A person has been exposed to a particular antigen and now experiences a repeat exposure. What stimulates a quicker immune response?a) Memory T cellsb) immunityc) antibodiesd) macrophages

Answer:

2.23 × 10^6 g of F- must be added to the cylindrical reservoir in order to obtain a drinking water with a concentration of 0.8ppm of F-

Explanation:

Here are the steps of how to arrive at the answer:

The volume of a cylinder = ((pi)D²/4) × H

Where D = diameter of the cylindrical reservoir = 2.02 × 10^2m

H = Height of the reservoir = 87.32m

Therefore volume of cylindrical reservoir = (3.142×202²/4)m² × 87.32m = 2798740.647m³

1ppm = 1g/m³

0.8ppm = 0.8 × 1g/m³

= 0.8g/m³

Therefore to obtain drinking water of concentration 0.8g/m³ in a reservoir of volume 2798740.647m³, F- of mass = 0.8g/m³ × 2798740.647m³ = 2.23 × 10^6 g must be added to the tank.

Thank you for reading.

Answer:

4.225 J

Explanation:

Elastic Potential Energy: This is the potential energy stored in an elastic material.This also the energy required to stretch an elastic material. The S.I unit is Joules.

Mathematically it is expressed as

E = 1/2ke²....................... Equation 1

Where E =elastic potential Energy, k = spring constant, e = extension.

Given: k = 5.0 N/m, e = 3.93-2.63 =  1.3 m.

Substitute into equation 1

E = 1/2(5)(1.3)²

E = 8.45/2

E = 4.225 J.

Thus the Elastic potential Energy = 4.225 J.

Answer:

The heavier wagon rolls 1/2 as fast as the lighter wagon.

Explanation:

When the compressed spring that joins them is released then the force acts on both wagons will be of equal magnitude but in the opposite direction. However as the mass of one wagon is twice that of other, so the acceleration  will become half of the heavier wagon in comparison with lighter one.

The five positions of the spaceship from left to right are based on the strength of the gravitational force that Earth exerts on the spaceship, from strongest to weakest is [tex]5, 1, 2, 4, 3[/tex]

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward one another.

The gravitation force that Earth exerts on the spaceship will be:[tex]F_{ES}=(Gm_1m_E)/r^2[/tex]

Where [tex]F_{ES}[/tex] the force exerted on the spaceship by Earth [tex]m_1\\\\[/tex] is the mass of the spaceship and r is the distance between the.

[tex]F_{ES}\ \alpha\ 1/r^2[/tex]

This indicates larger the distance smaller will be the force. The correct order is [tex]5, 1, 2, 4, 3[/tex].

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The strength of the gravitational force that Earth exerts on a spaceship varies depending on the distance between them. The force is strongest when the spaceship is closest to Earth and weakest when it is closest to the Moon.

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Answer with Explanation:

We are given that

Dipole moment=[tex]0.5 e nm=0.5\times 1.6\times 10^{-19}\times 10^{-9}=0.8\times 10^{-28}[/tex]C-m

Because [tex]1 e=1.6\times 10^{-19} C[/tex]

[tex]1 nm=10^{-9} m[/tex]

[tex]a^x\cdot a^y=a^{x+y}[/tex]

Magnitude of electric field,E=[tex]8\times 10^4[/tex] N/C

a.We have to find the magnitude of torque on the dipole when

dipole is parallel to the electric field

i.e[tex]\theta=0[/tex]

We know that

[tex]\tau=PEsin\theta[/tex]

Substitute the values then we get

[tex]\tau=0.8\times 10^{-28}\times 8\times 10^{4} sin0=0[/tex]

Because sin 0=0

[tex]\tau=0[/tex]

b.[tex]\theta=90^{\circ}[/tex]

[tex]\tau=0.8\times 10^{-28}\times 8\times 10^4sin90[/tex]

By using [tex]sin90^{\circ}=1[/tex]

[tex]\tau=6.4\times 10^{-28+4}=6.4\times 10^{-24}Nm[/tex]

[tex]\tau=6.4\times 10^{-24}[/tex]Nm

c.[tex]\theta=30^{\circ}[/tex]

[tex]\tau=0.8\times 10^{-28}\times 8\times 10^4sin 30[/tex]

