/(√( (x + d))^2 + y^2 + z^2))^2 - -k*2*q/(√( (x - d))^2 + y^2 + z^2))^2)

0 = (3/((x + d))^2 + y^2 + z^2) - 2/ (x - d))^2 + y^2 + z^2)

We want to find the values of x, y, z such that the above equation is true.

2/ (x - d))^2 + y^2 + z^2) = (3/((x + d))^2 + y^2 + z^2)

2*[((x + d))^2 + y^2 + z^2] = 3*[(x - d))^2 + y^2 + z^2]

2*(x + d)^2  + 2*y^2 + 2*z^2 = 3*(x - d)^2 + 3*y^2 + 3*z^2

2*(x + d)^2 - 3*(x - d)^2 =  3*y^2 + 3*z^2 -  2*y^2 - 2*z^2

2*(x + d)^2 - 3*(x - d)^2  = y^2 + z^2

2*x^2 + 2*2*x*d + 2*d^2 -  3*x^2 + 3*2*x*d - 3*d^2 = y^2 + z^2

-x^2 + 10*x*d - d^2 = y^2 + z^2

we can rewrite this as:

- ( x^2 - 10*x*d + d^2) =  y^2 + z^2

now we can add and subtract 24*d^2 inside the parenthesis to get

- ( x^2 - 10*x*d + d^2 + 24*d^2 - 24*d^2) =  y^2 + z^2

-( x^2 - 2*x*(5d) + 25d^2 - 24d^2) = y^2 + z^2

-(x^2 - 2*x*(5d) + (5*d)^2) + 24d^2 = y^2 + z^2

The thing inside the parenthesis is a perfect square:

-(x - 5d)^2 + 24d^2 = y^2 + z^2

we can rewrite this as:

24d^2 = y^2 + z^2 + (x - 5d)^2

This equation gives us the points (x, y, z) such that the electric field is zero.

Where we need to replace two of these values to find the other, for example, if y = z = 0

24d^2 = (x - 5d)^2

√(24d^2)  = x - 5d

√24*d = x - 5d

√24*d + 5d = x

so in the point (√24*d + 5d, 0, 0) the net field is zero.

Answer: I'd go with Option B if you're allowed to pick One Option Only.

Option A is wrong. Electric Forces arent Non - Conservative. They're Conservative forces.

Option B: We Can Only Define Potential Energies for conservative Forces/fields✅

Option C is wrong. Since the Electric Force is Conservative... It doesn't depend on the path taken.

Option D... There's a Point where the electric Potential Energy is Zero but the separation Distance Would be large.

E is wrong because the Workdone around a closed path is Zero.

The electric potential energy results from the conservative Coulomb forces.

The electric potential energy is the potential energy that results due to the conservative Coulomb forces and is always associated with the set of two charged particles.

Any object can have electric potential energy by two key elements first is its own charge and the second is its position with respect to the other charged particle.

The electric potential energy-containing only one point charge will be zero. Because there are no other sources of electrostatic force against which an external agent must do work in moving the point charge from infinity to its final position.

Thus the electric potential energy results from the conservative Coulomb forces.

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Answer:

belpw

Explanation:

The distance prior to the sliding friction dispersing her energy would be:

- The distance will remain unaffected by the sliding friction i.e. 354m

As we know, When Sliding friction dissolves her energy, leading her Kinetic Energy to turn 0 on coming to the state of rest. So,

[tex]1/2 mv^2 - 1/2 mu^2 = -W[/tex]            (∵ Work in -ve denotes it is done opposite to friction)

Given that,

m(mass) [tex]= 50 kg[/tex]

v(velocity) [tex]= 30 km/hr[/tex] or [tex]8.33 m/s[/tex]

The coefficient of Kinetic Friction [tex]= 0.01[/tex]

g(gravitational force) [tex]= 9.8 m/s^2[/tex]

Initial Velocity(u) [tex]= 30[/tex] × [tex]1000/3600 m/s[/tex]

[tex]= 8.33 m/s[/tex]

Now by employing the provided values,

[tex]F =[/tex] μ[tex]mg[/tex]

