All objects near the earths surface - regardless of size and weight - hhave the same force of gravityvacting on them.
A. True
B. False

Answer:

Part a)

A = 0.066 m

Part b)

maximum speed = 0.58 m/s

Explanation:

As we know that angular frequency of spring block system is given as

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

here we know

m = 3.5 kg

k = 270 N/m

now we have

[tex]\omega = \sqrt{\frac{270}{3.5}}[/tex]

[tex]\omega = 8.78 rad/s[/tex]

Part a)

Speed of SHM at distance x = 0.020 m from its equilibrium position is given as

[tex]v = \omega \sqrt{A^2 - x^2}[/tex]

[tex]0.55 = 8.78 \sqrt{A^2 - 0.020^2}[/tex]

[tex]A = 0.066 m[/tex]

Part b)

Maximum speed of SHM at its mean position is given as

[tex]v_{max} = A\omega[/tex]

[tex]v_{max} = 0.066(8.78) = 0.58 m/s[/tex]

Answer: [tex]1.8\°[/tex]

Explanation:

The diffraction angles [tex]\theta_{n}[/tex] when we have a slit divided into [tex]n[/tex] parts are obtained by the following equation:

[tex]dsin\theta_{n}=n\lambda[/tex] (1)

Where:

[tex]d=3.4(10)^{-5}m[/tex] is the width of the slit

[tex]\lambda=540 nm=540(10)^{-9}m[/tex] is the wavelength of the light  

[tex]n[/tex] is an integer different from zero.

Now, the second-order diffraction angle is given when [tex]n=2[/tex], hence equation (1) becomes:

[tex]dsin\theta_{2}=2\lambda[/tex] (2)

Now we have to find the value of [tex]\theta_{2}[/tex]:

[tex]sin\theta_{2}=\frac{2\lambda}{d}[/tex] (3)

Then:

[tex]\theta_{2}=arcsin(\frac{2\lambda}{d})[/tex]   (4)

[tex]\theta_{2}=arcsin(\frac{2(540(10)^{-9}m)}{3.4(10)^{-5}m})[/tex]   (5)

Finally:

[tex]\theta_{2}=1.8\°[/tex]   (6)

A) 392 N/m

The spring constant can be found by applying Hooke's Law:

F = kx

where

F is the force applied to the spring

k is the spring constant

x is the stretching of the spring

Here we have:

F is the weight of the block hanging from the spring, which is

[tex]F=mg=(2.0 kg)(9.8 m/s^2)=19.6 N[/tex]

The stretching of the spring is

[tex]x=15 cm - 10 cm = 5 cm = 0.05 m[/tex]

Therefore its spring constant is

[tex]k=\frac{F}{x}=\frac{19.6 N}{0.05 m}=392 N/m[/tex]

B) 17.5 cm

Now that we know the value of the spring constant, we can calculate the new stretching of the spring when a mass of m=3.0 kg is applied to it. In this case, the force applied on the spring is

[tex]F=mg=(3.0 kg)(9.8 m/s^2)=29.4 N[/tex]

Therefore the stretching of the spring is

[tex]x=\frac{F}{k}=\frac{29.4 N}{392 N/m}=0.075 m = 7.5 cm[/tex]

And since the natural length of the spring is 10 cm, the new length will be

L = 10 cm + 7.5 cm = 17.5 cm

48/4= 12

12/2= 6

Answer: C. 6 kg

Answer:

It takes 2.55 sec

Explanation:

First we need to find the aceleration with this equation:

F = m*a

[tex]a = \frac{F}{m}[/tex]

Where:   F = 1.3 Newtons

              m = 0.145 kg

Then      [tex]a = \frac{1.3 Newtons}{0.145 kg}[/tex]

              [tex]a = 8.9655 m/sec^{2}[/tex]

Now we are ready to calculate the time with the next equation:

[tex]V_{f} = V_{o} + a*t[/tex]

[tex]V_{f} - V_{o} = a*t[/tex]

[tex]t = \frac{V_{f} - V_{o}}{a}[/tex]

Where:   [tex]V_{o} = 22.9 m/sec[/tex]   (at the beginning)

              [tex]V_{f} = 0 m/sec[/tex]   (at the end because it stops)

We must use [tex]a = - 8.9655 m/sec^{2}[/tex]   because in this case speed is decreasing

Finally:   [tex]t = \frac{0 m/sec - 22.9 m/sec}{- 8.9655 m/sec^{2} }[/tex]

              t = 2.55 sec

By applying Newton's second law of motion and the motion equation, we find that it will take approximately 2.55 seconds for the Acme Tractor Beam to slow down the baseball to a stop in space.

This problem is a classic example of the application of Newton's second law of motion which states: F = ma, where F is the force, m is the mass, and a is the acceleration. Here we are given the force F exerted by your Acme Tractor Beam (1.3 N) and the mass of the baseball m (0.145 kg).

First, use F=ma to calculate acceleration a. The acceleration a = F/m = 1.3 N / 0.145 kg = 8.97 m/s². This is the rate at which the baseball would slow down under the influence of the tractor beam.