[tex]\tau=6.4\times 10^{-24}\times \frac{1}{2}[/tex] Nm

By using [tex] sin30^{\circ}=\frac{1}{2}[/tex]

[tex]tau=3.2\times 10^{-24} Nm[/tex]

d.Potential energy, U=[tex]-PEcos\theta[/tex]

[tex]\theta=0[/tex]

[tex]U=-0.8\times 10^{-28}\times 8\times 10^4cos 0=-6.4\times 10^{-28}J[/tex]

Because cos 0degree=1

By having the p, E, and anglёs, we can calculate the τ value and the U values. a) 0 Nm, b) 6.4x10⁻²⁴ Nm, c) 3.2x10⁻²⁴ Nm. d) U = 6.4x10⁻²⁴, U = 0, U = 5.57x10⁻²⁴

First, we need to change the units of the given dip0lё momёnt, p.

The result is

p = 0.8 x 10 ⁻²⁸ Cm

Now we can calculate the t0rquё values.

T0rque, t = p x E x sёn θ

The results are

p0tёntial energy, U = p x E x c0s θ

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The sympathetic and parasympathetic divisions of the autonomic nervous system release different neurotransmitters.

In the autonomic nervous system, there are two main divisions - the sympathetic and parasympathetic. These divisions have different effects on the body due to the neurotransmitters they release. Sympathetic preganglionic fibers release acetylcholine (ACh), whereas parasympathetic preganglionic fibers also release ACh. However, parasympathetic postganglionic fibers release norepinephrine (NE), and sympathetic postganglionic fibers also release NE.

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In the autonomic nervous system, preganglionic fibers release ACh and target ganglionic neurons through nicotinic receptors. Postganglionic fibers release NE, except for certain fibers that release ACh.

In the autonomic nervous system, both sympathetic and parasympathetic preganglionic fibers release ACh. The ganglionic neurons, which are the targets of these preganglionic fibers, have nicotinic receptors. These receptors are ligand-gated cation channels that cause depolarization of the postsynaptic membrane. On the other hand, postganglionic sympathetic fibers release norepinephrine (NE), except for those that project to sweat glands and blood vessels associated with skeletal muscles, which release ACh.

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Answer:

B_m = 3.186 x 10⁻³ T

Explanation:

given,

diameter of the beam = 0.863 mm

Amplitude = 0.955 MV/m

speed of light = 2.99792 × 10⁸ m/s

he permeability of free space= 4π × 10⁻⁷ T· N/A

Amplitude of the magnetic field is given by

[tex]B_m = \dfrac{E_m}{c}[/tex]

E_m is amplitude of the electric field.

[tex]B_m = \dfrac{0.955\times 10^{6}}{2.99792\times 10^8}[/tex]

     B_m = 0.31855 x 10⁻² T

     B_m = 3.186 x 10⁻³ T

The amplitude of magnetic field is equal to 3.186 x 10⁻³ T

Answer:

I= 12.09×10^8 W/m^2

Explanation:

Em = amplitude of electric field = 0.955 MV/m = 0.955 x 10^6 V/m

B_m = amplitude of magnetic field = ?

c = speed of light = 2.99792 x 10^8 m/s

amplitude of magnetic field is given as

B_m = E_m /c

B_m = (0.955 x 10^6)/(2.99792 x 10^8 )

B_m = 0.00318 T

b)

intensity is given as

[tex] I=(0.5)\epsilon\times E_m^2 c [/tex]

[tex]I=0.5(8.85\times10^{-12})(0.955\times10^6)^2(2.99792\times10^8)[/tex]

I= 1209873759.69

I= 12.09×10^8 W/m^2

Complete question

The complete question is shown on the first and second uploaded image

Answer:∈

Answer to first question is shown on the second uploaded image.

Part B the Answer is:

The ratio  [tex]\frac{R}{a}[/tex] is evaluated to be 49.99

Explanation:

The explanation is shown on the third ,fourth and fifth image.

The ratio  [tex]\frac{R}{a}[/tex] is "49.9975".

