The liquid emerges into a vertical jet as it drains from the container, with the velocity profile in the jet remaining uniform. The outlet of the container is located 2.0 m above ground, and the radius of the emerging liquid jet changes with vertical distance from the bottom of the container as it accelerates under the action of gravity. Neglecting viscous losses and surface tension effects in the liquid jet, what is the velocity of the water jet as it strikes the ground when the container begins to drain

Answer:

a. The wooden cylinder b. the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.

Explanation:

a. Who reaches the bottom first

The kinetic energy of the objects is given by

K = 1/2mv² + 1/2Iω² where m = mass of object, v = velocity of object, I = moment of inertia and ω = angular velocity = v/r where r = radius of object

For the wooden cylinder, I = mr²/2 where m = mass of wooden cylinder and r = radius of wooden cylinder and v = velocity of wooden cylinder

So, its kinetic energy, K = 1/2mv² + 1/2(mr²/2)(v/r)²

K = 1/2mv² + 1/4mv²

K = 3mv²/4

For the steel hoop, I' = mr'² where m' = mass of steel hoop and r' = radius of steel hoop and v' = velocity of steel hoop

So, its kinetic energy, K' = 1/2m'v'² + 1/2(m'r'²)(v'/r')²

K' = 1/2m'v'² + 1/2m'v'²

K' = m'v'²

Since both kinetic energies are the same, since the drop from the same height,

K = K'

3mv²/4 = m'v'²

v²/v'² = 4m/3m'

v²/v'² = 4/3(m/m')

v/v' = √[4/3(m/m')]

Since the hoop weighs more than the cylinder m/m' < 1 and 4/3(m/m') < 4/3 ⇒ √ [4/3(m/m')] < √4/3 ⇒ v/v' < 1.16 ⇒ v'/v > 1/1.16 ⇒ v'/v > 0.866. Since 0.866 < 1, it implies v' < v.

Since v' = speed of steel hoop < v = speed of wooden cylinder, the wooden cylinder reaches the bottom first.

b. Why

Since the kinetic energy, K = translational + rotational

We find the translational kinetic energy of each object.

For the wooden cylinder,

K = K₀ + 1/2Iω² where K₀ = translational kinetic energy of wooden cylinder

K - 1/2Iω² = K₀

3/4mv² - 1/2(mr²/2)(v/r)² = K₀

3/4mv² - 1/4mv² = K₀

K₀ = 1/2mv²

For the steel hoop,

K' = K₁ + 1/2I'ω'² where K₁ = translational kinetic energy of steel hoop

K' - 1/2I'ω'² = K₁

m'v'² - 1/2(m'r'²)(v'/r')² = K₁

m'v'² - 1/2m'v'² = K₁

K₁ = 1/2m'v'²

So, K₀/K₁ =  1/2mv²÷1/2m'v'² = mv²/m'v'² = (m/m')(v²/v'²) = (m/m')4/3(m/m') = 4/3(m/m')².

Since (m/m') < 1 ⇒  (m/m')² < 1 ⇒ 4/3(m/m')² < 4/3 ⇒ K₀/K₁  < 1.33 ⇒ K₀ > K₁

So, the kinetic energy of the wooden cylinder is greater than that of the steel hoop.

So, the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.

a. The wooden cylinder b. the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.

The energy of the body due to its movement in a particular direction under the influence of a force like a free-falling body due to gravitaional force is called  Kinetic energy.

The kinetic energy of the objects is given by

[tex]K = \dfrac{1}{2}mv^2 + \dfrac{1}{2}Iw^2[/tex]

where

m = mass of object,

v = velocity of object,

I = moment of inertia and

ω = angular velocity = v/r where r = radius of object

For the wooden cylinder, I = mr²/2 where m = mass of wooden cylinder and r = radius of wooden cylinder and v = velocity of wooden cylinder

So, its kinetic energy,

[tex]K = \dfrac{1}{2}mv^2 + \dfrac{1}{2}(\dfrac{mr^2}{2})\dfrac{v}{r}^2[/tex]

[tex]K = \dfrac{3mv^2}{4}[/tex]

For the steel hoop,

I' = mr'²

where

m' = mass of steel hoop and

r' = radius of steel hoop and

v' = velocity of steel hoop

So, its kinetic energy,

[tex]K' = \dfrac{1}{2}m'v'^2 + \dfrac{1}{2}(m'r'^2)\dfrac{v'}{r'}^2[/tex]