[tex]= (0.01) (50) (9.8)[/tex]

[tex]= 4.9[/tex]

∵ [tex]F = 4.9 N[/tex]

By using the above expression, we will find the distance;

[tex]1/2 mv^2 - 1/2 mu^2 = -W[/tex]

⇒ [tex]1/2 (50) (0)^2 - 1/2 (50) (8.33)^2 = -4.9(S)[/tex]

⇒ [tex]1734.7225 = 4.9S[/tex]

⇒ [tex]S = 1734.7225/4.9[/tex]

∵ [tex]S = 354 m[/tex]

Because [tex]1/2 mv^2 - 1/2 mu^2 = -W[/tex]  [tex]= -[/tex] μmgS

⇒ [tex]S = (u^2 - v^2)[/tex]/2μ[tex]g[/tex]

Thus, the distance will remain unaffected by the sliding friction i.e. 354m

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Answer: [tex]68.75\ kg, 0.06[/tex]

Explanation:

Mary applies a force of 73 N to create an acceleration of [tex]0.48\ m/s^2[/tex]

When She increases force to 84 N, it creates an acceleration of [tex]0.64\ m/s^2[/tex]

Friction opposes the motion of box

[tex]\Rightarrow 73-f=m\times 0.48\quad \ldots(i)\\\Rightarrow 84-f=m\times 0.64\quad \ldots(ii)[/tex]

Subtract (i) from (ii)

[tex]\Rightarrow 11=m(0.64-0.48)\\\Rightarrow m=68.75\ kg[/tex]

Therefore friction is

[tex]\Rightarrow f=73-68.75\times 0.48\\\Rightarrow f=73-33\\\Rightarrow f=40\ N[/tex]

Here, friction is kinetic friction which is given by

[tex]\Rightarrow f=\mu_kmg\\\Rightarrow 40=\mu_k 68.75\times 9.8\\\Rightarrow \mu_k=0.061[/tex]

Answer:

The ceramic tile will stand the force of 5 N.

Explanation:

Step 1: Calculate the area (A) of the ceramic tile

We will use the formula for the area of a square.

A = 50 cm × 50 cm = 2500 cm²

Step 2: Convert "A" to in²

We will use the conversion factor 1 in² = 6.45 cm².

2500 cm² × 1 in²/6.45 cm² = 3.9 × 10² in²

Step 3: Calculate the pressure (P) exerted by a force (F) of 5 N

We will use the following expression.

P = F/A

P = 5 N / 3.9 × 10² in² = 0.013 N/in²

Since the pressure exerted would be less than the maximum pressure resisted (40 N/in²), the ceramic tile will stand the force of 5 N.

Answer:

Newton's third law states that for every action, there is an equal and opposite reaction. That means when you exert a force on an object, the object exerts a force back on you. ... Using shock-absorbing materials can help reduce the amount of force exchanged between the ground and the egg.

Explanation:

I hope it helps you

When one of the tall straws hits the ground, the energy is transferred to the center of the pyramid and then to the egg, but as the middle straw is connected to the outer surface of the egg, energy enters trying to make the egg rotate. This is governed by Newton's third law.

If an object exerts a force on another object, then another object must exert a force of equal magnitude and opposite direction back on first object.

Examples of Newton's third law are:

A swimmer moves forward by pushing off the side of pool. This way, the wall pushes in opposite direction and giving acceleration.

Another example is rockets move forward by expelling gas backward at high velocity. This means the rocket exerts a large backward force on the gas in the rocket combustion chamber, and the gas therefore exerts a large reaction force forward on the rocket. This reaction force is called thrust.

Helicopters similarly create lift by pushing air down, thereby experiencing an upward reaction force. Birds and airplanes also fly by exerting force on air in a direction opposite to that of whatever force they need. For example, the wings of a bird force air downward and backward in order to get lift and forward motion.

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Answer:

Option C

Explanation:

C. Convection...

The phrase 'hot air rises'describe the convection as a type of heat transfer therefore the correct answer is option C.