For the last part, we should have

[tex]\to E = 0.99 \frac{\eta }{\varepsilon_0 }[/tex]

Therefore we should have

[tex]\to \frac{\eta}{\varepsilon_0}(1-\frac{1}{\sqrt{ (\frac{2R}{a})^2+1}}) = 0.99 \frac{\eta}{\varepsilon_0}[/tex]

[tex]\to (1-\frac{1}{\sqrt{ (\frac{2R}{a})^2+1}}) = 0.99 \\\\\to 1-0.99= \frac{1}{\sqrt{ (\frac{2R}{a})^2+1}}\\\\ \to 0.01= \frac{1}{\sqrt{ (\frac{2R}{a})^2+1}} \\\\\to \sqrt{ (\frac{2R}{a})^2+1}= 100\\\\\to (\sqrt{ (\frac{2R}{a})^2+1})^2= 100^2\\\\\to (\frac{2R}{a})^2+1= 10000\\\\\to (\frac{2R}{a})^2= 10000-1\\\\\to (\frac{2R}{a})^2= 9999\\\\\to \frac{2R}{a}= 99.9995\\\\\to \frac{R}{a}= 49.9975\\\\[/tex]

Note:

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Answer:

[tex]g_n=\dfrac{2}{9}g[/tex]

Explanation:

M = Mass of Earth

G = Gravitational constant

R = Radius of Earth

The acceleration due to gravity on Earth is

[tex]g=\dfrac{GM}{R^2}[/tex]

On new planet

[tex]g_n=\dfrac{G2M}{(3R)^2}\\\Rightarrow g_n=\dfrac{2GM}{9R^2}[/tex]

Dividing the two equations we get

[tex]\dfrac{g_n}{g}=\dfrac{\dfrac{2GM}{9R^2}}{\dfrac{GM}{R^2}}\\\Rightarrow \dfrac{g_n}{g}=\dfrac{2}{9}\\\Rightarrow g_n=\dfrac{2}{9}g[/tex]

The acceleration due to gravity on the other planet is [tex]g_n=\dfrac{2}{9}g[/tex]

Answer:

2 g/9

Explanation:

mass of planet, Mp = 2 x Me

radius of planet, Rp = 3 x Re

Where, Me is the mass of earth and Re is the radius of earth.

The formula for acceleration due to gravity on earth is given by

[tex]g = \frac{GM_{e}}{R_{e}^{2}}[/tex]     .... (1)

The acceleration due to gravity on the planet is given by

[tex]g' = \frac{GM_{p}}{R_{p}^{2}}[/tex]

By substituting the values, we get

[tex]g' = \frac{2GM_{e}}{9R_{e}^{2}}[/tex]    ..... (2)

Divide equation (2) by equation (1), we get

g'/g = 2/9

g' = 2 g/9

Thus, the acceleration due to gravity on th enew planet is 2 g/9.  

Answer:

a=19.8977 m/s²

Explanation:

Given data

ω=3.00 rad/s

r=1.40 m

α=11.0 rad/s²

To find

Acceleration

Solution

As the object moves in a circle so it has tangential acceleration also due to circular motion  is  has centripetal acceleration

The total acceleration can be found by

[tex]a=\sqrt{(a_{c})^{2}+(a_{T})^{2}}[/tex]

where

at is tangential acceleration

ac is centripetal acceleration

First we need to find centripetal acceleration

so

[tex]a_{c}=rw^{2}[/tex]

put the values or r and ω

[tex]a_{c}=(1.40m)*(3.00rad/s)^{2}\\a_{c}=12.6 m/s^{2}[/tex]

Now for tangential acceleration

[tex]a_{t}=ra\\a_{t}=(1.40m)*(11.0rad/s^{2} )\\a_{t}=15.4 m/s^{2}[/tex]

Put values of ac and at to find total acceleration

So

[tex]a=\sqrt{(a_{t})^{2} +(a_{c})^{2} }\\ a=\sqrt{(15.4m/s^{2} )^{2}+(12.6m/s^{2} )^{2}  }\\ a=19.8977m/s^{2}[/tex]

The magnitude of the total acceleration at a point on the rotating platform is approximately 19.79 m/s².

