For a particular scientific experiment, it is important to be completely isolated from any magnetic field, including the earth's field. The earth's field is approximately 50 μT, but at any particular location it may be a bit more or less than this. A 1.00-m-diameter current loop with 200 turns of wire is adjusted to carry a current of 0.203 A ; at this current, the coil's field at the center is exactly equal to the earth's field in magnitude but opposite in direction, so that the total field at the center of the coil is zero.

Answer:

So amount of work produced will be [tex]10{-4}J[/tex]

Explanation:

We have given diameter of ammonia bubble is changes from 1 cm to 3 cm

So radius changes from 0.5 cm to 1.5 cm

Surface area of bubble[tex]=4\pi r^2[/tex]

So change in area of bubble [tex]=4\pi (0.015^2-0.005^2)=8\times 3.14\times (0.015^2-0.005^2)=0.00251m^2[/tex]

Surface tension of ammonia = 0.04 N/m

So work done will be [tex]Work\ done=surface\ tension\times change\ in\ area=0.04\times 0.00251= 10^{-4}J[/tex]

Answer:

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

Explanation:

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:

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.

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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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:

A) The ball's gravitational potential energy is greatest at the instant when the ball is at its highest point.

Explanation:

Suppose you kick a soccer ball straight up to a height of 10 meters. Which of the following is true about the gravitational potential energy of the ball during its flight?

A) The ball's gravitational potential energy is greatest at the instant when the ball is at its highest point. (true)

B) The ball's gravitational potential energy is always the same. (false)

    because the gravitational potential energy is changed as the height changed.

C) The ball's gravitational potential energy is greatest at the instant the ball leaves your foot. (false)

    Because The ball's gravitational potential energy is greatest at the instant when the ball is at its highest point.

D) The ball's gravitational potential energy is greatest at the instant it returns to hit the ground. (false)

     The ball's gravitational potential energy is greatest at the instant when the ball is at its highest point. not when return to the ground

Final answer:

The gravitational potential energy of a soccer ball kicked straight up is A) The ball's gravitational potential energy is greatest at the instant when the ball is at its highest point.

Explanation:

If you kick a soccer ball straight up to a height of 10 meters, the gravitational potential energy of the ball is greatest at the instant when the ball is at its highest point. At the highest point, all the energy in the system is gravitational potential energy.

This is because gravitational potential energy is calculated by the formula PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height above the reference point, which in this case is the ground. At the ball's highest point, the h value is at its maximum of 10 meters. Therefore, the correct answer to the question is A) The ball's gravitational potential energy is greatest at the instant when the ball is at its highest point.

In 1932, James Chadwick proved the existence of neutrons by bombarding Beryllium-9 with alpha particles. The reaction resulted in the production of neutrons and likely also Carbon-12.

In the experiment conducted by James Chadwick in 1932, he bombarded a sample of Beryllium-9 with alpha particles. The reaction resulted in two products: a neutron, which was significant as it directly demonstrated the existence of neutrons, and another product. This missing product has not been mentioned in the question, but based on the options provided, one can infer that the most likely answer is Carbon-12. This was identified because the carbon-12 isotope is a stable one usually formed in nuclear reactions like Chadwick's.

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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:

32.4289 N

Explanation:

A = Amplitude = 20 cm

[tex]v_m[/tex] = Maximum velocity = 44 cm/s

k = Spring constant = 16 N/m

g = Acceleration due to gravity = 9.81 m/s²

m = Mass of object

Maximum velocity is given by

[tex]v_m=A\omega[/tex]

Angular velocity is given by

[tex]\omega=\sqrt{\dfrac{k}{m}}[/tex]

[tex]v_m=A\sqrt{\dfrac{k}{m}}\\\Rightarrow m=\dfrac{A^2k}{v_m^2}\\\Rightarrow m=\dfrac{0.2^2\times 16}{0.44^2}\\\Rightarrow m=3.3057\ kg[/tex]

Weight is given by

[tex]W=mg\\\Rightarrow W=3.3057\times 9.81\\\Rightarrow W=32.4289\ N[/tex]

The weight of the bananas is 32.4289 N

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:

[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:

I = 1.525 kg.m/s

Explanation:

given,

mass of the ball = 0.165 Kg

height of drop, h = 1.25 m

ball rebound and reach to height, h' = 0.940 m

impulse = ?

using conservation of energy

Potential energy is converted into kinetic energy

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

[tex]v=\sqrt{2gh}[/tex]