It is the type of  heat transfer in which the heat is transferred from the bulk motion of the particles of liquid and gases due to the presence of temperature gradient.
The hot air rises is one of the best example of convection currents
The boiling water is also an example of convection heat transfer process in which the hot water rises to the top of the surface due to the bulk molecular movement of convection current .

The hot air rides is the bulk movement of the gas molecules because of the presence of the temperature gradients resulting in the varied density of air ,the hot air rising to the surface have less density as compared to the air settling near the surface ,the convection current phenomenon is responsible for the phrase  "hot air rises" ,therefore the correct option is the option C.

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Answer:

the mass of the car is 890 kg

Explanation:

Given;

mass of the man, m = 92 kg

displacement of the car's spring, x = 4.5 cm = 0.045 m

acceleration due to gravity, g = 9.8 m/s²

The spring constant of the car,

f = kx

where;

f is the weight of the man on the car = mg

mg = kx

k = mg/x

k = (92 x 9.8) / 0.045

k = 20,035.56 N/m

The angular speed of car, ω, when the is inside is given as 4.52 rad/s

The total mass of the car and the man is calculated as;

[tex]\omega = \sqrt{\frac{k}{m} } \\\\\omega^2 = \frac{k}{m} \\\\m = \frac{k}{\omega^2} = \frac{20,035.56}{(4.52)^2} = 980.7 \ kg[/tex]

The mass of the car alone = 980.7 kg - 92 kg

                                            = 888.7 kg

                                             ≅ 890 kg

Therefore, the mass of the car is 890 kg

Answer:

Stars emit colors of many different wavelengths, but the wavelength of light where a star's emission is concentrated is related to the star's temperature - the hotter the star, the more blue it is; the cooler the star, the more red it is

Answer:

Stars emit colors of many different wavelengths, but the wavelength of light where a star's emission is concentrated is related to the star's temperature – the hotter the star, the more blue it is; the cooler the star, the more red it is.

Explanation:

Pa brainliest po ty

The voltage across the element is = 240 V

I hope you understand....

Mark me as brainliest....

Thanks...

Explanation:

It is known that charges tend to move from a higher potential towards lower potential. As a result, charges tend to move from a positive terminal to negative terminal of the battery.

For example, at a certain height water is stored in a water tank. This height is correspondent to the constant potential and water contained is the charge present in the battery.

When a pipe is connected from the tank to the ground then water will start moving towards the ground and similarly if a conducting wire is connected across the battery then charge will also begin to flow in the same direction which is called current.

Answer:

1. 5.825 × 10¹⁷ J

2. i. $ 29.125 billion ii. I would not invest in the company

3. A nuclear reaction would occur if the payload hits an airplane flying overhead and dissipates all its kinetic energy in the collision.

4. a i. The momentum will not be relativistic

ii. This is because objects with large masses do not move at relativistic speeds

b i. 155 m/s

ii. This speed wouldn't be a problem for the ship.

Explanation:

1.  A typical payload they claim to launch will weigh 1 kilogram and be accelerated to 90% the speed of light. How much electrical energy will the rail gun require to launch the probe, assuming it is 20% efficient at converting electrical energy to projectile kinetic energy?

The kinetic energy of the payload is K = (γ - 1)mc² where m = mass of payload = 1 kg, c = speed of light = 3 × 10⁸ m/s and γ = 1/√(1 - β²) where β = 0.9 (since the payload moves at 90 % speed of light)

So, K = (γ - 1)mc²

= (1/√(1 - β²) - 1)mc²

= (1/√(1 - (0.9)²) - 1) × 1 kg × (3 × 10⁸ m/s)²

= (1/√(1 - 0.81) - 1) × 1 kg × (3 × 10⁸ m/s)²

= (1/√0.19 - 1) × 1 kg × (3 × 10⁸ m/s)²

= (1/0.436 - 1) × 1 kg × (3 × 10⁸ m/s)²

= (2.294 - 1) × 1 kg × (3 × 10⁸ m/s)²

= 1.294 × 1 kg × 9 × 10¹⁶ m²/s²

= 11.65 × 10¹⁶ kgm²/s²

= 1.165 × 10¹⁷ J

Let E be the total electrical energy of the rail gun. Since 20 % of this energy is converted to kinetic energy of the payload, we have

20 % of E = K

0.2E = K

E = K/0.2

= 1.165 × 10¹⁷ J/0.2

= 5.825 × 10¹⁷ J

2 Given that typical electrical costs are about 5 cents/MJ, how much would this launch cost? Would you invest in this company?

i. how much would this launch cost?