To find the magnitude of the total acceleration at a point on the rotating platform, we need to consider both the tangential acceleration and the centripetal acceleration. The tangential acceleration is given by the product of the angular acceleration and the radius, while the centripetal acceleration is given by the square of the angular speed times the radius. Adding these two accelerations together will give us the magnitude of the total acceleration at that point.

First, calculate the tangential acceleration:

Tangential acceleration = angular acceleration × radius

Tangential acceleration = 11.0 rad/s² × 1.40 m = 15.4 m/s²

Then, calculate the centripetal acceleration:

Centripetal acceleration = (angular speed)² × radius

Centripetal acceleration = (3.00 rad/s)² × 1.40 m = 12.60 m/s²

Finally, find the vector sum of the tangential acceleration and the centripetal acceleration:

Total acceleration = √((tangential acceleration)² + (centripetal acceleration)²)

Total acceleration =√((15.4 m/s²)² + (12.60 m/s²)²)

Total acceleration ≈ 19.79 m/s²

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Answer:

What soil conditions favor the use of belled caissons?

Answer:

- where the bell can be unearthed from a solid surface.

- where the supporting stratum below the bottom of the caisson is impermeable to water movement.

What soil conditions favor piles over caissons?

Answer:

- non-cosheal soils

- subterranean water or excessive depth of bearing strata make caisson unworkable

What type of piles are especially well suited to repair or improvement of existing foundations ?

Answer:

Without hammering, minipiles or helical piles are placed which escapes much of the vibration and noise associated with traditional pile installation. for working close to existing buildings or for improving the exiting foundations where excessive vibration could damage exiting structures or noise may interfere with ongoing activities these piles are good options.

Why?

Their slenderness involves little or no displacement of the soil, thus minimizing the risk of disturbance to nearby foundations.

List and explain some cost thresholds frequently encountered in foundation design.

Answer:

building below the water table- site dewatering must occur, strengthening of slopes supper system must be done and waterproofing of the foundation all of which entails money

building near existing building - this requires underpinning(The process of reinforcing the base of an existing building or other structure underpins it.)

increase in column/wall load- building height determines the foundation depth

The answer discusses the use of belled caissons, piles, and helical piles in different soil conditions, along with common cost thresholds in foundation design.

Belles caissons are favored in soil conditions with the potential for liquefaction, as driving deep piles or piers can strengthen the soil and reduce liquefaction risk. On the other hand, piles are preferred over caissons in soil conditions that are unsuitable for drilling due to hard rock or boulders. Helical piles are especially well-suited for repairing or improving existing foundations as they can be installed quickly with minimal noise and vibration, making them ideal for retrofitting projects. Some common cost thresholds in foundation design include budgets for materials, labor, and specialized equipment, all of which can impact the overall project cost.

Answer:

analog-to-digital

Explanation:

An analog-to-digital converter, or ADC as it is more commonly called, is a device that converts analog signals into digital signals.

Answer:

4. nuclear fusion.

Explanation:

The process that helps stars generate heat energy from atomic nuclei is called nuclear fusion. Due to gravity, pressure on the hydrogen gas in the center or core of the stars are enormous causing temperature to reach about 27 million°F (15 million°C).  This hotness makes hydrogen atoms to fuse together to form helium atoms. This process is called nuclear fusion. Vast amount of energy is released which enables the star to shine.  

Answer:

The work done by the hoop is equal to 5.529 Joules.

Explanation:

Given that,

Mass of the hoop, m = 96 kg

The speed of the center of mass, v = 0.24 m/s

To find,

The work done by the hoop.

Solution,

The initial energy of the hoop is given by the sum of linear kinetic energy and the rotational kinetic energy. So,

[tex]K_i=\dfrac{1}{2}mv^2+\dfrac{1}{2}I\omega^2[/tex]

I is the moment of inertia, [tex]I=mr^2[/tex]

Since, [tex]\omega=\dfrac{v}{r}[/tex]

[tex]K_i=mv^2[/tex]

[tex]K_i=96\times (0.24)^2=5.529\ J[/tex]

Finally it stops, so the final energy of the hoop will be, [tex]K_f=0[/tex]

The work done by the hoop is equal to the change in kinetic energy as :

[tex]W=K_f-K_i[/tex]

W = -5.529 Joules

So, the work done by the hoop is equal to 5.529 Joules. Therefore, this is the required solution.