[tex]v=\sqrt{2\times 9.8 \times 1.25}[/tex]

  v = 4.95 m/s

velocity of the ball after rebound

again using conservation of energy

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

[tex]v'=\sqrt{2gh}[/tex]

[tex]v'=\sqrt{2\times 9.8 \times 0.94}[/tex]

  v' = 4.29 m/s

impulse is equal to change in momentum

I = m ( v' - v )

I = 0.165 x ( 4.29 - (-4.95))

I = 1.525 kg.m/s

There is one mistake in the question as unit of height of building is not given.So I assume it as meter.The complete question is here

You are on the roof of the physics building, 46.0 m above the ground. Your physics professor, who is 1.80 m tall, is walking alongside the building at a constant speed of 1.20 m/s. If you wish to drop an egg on your professor’s head, where should the professor be when you release the egg? Assume that the egg is in free fall.  

Answer:

d=3.67 m

Explanation:

Height of building=46.0 m

First we need to find time taken by egg to reach 1.80 m above the surface

So to find time use below equation

[tex]S=vt+\frac{1}{2} gt^{2}\\ (46.0-1.80)m=(om/s)t+\frac{1}{2}(9.8m/s^{2} )t^{2}\\t=\sqrt{\frac{(46.0-1.80)m}{4.9} }\\ t=3.06s[/tex]

As velocity 1.20m/s is given and we have find time.So we can easily find the distance

So

[tex]distance=velocity*time\\d=v*t\\d=(1.20m/s)*(3.06s)\\d=3.67m[/tex]

Explanation:

Force is given by rate of change of momentum.

Mass of object = 200 kg

Initial velocity = 5 m/s

Final velocity = 25 m/s

a) Change in momentum = 200 x 25 - 200 x 5

Change in momentum = 4000 kg m/s in the direction of motion

b) Time taken = 50 s

Rate of change of momentum = Change in momentum ÷ Time

Rate of change of momentum = 4000 ÷ 50

Rate of change of momentum = 80 N

Force = 80 N

Magnitude of the force is 80 N

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 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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Answer:

Constant pressure heat addition in a boiler,

Isentropic compression in a pump,

constant pressure heat rejection in a condenser and Isentropic expansion in a turbine

B

Explanation:

The Rankine cycle is a model used to predict the performance of steam turbine systems. It involves the use of these four components

1. Pump

2. Boiler

3. Turbine

4. Condenser

It includes the following processes;

1. Isentropic compression in pump

2. Constant pressure heat addition in boiler

3. Isentropic expansion in turbine

4. Constant pressure heat rejection in condenser

All this processes make up a Rankine cycle.

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:

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:

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.

Complete question

A student measures the mass of a 1.0 kg standard bar. He obtains measurements of 0.77 kg, 0.78 kg, and 0.79 kg. Which describes his measurements

a)precise but not accurate

b)accurate but not precise

c)neither precise nor accurate

d)both precise and accurate

Answer:

The measurement is precise but not accurate

Explanation:

A measurement can either be precise or accurate.

In this question, the measured values (0.77 kg, 0.78 kg and 0.79 kg) are far from the true value (1.0 kg), therefore the measurement is not accurate.

However, the measured values (0.77 kg, 0.78 kg and 0.79 kg) are close to each other, therefore the measurement is precise.

Therefore the correct option is 'a' the measurement is precise but not accurate

Answer:

precise but not accurate

Explanation:

precise but not accurate

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.  

The orbital speed of the satellite can be found using the equations for gravitational force and centripetal acceleration. By equating these two equations, we can solve for the orbital speed. Plugging in the given values, we find that the orbital speed of the satellite is approximately 6.43 x 10^3 m/s.

To find the orbital speed of the satellite, we can use the equation for gravitational force: F = ma, where F is the gravitational force, m is the mass of the satellite, and a is the centripetal acceleration. We can also use the equation for centripetal acceleration: a = v^2 / r, where v is the orbital speed and r is the distance between the satellite and the center of Jupiter. By equating the two equations, we can solve for v.

The gravitational force acting on the satellite is given by the formula F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 is the mass of Jupiter, and r is the distance between the satellite and the center of Jupiter.

Plugging in the values given in the question, we can solve for v:

v^2 = (G * m1) / r

v = sqrt((G * m1) / r)

Using the given values of m1 = 1.90 x 10^27 kg, r = 8.52 x 10^5 m, and the gravitational constant G = 6.67 x 10^-11 Nm^2/kg^2, we can calculate the orbital speed of the satellite:

v = sqrt((6.67 x 10^-11 Nm^2/kg^2 * 1.90 x 10^27 kg) / (8.52 x 10^5 m))

v ≈ 6.43 x 10^3 m/s

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=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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Final answer:

To find the speed of the eight ball after an elastic collision with the cue ball in motion, apply conservation laws of momentum and kinetic energy.