Since the total energy required is E = 5.825 × 10¹⁷ J = 5.825 × 10¹¹ MJ and it costs 5 cent/MJ. So the total cost of energy will be total energy rate = 5.825 × 10¹¹ MJ × 5 cent/MJ = 29.125 × 10¹¹ = 2.9125 × 10¹² cents. Converting this to dollars, we have 2.9125 × 10¹² cents/100 cents/dollar = 2.9125 × 10¹⁰ dollars = 29.125 × 10⁹ dollars = 29.125 billion dollars = $ 29.125 billion

ii. Would you invest in this company?

I would not invest in the company

3. You are also concerned about safety. What happens if this projectile were to hit an airplane that is flying overhead and dissipate all of its kinetic energy in the collision? To give you a sense of scale, a large nuclear explosion generates about 1015 J of energy.

Since the kinetic energy of the payload is 1.165 × 10¹⁷ J and a nuclear explosion generates about 10¹⁵ J of energy,  then a nuclear reaction would occur if the payload hits an airplane flying overhead and dissipates all its kinetic energy in the collision.

4. The system must be able to launch probes to all parts in the sky and must be transportable on a ship. Assume that the rail gun is mounted on a frigate-class navy ship (weight = 4,000 metric tons).

a. Will the recoil momentum of the ship be relativistic? Justify your argument.

i. Will the recoil momentum of the ship be relativistic?

The momentum will not be relativistic.

ii. Justify your argument.

This is because objects with large masses do not move at relativistic speeds. Since the speed cannot be relativistic, its momentum which is the product of mass and speed is non-relativistic

b. At what speed will the ship recoil after it launches a probe? Do you think that this is a problem for the ship?

i. At what speed will the ship recoil after it launches a probe?

Since the total energy of the payload E' = K + mc² = 1.165 × 10¹⁷ J + 1 kg × (3 × 10⁸ m/s)² = 1.165 × 10¹⁷ J + 1 kg × 9 × 10¹⁶ m²/s² = 11.65 × 10¹⁶ J + 9 × 10¹⁶ J = 20.65 × 10¹⁶ J

Also, E'² = (pc)² + (mc²)² where p = momentum of payload

So, making p subject of the formula, we have

(pc)² = E'² - (mc²)²

pc = √[E'² - (mc²)²]

p = √[E'² - (mc²)²]/c

substituting the values of the variables into the equation, we have

p = √[E'² - (mc²)²]/c

p = √[(20.65 × 10¹⁶ J)² - 1kg × (3 × 10⁸ m/s²)²]/3 × 10⁸ m/s

p = √[(20.65 × 10¹⁶ J)² - (1kg × 9 × 10⁸ m²/s²)²]/3 × 10⁸ m/s

p = √[426.4225 × 10³² J² - 81 × 10³² J²]/3 × 10⁸ m/s

p = √[345.4225 × 10³² J²]/3 × 10⁸ m/s

p = 18.59 × 10¹⁶/3 × 10⁸ m/s

p = 6.20 × 10⁸ kgm/s

From the law of conservation, this momentum of the payload equals the momentum of recoil of the ship.

So, p = m'v where m' = mass of navy ship = 4,000 metric tons = 4,000 × 1000 kg = 4 × 10⁶ kg and v = speed of navy ship

So, v = p/m'

= 6.20 × 10⁸ kgm/s ÷ 4 × 10⁶ kg

= 1.55 × 10² m/s

= 155 m/s

ii. Do you think that this is a problem for the ship?

Since the ship's speed is 155 m/s, which is small for an object with such a large mass, this speed wouldn't be a problem for the ship.

Answer:

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