Answer:

Fr= 5400 N

Explanation:

Given that

m = 1200 kg

v= 32 m/s

μ = 0.45

Given that car is moving with constant speed it means that acceleration of the car is zero or we can say that total force on the car is zero.That is why ,only force needed to over come the friction force.

Fr= μ m g

Fr= 0.45 x 1200 x 10  N

Fr= 5400 N

That is why the total force should be 5400 N.

Answer:

Explanation:

mass, m  = 1200 kg

v = 32 m/s

coefficient of friction, μ = 0.45

As the car is moving with constant speed so the net force is zero, but the force applied by the car engine to run is the friction force.

F = μ mg = 0.45 x 1200 x 9.8 = 5292 N

Answer:

Earth crust and specifically the continental crust.

Explanation:

If we examine the earth crust there is mostly the granite and basalt and most of the granite is present in the continental crust part which is less thicker and denser. That's why we say that the continental crust has the composition similar to that of granite.

Answer:

By suspending the needles on in the air, the needle which orients itself in the north-south direction is magnetized

Explanation:

The mass (M) of the target and the final speed (V) of the bullet and target combined after an inelastic collision can be determined by setting the total momentum before the collision equal to the total momentum after the collision and solving for M and V using the given information.

The question deals with the concept of conservation of momentum in an inelastic collision. Since the bullet and the target paper are involved in an inelastic collision, the total momentum before the collision is equal to the total momentum after the collision. This can be defined as m*v=(m+M)*V, where m and v are the mass and velocity of the bullet respectively, M is the mass of the target, and V is the final velocity of the bullet and target combined.

Given in the question is that after collision, the speed of the bullet becomes (0.516)*v, therefore the velocity V of the bullet and the target combined, the moment after the collision would be V = 0.516 * v. Solving these equations will give the required values for M and V in terms of the initial mass and velocity of the bullet.

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The question involves an inelastic collision between a bullet and a target. Using conservation of momentum, the target's mass is found to be 0.937 times the bullet's, and the target's speed immediately after collision is approximately 0.484 times the bullet's initial speed.

Given that the collision is inelastic, the quantity of momentum before and immediately after the collision is conserved. Hence, we can express this conservation of momentum as: m*v = (m+M)V. From this we get the mass M of the target as: M = [m*(1 - 0.516)]/0.516 = 0.937m which means the mass of the target is approximately 0.937 times the mass of the bullet.

Subsequently, we can solve for the speed V of the target using the above conservation of momentum giving: V = (m*v)/(m+M) = v/(1+1.064) = 0.484v approximately.

In conclusion, the mass M of the target the instant after the collision is 0.937m and the speed V of the target is 0.484v in terms of the mass m of the bullet and initial speed v of the bullet.

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Answer:

[tex]\vec{v} = <-11,15.08,-5>[/tex]

Explanation:

given,

location of the ball ⟨7,0,−8⟩

initial velocity of the ball ⟨-11,19,−5⟩

time = 0.4 s

speed of the ball = ?

using Momentum Principle

change in momentum = Force x time

[tex]m \vec{v} - m \vec{u}= \vec{F}\times \Delta t[/tex]

[tex]\vec{v} =\vec{u} + \dfrac{\vec{F}}{m}\times \Delta t[/tex]

Net force acting in this case will be equal to force due to gravity because air resistance is negligible.

F_net = F_g = ⟨0 ,-9.8 m , 0⟩

now,

[tex]\vec{v} = <-11,19,-5>+ \dfrac{<0 ,-9.8 m , 0>}{m}\times (0.4-0)[/tex]

[tex]\vec{v} = <-11,19,-5>+ <0 ,-3.92 , 0>[/tex]

[tex]\vec{v} = <-11,15.08,-5>[/tex]

hence, the velocity of the ball 0.4 s after being kicked is equal to [tex]\vec{v} = <-11,15.08,-5>[/tex]

The velocity of the ball 0.4 seconds after being kicked is; v = (-11, 15.08, -5) m/s

We are given;

From the Momentum Principle, we know that;

Change in momentum = Impulse

Thus;

m(v - u) = F * Δt

Divide through by m and make v the subject to get;

v = u + [(F/m)Δt]