[tex]K' = \dfrac{1}{2}m'v'^2 + \dfrac{1}{2}m'v'^2[/tex]

K' = m'v'²

Since both kinetic energies are the same, since the drop from the same height,

K = K'

[tex]\dfrac{3mv^2}{4 }= m'v'^2[/tex]

[tex]\dfrac{v^2}{v'^2} =\dfrac{ 4m}{3m'}[/tex]

[tex]\dfrac{v^2}{v'^2} = \dfrac{4}{3}(\dfrac{m}{m'})[/tex]

[tex]\dfrac{v}{v'} = \sqrt{[\dfrac{4}{3}(\dfrac{m}{m'})][/tex]

Since the hoop weighs more than the cylinder m/m' < 1 and 4/3(m/m') < 4/3 ⇒ √ [4/3(m/m')] < √4/3 ⇒ v/v' < 1.16 ⇒ v'/v > 1/1.16 ⇒ v'/v > 0.866. Since 0.866 < 1, it implies v' < v.

Since v' = speed of steel hoop < v = speed of wooden cylinder, the wooden cylinder reaches the bottom first.

(b) Since the kinetic energy, K = translational + rotational

We find the translational kinetic energy of each object.

For the wooden cylinder,

[tex]K = K_o + \dfrac{1}{2}Iw^2[/tex]

where

K₀ = translational kinetic energy of wooden cylinder

[tex]K - \dfrac{1}{2}Iw^2 = K_o[/tex]

[tex]\dfrac{3}{4}mv^2 - \dfrac{1}{2}(\dfrac{mr^2}{2})(\dfrac{v}{r})^2 = K_a[/tex]

[tex]\dfrac{3}{4}mv^2 - \dfrac{1}{4}mv^2 = K_o[/tex]

[tex]K_o = \dfrac{1}{2}mv^2[/tex]

For the steel hoop,

[tex]K' = K_1 + \dfrac{1}{2}I'w'^2[/tex]

where

K₁ = translational kinetic energy of steel hoop

[tex]K' - \dfrac{1}{2}I'w'^2 = K_1[/tex]

[tex]m'v'^2 - \dfrac{1}{2}(m'r'^2)(\dfrac{v'}{r'})^2 = K_1[/tex]

[tex]m'v'^2 - \dfrac{1}{2}m'v'^2 = K_1[/tex]

[tex]K_1= \dfrac{1}{2}m'v'^2[/tex]

So, K₀/K₁ =  1/2mv²÷1/2m'v'² = mv²/m'v'² = (m/m')(v²/v'²) = (m/m')4/3(m/m') = 4/3(m/m')².

Since (m/m') < 1 ⇒  (m/m')² < 1 ⇒ 4/3(m/m')² < 4/3 ⇒ K₀/K₁  < 1.33 ⇒ K₀ > K₁

So, the kinetic energy of the wooden cylinder is greater than that of the steel hoop.

So, the wooden cylinder reaches the bottom first because its translational kinetic energy is greater.

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Answer:

3.53×10⁶ N/c due west

Explanation:

From the question

E = F'/q........................ Equation 1

Where E =  Electric Field, F = Net Force, q = Charge.

But,

F' = F₂-F₁...................... Equation 2

Substitute equation 2 into equation 1

E = (F₂-F₁)/q................ Equation 3

Given: F₁ = 3 N due east, F₂ = 15 N due west,  q = 3.4×10⁻⁶ C

Substitute these values into equation 1

E = (15-3)/(3.4×10⁻⁶)

E = 12/(3.4×10⁻⁶)

E = 3.53×10⁶ N/c due west

Answer:

xplanation:

Angle of reflection is measured between the incident ray and the angle which it makes with the normal at the point where incident ray strikes the mirror surface.

Further on reflection, it makes the same angle i.e. angle of reflection is equal to angle of reflection.

Hence, as angle of incidence is 55∘ angle of reflection too is 55∘ and the angle between the incident ray and the reflected ray is 55∘+55∘=110∘

Answer:

Hydraulic fracturing

Explanation:

Answer:

3.67 N

Explanation:

From the question given above, the following data were obtained:

Charge of 1st object (q₁) = +15.5 μC

Charge of 2nd object (q₂) = –7.25 μC

Distance apart (r) = 0.525 m

Force (F) =?