Explanation:

A cue ball initially moving at 2.5 m/s strikes a stationary eight ball of the same size and mass. After the collision, the cue ball’s final speed is 1.2 m/s at an angle of ? With respect to its original line of motion. To find the eight ball’s speed after the collision, we can apply the principles of conservation of momentum and conservation of kinetic energy.

Let's denote the velocities: V1 (initial cue ball velocity), V2 (initial eight ball velocity), V1' (final cue ball velocity), and V2' (final eight ball velocity). Considering an elastic collision, where momentum and kinetic energy are conserved, we can set up equations to solve for V2'.

By using the conservation laws, we can determine that the eight ball's speed after the collision is approximately 2.3 m/s.

Answer:

0.09852 seconds

Explanation:

[tex]\mu[/tex] = Linear density = 0.0292 kg/m

[tex]T_A[/tex] = Tesnsion in string A = [tex]33\times 10^2\ N[/tex]

[tex]T_B[/tex] = Tesnsion in string B = [tex]3.76\times 10^2\ N[/tex]

t = Time taken till the pulses pass each other

Velocity of wave in a string is given by

[tex]v_A=\sqrt{\dfrac{T_A}{\mu}}\\\Rightarrow v_A=\sqrt{\dfrac{33\times 10^2}{0.0292}}[/tex]

[tex]v_B=\sqrt{\dfrac{T_2}{\mu}}\\\Rightarrow v_B=\sqrt{\dfrac{3.76\times 10^2}{0.0292}}[/tex]

[tex]Distance=Speed\times Time[/tex]

[tex]L=(v_A+v_B)t\\\Rightarrow t=\dfrac{L}{v_A+v_B}\\\Rightarrow t=\dfrac{44.3}{\sqrt{\dfrac{33\times 10^2}{0.0292}}+\sqrt{\dfrac{3.76\times 10^2}{0.0292}}}\\\Rightarrow t=0.09852\ s[/tex]

The time taken is 0.09852 seconds

Answer:

[tex]t=0.0985\ s[/tex]

Explanation:

Given:

Now, the velocity of the wave pulse in the stretched spring is given as:

FOR A:

[tex]v_a=\sqrt{\frac{T_a}{\mu_a} }[/tex]

[tex]v_a=\sqrt{\frac{3300}{0.0292} }[/tex]

[tex]v_a=336.175\ m.s^{-1}[/tex]

FOR B:

[tex]v_b=\sqrt{\frac{T_b}{\mu_b} }[/tex]

[tex]v_b=\sqrt{\frac{376}{0.0292} }[/tex]

[tex]v_b=113.476\ m.s^{-1}[/tex]

Let the distance at which the wave of A meets the wave of B be x from left then the distance from B is (44.3-x) meters.

Now the time taken is constant:

[tex]t=\frac{x}{v_a} =\frac{x-44.3}{v_b}[/tex]

[tex]\frac{x}{336.175} =\frac{x-44.3}{113.476}[/tex]

[tex]x=33.12\ m[/tex] is the distance travelled by pulse in wire A in when the pulse in the wire B meets

Now the time taken to travel this distance by pulse in wire A:

[tex]t=\frac{x}{v_a}[/tex]

[tex]t=\frac{33.12}{336.175}[/tex]

[tex]t=0.0985\ s[/tex] is the time taken by the two waves to pass each other.

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

The package takes approximately 0.117 seconds to reach the ground. The velocity just before it lands is 25.364 m/s (upwards).

To find the time it takes for the package to reach the ground, we can use the equation for uniform acceleration: acceleration (a) = g - (-g) = 2g, where g is the acceleration due to gravity (9.8 m/s^2) and the negative sign represents the direction of motion. Using v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (2.3 m/s), and a is the acceleration, we can find the time (t) it takes for the package to reach the ground. Rearranging the equation, we have t = (v - u)/a. Plugging in the values, we have t = (0 - 2.3)/(2g) = -2.3/19.6 = 0.117 seconds. The package takes approximately 0.117 seconds to reach the ground.

To find the velocity just before it lands, we can use the equation v = u + at, where u is the initial velocity, a is the acceleration, and t is the time. Rearranging the equation, we have v = u + at. Plugging in the values, we have v = 2.3 + (2g)(0.117) = 2.3 + 23.064 =  25.364 m/s (upwards).

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