In this question, due to the fact that air resistance is negligible, the net force acting will be equal to force due to gravity. Thus;

F_net = F_g = mg

Since acceleration due to gravity is 9.8 m/s², then;

F = (0, -9.8m, 0)

Thus;

v = (-11, 19, −5) + [((0, -9.8m, 0)/m) * (0.4 - 0)]

v = (-11, 19, −5) + (0, -3.92m, 0)

v = (-11, 15.08, -5) m/s

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Answer:

a. 0.0 m/s

Explanation:

According to the law of conservation of energy, the maximum potential energy of the body is equal to the minimum kinetic energy:

P+K=const; Pmax=mgH Kmin=mv^2/2=0 (because v=0)

At the maximum height, the speed of the ball is equal to zero.  Therefore, option (A) is correct.

Speed can be explained as a scalar measurement of the motion of an object with time. The speed of an object can be described as the change in position w.r.t. time.

Speed is a scalar parameter as it exhibits only magnitude and no direction. A formula that can be used to calculate the speed of a moving body.

S = d / t

where S is the speed, d is the distance the object moved, and t is the time.

Although the SI unit for speed is m/s and can also represent in miles per hour (mph), and kilometers per hour (kph).

The speed of a ball thrown upwards decreases with time because the ball is moving against gravity, and the eventually becomes zero when the ball reaches maximum height.

Thus, the speed of the ball thrown above the surface of the Earth is zero when the ball reaches maximum height.

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Answer:

E- The star becomes a red giant (LATEST STAGE)

F- The surface of the star becomes brighter and cooler

C- Pressure from the star's hydrogen-burning shell causes the non burning envelope to expand

A- The shell of hydrogen surrounding the star's nonburning helium core ignites.

D- The star's non burning helium core starts to contract and heat up

B- Pressure in the star's core decreases (EARLIEST STAGE)

(A star moves away from the main sequence once its core runs out of hydrogen to fuse into helium. The energy once supplied by hydrogen burning reduces and the core starts to compress under the force of gravity. This contraction allows the core and surrounding layers to heat up. Finally, the hydrogen shell around the core becomes hot enough to ignite hydrogen burning.

Final answer:

Explanation of the stages in stellar evolution from subgiant to red giant.

Explanation:

Ranking the stages of stellar evolution from subgiant to red giant:

The shell of hydrogen surrounding the star's non-burning helium core ignites.

The star's non-burning helium core starts to contract and heat up.

The surface of the star becomes brighter and cooler.

Pressure from the star's hydrogen-burning shell causes the non-burning envelope to expand.

Pressure in the star's core decreases.

The star becomes a red giant.

B) Nuclear fission

Explanation:

Nuclear power plants work by using the process of nuclear fission.

Nuclear fission occurs when a heavy, unstable radioactive nuclei decays, breaking apart into two or more lighter nuclei, more stable. In the process, several neutrons are also released, alongside with energy.

In nuclear power plants, the nucleus used for the process is the Uranium-235. When an atom of uranium-235 absorbs a slow neutron, it becomes a very unstable nucleus of uranium-236, which quickly decays into a nucleus of Barium-141, Kripton-92 and 3 neutrons.

The uranium nuclei are located in the so-called fuel rods, which are placed in a moderator (usually water). The purpose of the moderator is to slow down the neutrons emitted in the reaction: this way, these neutrons can be absorbed by other nuclei of uranium-235, causing more fission reactions to occur.

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Answer:

0.035 N

Explanation:

Density = mass/volume

D = m/v

m = D× v ..................... Equation 1

Where D = density of the ping-pong, v = volume of the ping-pong, m = mass of the ping-pong

Note: The ping-pong is spherical in shape.

v = 4/3πr²

Where r = radius,  π = pie

d = 1.99 cm, π = 3.14

v = 4/3(1.99/2)²(3.14)

v = 4.12 cm³

Also D = 0.121 g/cm³

Therefore,

m = 0.121(4.12)

m = 0.499 g

W = mg

Where W = weight of the ping-pong

W = (0.499/1000)×9.81

W = 0.005 N.

From Archimedes principle,

Upthrust = density of water × volume of water displaced × acceleration due to gravity.