Next, we shall convert micro coulomb (μC) to coulomb (C). This can be obtained as follow:

For the 1st object

1 μC = 1×10¯⁶ C

Therefore,

15.5 μC = 15.5 × 1×10¯⁶

15.5 μC = 15.5×10¯⁶ C

For the 2nd object:

1 μC = 1×10¯⁶ C

Therefore,

–7.25 μC = –7.25 × 1×10¯⁶

–7.25 μC = –7.25×10¯⁶ C

Finally, we shall determine the force. This can be obtained as follow:

Charge of 1st object (q₁) = +15.5×10¯⁶ C

Charge of 2nd object (q₂) = –7.25×10¯⁶ C

Distance apart (r) = 0.525 m

Electrical constant (K) = 9×10⁹ Nm²/C²

Force (F) =?

F = Kq₁q₂ / r²

F = 9×10⁹ × 15.5×10¯⁶ × 7.25×10¯⁶ / 0.525²

F = 3.67 N

Therefore, the force on the object is 3.67 N

Answer:

Role of government in regulating production

Explanation:

The role of government in regulating show , provides the legal and social framework, uphold competition, provides public goods and services.

The community's role in conserving and enhancing common-property resources is well known.

In extra, its role in helping market growth by its power to execute trade agreements among transacting parties belonging to the community network is stressed.

Thus, it provides the legal and social framework, maintains competition, and provides public goods and services.

To learn more about  economics in community click here:

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Answer:

B. There are no forces acting on the ball.

Explanation:

There are no forces acting on the ball.

Answer:

No forces acting upon the ball

Explanation:

newtons law, an object at rest will remain at rest until an force is acted upon the object

Answer:

it is safe to stand at the end of the table

Explanation:

For this exercise we use the rotational equilibrium condition

         Στ = 0

         W x₁ - w x₂ - w_table x₃ = 0

         M x₁ - m x₂ - m_table x₃ = 0

where the mass of the large rock is M = 380 kg and its distance to the pivot point x₁ = 850 cm = 0.85m

the mass of the man is 62 kg and the distance

            x₂ = 4.5 - 0.85

            x₂ = 3.65 m

the mass of the table (m_table = 22 kg) is at its geometric center

            x_{cm} = L/2 = 2.25 m

            x₃ = 2.25 -0.85

            x₃ = 1.4 m

let's look for the maximum mass of man

            m_{maximum} = [tex]\frac{ M x_1 -m_{table} x_3}{ x_2}[/tex]

let's calculate

             m_{maximum} = [tex]\frac{ 380 \ 0.85 - 22 \ 1.4}{3.65}[/tex](380 0.85 - 22 1.4) / 3.65

             m_{maximum} = 80 kg

we can see that the maximum mass that the board supports without turning is greater than the mass of man

             m_{maximum}> m

consequently it is safe to stand at the end of the table

Answer: 2.67

Explanation: it said he went from 0 to 8 in 3 seconds so if we divide eight By three we get 2.67 rounded to the nearest hundredth so you accelerated that 2.67 m/s

Answer:

Explanation:

angle of incidence.

Answer:

Potential and kinetic

Explanation:

Answer:

because they are found freely in nature uncombined so they are highly reactive with other elements

Answer: [tex]240\ rad/s^2[/tex]

Explanation:

Given

Length of beam [tex]l=2\ m[/tex]

mass of beam [tex]m=5\ kg[/tex]

Two forces of equal intensity acted in the opposite direction, therefore, they create a torque of magnitude

[tex]\tau =F\times l=200\times 2=400\ N.m[/tex]

Also, the beam starts rotating about its center

So, the moment of inertia of the beam is

[tex]I=\dfrac{ml^2}{12}=\dfrac{5\times 2^2}{12}\\\\I=\dfrac{5}{3}\ kg.m^2[/tex]

Torque is the product of moment of inertia and angular acceleration

[tex]\Rightarrow \tau=I\alpha\\\\\Rightarrow 400=\dfrac{5}{3}\times \alpha\\\\\Rightarrow \alpha =240\ rad/s^2[/tex]

Answer:

b I'm pretty sure sorry if I'm wrong

Answer:

I think the answer is B

Explanation:

The warm air turns cold and then it goes back to clouds

Answer:

[tex]36.44\ \text{kg m/s}\hat{i}[/tex]

Explanation:

I = Moment of inertia of sphere = [tex]\dfrac{2}{5}MR^2[/tex]

M = Mass of sphere = 29 kg

R = Radius of sphere = 0.5 m

T = Time taken for one revolution = 0.5 s

[tex]\omega[/tex] = Angular velocity = [tex]\dfrac{2\pi}{T}[/tex]

[tex]L=I\omega\\\Rightarrow L=\dfrac{2}{5}MR^2\dfrac{2\pi}{T}\\\Rightarrow L=\dfrac{4MR^2\pi}{5T}\\\Rightarrow L=\dfrac{4\times 29\times 0.5^2\pi}{5\times 0.5}\\\Rightarrow L=36.44\ \text{kg m/s}[/tex]

The rotational angular momentum of the sphere is [tex]36.44\ \text{kg m/s}\hat{i}[/tex].

Answer:

The team must have a vast knowledge of thermodynamics

Explanation:

Just took the test!!!

Answer:

C. Thermodynamics

Explanation:

Answer:

the magnitude of the magnetic force on the wire is 0.2298 N

Explanation:

Given the data in the question;

we know that, the magnitude of magnetic force is given as;

|F[tex]_{mg}^>[/tex] | = I([tex]B^>[/tex] × [tex]L^>[/tex] )

given that

I = 2.6 A

[tex]B^>[/tex] = 0.17

[tex]L^>[/tex] = 0.52

so we substitute

|F[tex]_{mg}^>[/tex] | = 2.6( 0.17i" × 0.52j" )

|F[tex]_{mg}^>[/tex] | = 0.2298 N

Therefore, the magnitude of the magnetic force on the wire is 0.2298 N

Explanation:

Entrepreneurs are not wild risk takers but are instead calculating risk takers. They appear to be risk takers because they see the market differently than the rest of us do. 3. ... Entrepreneurs tend to be optimistic about their chances for success, and usually their optimism is based in reality.

Answer: Kinectic Energy (KE) is equal to half of an object's mass (1/2*m) multiplied by the velocity.

Explanation: If an object with a mass of 10 kg (m=10 kg) is moving at a velocity of 5 meters per second (v=5 m/s), the kinetic energy is equal to 125 Joules, or (1/2* 10 kg) * 5 m/s^2.

Answer:

The human body carries out its main functions by consuming food and turning it into usable energy. Immediate energy is supplied to the body in the form of adenosine triphosphate (ATP). Since ATP is the primary source of energy for every body function, other stored

Explanation:

this what teacher explain to us

Answer:

a. 660 gallons

b.665 gallons

c. 1,800

Answer:

In absorption, the frequency of the incoming light wave is at or near the energy levels of the electrons in the matter. The electrons will absorb the energy of the light wave and change their energy state.

Explanation:

Answer:

1 and 3

Explanation:

because they are going up from 0

Answer:

work done by friction = 5889 J

Explanation:

We are given;

Mass of car; m = 130 kg

Speed at point A; v1 = 25 m/s

Speed at point B: v2 = 8 m/s

Since radius is 12 m

At point A, distance is; y1 = 12 m

At point B, distance is; y2 = -12 m

Now, formula for work done by all the forces is given by the equation;

Total work;

W_gravity + W_others = K2 - K1

Where W_others is work done by other forces which is equal to work done by friction

Where K2 - K1 is change in kinetic energy.

W_grav is also change in potential energy and is expressed as;

W_grav = mgy1 - mgy2

K2 - K1 = ½m(v1)² - ½m(v2)²

Thus;

mgy1 - mgy2 + W_others = ½m(v1)² - ½m(v2)²

Making W_others the subject;

W_others = ½m(v1)² - ½m(v2)² + mgy2 - mgy1

Plugging in the relevant values;

W_others = (½ × 130 × 25²) - (½ × 130 × 8²) + (130 × 9.8 × -12) - (130 × 9.8 × 12)

W_others = 5889 J

Recall that I earlier said W_others = work done by friction.

Thus, work done by friction = 5889 J

Answer: D) All of the above

Explanation:

B, the body at rest becomes reluctant to start moving or a body in motion becomes

reluctant and stop moving once in motion in a straight line

Answer:

Light is being absorbed

Hope this helps!

Light is being absorbed