U = D'vg/1000...................... Equation 2

Note: The volume of water displaced is equal to the volume of the ping-pong.

given: v = 4.12 cm³, g = 9.81 m/s², D' = 1 g/cm³

Substitute into equation 2

U = 1(4.12)(9.81)/1000

U = 0.04 N

The force required to hold the ball completely submerged under water = U-W

= 0.04-0.005 = 0.035 N

There are mistakes in the question.The correct question is here

A 2.0 kg, 20-cm-diameter turntable rotates at 100 rpm on frictionless bearings. Two 500 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is the turntable’s angular velocity, in rpm, just after this event?

Answer:

w=50 rpm

Explanation:

Given data

The mass turntable M=2kg

Diameter of the turntable d=20 cm=0.2 m

Angular velocity ω=100 rpm= 100×(2π/60) =10.47 rad/s

Two blocks Mass m=500 g=0.5 kg

To find

Turntable angular velocity

Solution

We can find the angular velocity of the turntable as follow

Lets consider turntable to be disk shape and the blocks to be small as compared to turntable

[tex]I_{turntable}w=I_{block1}w^{i}+I_{turntable}w^{i}+I_{block2}w^{i}[/tex]

where I is moment of inertia

[tex]w^{i}=\frac{I_{turntable}w}{I_{block1}w^{i}+I_{block2}w^{i}+I_{turntable}w^{i}}\\ So\\I_{turntable}=M\frac{r^{2} }{2}\\I_{turntable}=2*(\frac{(0.2/2)}{2} )\\ I_{turntable}=0.01 \\And\\I_{block1}=I_{block2}=mr^{2}\\I_{block1}=I_{block2}=(0.5)*(0.2/2)^{2} \\ I_{block1}=I_{block2}==0.005\\so\\w^{i}=\frac{I_{turntable}w}{I_{block1}w^{i}+I_{block2}w^{i}+I_{turntable}w^{i}}\\w^{i}=\frac{0.01*(10.47)}{0.005+0.005+0.01} \\w^{i}=5.235 rad/s\\w^{i}=5.235*(60/2\pi )\\w^{i}=50 rpm[/tex]

The problem is a case of angular momentum conservation within the domain of rotational dynamics in physics. The turntable's initial angular momentum remains conserved despite the addition of the blocks. By accounting for the added moment of inertia from the blocks, the final angular velocity of the system can be calculated.

The subject we're discussing here comes under the physics concept of rotational dynamics particularly focusing on the conservation of angular momentum.

Before the blocks hit the turntable, we know that the turntable is rotating with an angular velocity given in RPM (revolutions per minute), which we can convert to rad/s for our calculations. So, the initial angular momentum can be represented as Lim = (moment of inertia of the system) * (initial angular velocity).

Once the blocks fall onto the turntable, they contribute to the moment of inertia of the system, while the angular momentum of the system remains conserved. Thus resulting in a decreased angular velocity. The final angular momentum can be represented as Lfm = (moment of inertia including the blocks) * (final angular velocity).

Since the initial and final angular momenta need to be equal (Lfm = Lim), we can solve the resulting equation for the final angular velocity.

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Answer:

Timmy is 1 meters away from the center.

Explanation:

Given:

Distance of Suzie from center = 2 m

Weight of Suzie = 400 N

Weight of Timmy = 800 N

The see saw is balanced

To find the distance of Timmy from the center.

Solution:

Since the see saw is balanced,

So, the sum of clockwise moment = Sum of anticlockwise moments

Moment is given by:

⇒ [tex]Force\times Perpendicular\ distance\ from\ the\ center[/tex]

Let Suzies have moment in clockwise direction.

Moment of Suzie would be = [tex]400\ N \times 2\ m= 800\ Nm[/tex]

Timmy would have moment in anticlockwise direction.

Let Timmy be [tex]l[/tex] meters away from center

Moment of Timmy would be = [tex]800\ N\times l\ m=800l\ Nm[/tex]

Since, the see saw is balanced, the system is in equilibrium.

Thus, we have,

Anticlockwise Moment = Clockwise moment

[tex]800l=800[/tex]

Dividing both sides by 800.

[tex]\frac{800l}{800}=\frac{800}{800}[/tex]

[tex]l=1\ m[/tex]

Thus, Timmy is 1 meters away from the center.

Answer:

51.019 μT

Explanation:

[tex]\mu_0[/tex] = Vacuum permeability = [tex]4\pi \times 10^{-7}\ H/m[/tex]

i = Current in wire = 0.203 A

N = Number of turns = 200

d = Diameter = 1 m

Magnetic field is given by

[tex]B=\dfrac{N\mu_0i}{d}\\\Rightarrow B=\dfrac{200\times 4\pi \times 10^{-7}\times 0.203}{1}\\\Rightarrow B=0.000051019\ T[/tex]

The strength of the magnetic field at this location would be 51.019 μT

The magnetic field at the given point is 51.019 μT.

It is given that the current in the coil is I = 0.203A

the diameter of the loop carrying the current is d = 2r = 1m

and the number of turns is N = 200.

The magnetic field to a current-carrying loop having N number of turns and carrying a current I with the radius of the loop being r is given by:

[tex]B=\frac{\mu_oNI}{2r} \\\\B=\frac{4\pi\times10^{-7}\times200\times0.203}{1}\\\\B=51.019\;\mu T[/tex]

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Answer:uigu

Explanation:nvhv

The force that is experienced by the ladybug is being exerted by the can.

According to Newtons's third law of motion, action and reaction are equal and opposite. As a centripetal force is exerted on the can as it moves round the circle, the can also exerts a force back on the ladybug resting on its bottom.

Hence, the force that is experienced by the ladybug is being exerted by the can on which the ladybug sits.

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Answer:

120.125 m

Explanation:

Density = Mass/volume

D = m/v .............................. Equation 1.

Where D = Density of the solid copper sphere, m = mass of the solid copper sphere, v = volume of the solid copper sphere.

Making v the subject of the equation,

v = m/D............................... Equation 2

Given: m = 76.5 kg,

Constant: D = 8960 kg/m .

Substituting into equation 2

v = 76.5/8960

v = 0.0085379 m³

Since the copper sphere is to be drawn into wire,

Volume of the copper sphere = volume of the wire

v = volume of the wire

Volume of wire = πd²L/4

Where d = diameter of the wire, L = length of the wire.

Note: A wire takes the shape of a cylinder.

v = πd²L/4 ........................ equation 3.

making L the subject of the equation,

L = 4v/πd²..................... Equation 4

Given: v = 0.0085379 m³, d = 9.50 mm = 0.0095  and π = 3.14

Substitute into equation 4

L = 4×0.0085379/(3.15×0.0095²)

L = 0.0341516/0.0002843

L = 120.125 m.

L = 120.125 m

Thus the length of the wire produced = 120.125 m

The correct answer is that the speed of the ball when it returns to the point of launch is less than its speed when it was initially launched, due to the effects of air resistance.

The subject of this question is Physics, specially mechanics that is a part of Physics dealing with motion and the forces that produce motion.

The correct answer is option b. 'The speed at which the ball returns to the point of launch is less than its speed when it was initially launched'. This is due to the presence of air resistance, which counteracts the force of gravity and slows the ball down both on its way up and on its way down. Therefore, the speed of the ball when it returns to the hand will be less than the speed at which it was launched.

Option a is incorrect because the net work done by gravity is zero since the ball returns to its original position. Option c is also incorrect because air resistance always does work on the ball as it changes its velocity. Lastly, option d is incorrect because the direction of air resistance changes; it is upward when the ball is rising and downward when the ball is falling.

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The correct answer is b. The ball's return speed is less than its launch speed due to the opposing forces of air resistance during its upward and downward motion.

The correct statement is b. The speed at which the ball returns to the point of launch is less than its speed when it was initially launched. This is because air resistance, a form of friction, works against the motion of the ball. When the ball is launched upward, air resistance acts downwards, slowing it down. Similarly, when the ball falls downwards, air resistance acts upwards, again slowing it down.

As a result, the return speed of the ball is less than the launch speed. It’s important to remember that, in an ideal scenario without air resistance, the return speed would be equal to the launch speed because of the conservation of energy. However, in real-world situations like this one, air resistance, a form of energy dissipation, reduces the speed.

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