Next, use the formula v = u + at, where 'v' is the final velocity, 'u' is the initial velocity, 't' is the time, and 'a' is the acceleration we just calculated. We want to know the time 't' when the baseball comes to stop (v = 0), so we rearrange this equation to solve for 't': t = (v - u) / a.

Plugging in the given numbers: t = (0 - 22.9 m/s) / -8.97 m/s², we find t = 2.55 s.

So it will take approximately 2.55 seconds for your Acme Tractor Beam to slow down the baseball to a stop.

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Answer:

The average acceleration of the driver during the collision is [tex]-348.4\frac{m}{s^{2}}[/tex]

Explanation:

Initial speed of car , [tex]u=85\frac{km}{h}=\frac{85\times 5}{18}\frac{m}{s}[/tex]

=>[tex]u=23.61\frac{m}{s}[/tex]

Finally the car comes to rest .

Therefore final speed of the car , [tex]v=0\frac{m}{s}[/tex]

Distance traveled while coming to rest , s = 0.80 m

Using equation of motion

[tex]v^{2}=u^{2}+2as[/tex]

=>[tex]0^{2}=23.61^{2}+2\times 0.80\times a[/tex]

=>[tex]a=-348.4\frac{m}{s^{2}}[/tex]

Thus the average acceleration of the driver during the collision is [tex]-348.4\frac{m}{s^{2}}[/tex]

Answer:

A sloping surface separating air masses that differ in temperature and moisture content is called a front.

A sloping surface separating air masses that differ in temperature and moisture content is called a front.

A sloping surface separating air masses that differ in temperature and moisture content is called a front. Fronts occur when warm air and cold air meet, creating a boundary between them. The warm air is forced to rise over the cold air, resulting in changes in weather conditions.

There are several types of fronts, each associated with distinct weather patterns:

Cold Front: A cold front forms when a cold air mass advances and replaces a warmer air mass. As the cold air displaces the warm air, it forces the warm air to rise rapidly, leading to the formation of cumulonimbus clouds and potentially severe weather conditions such as thunderstorms.

Warm Front: In contrast, a warm front occurs when a warm air mass advances and overtakes a retreating cold air mass. As the warm air rises over the colder air, it produces widespread stratiform clouds and precipitation over an extended area.

Stationary Front: When two air masses meet but neither advances, a stationary front is formed. This results in a prolonged period of cloudy and wet weather along the boundary.

Occluded Front: An occluded front develops when a fast-moving cold front overtakes a slow-moving warm front. This complex type of front often leads to a mix of weather conditions, including precipitation and strong winds.

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Answer:[tex]\frac{g}{2}[/tex]

Explanation:

Given

mass of stone[tex]\left ( m\right )[/tex]=0.250 kg

Let initial velocity with which it is thrown upward is u

therefore after time t it's velocity is zero at highest point

t=[tex]\frac{u}{g}[/tex]

where g= gravity at earth

therefore [tex]T=2\times \frac{u}{g}[/tex]-------1

Now same thing is done in Planet X where gravity is g'

therefore time taken by stone to reach surface is

[tex]T'=T=2\times \frac{u}{g'}[/tex]-------2

Divide 1 & 2

[tex]\frac{T}{T'}[/tex]=[tex]\frac{g'}{g}[/tex]

[tex]\frac{1}{2}[/tex]=[tex]\frac{g'}{g}[/tex]

g'=[tex]\frac{g}{2}[/tex]

The true statements are: (A) At any junction point in a circuit, the sum of all the currents entering the junction must equal the sum of all the currents leaving the junction. (C) The sum of the changes in potential around any closed loop of a circuit must equal zero. (D) Kirchhoff's loop rule is based on the conservation of energy.

(A) At any junction point in a circuit, the sum of all the currents entering the junction must equal the sum of all the currents leaving the junction. This is known as Kirchhoff's junction rule or the law of conservation of charge.

(B) Kirchhoff's junction rule is based on the conservation of charge, not the conservation of energy.

(C) The sum of the changes in potential around any closed loop of a circuit must equal zero. This is known as Kirchhoff's loop rule or the law of conservation of energy.

(D) Kirchhoff's loop rule is based on the conservation of energy, not the conservation of charge.

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Answer:

The answer is 'D' none

Explanation:

In the figure shown we have

[tex]2Tsin(\theta )=mg\\\\\therefore T=\frac{mg}{2sin(\theta )}[/tex]

From the figure we can see that

[tex]cos(\theta )=\frac{\frac{3L}{8}}{\frac{L}{2}}\\\\\therefore \theta =cos^{-1}(\frac{3}{4})\\\\sin(\theta )=\frac{\sqrt{7}}{4}[/tex]

Thus value of tension be will be

[tex]T=\frac{2mg}{\sqrt{7}}[/tex]

The tension in the string when an object of mass m is suspended from the center is given by T = (mg)/(2L), where T is the tension, m is the mass of the object, g is the acceleration due to gravity, and L is the length of the string. So, the correct answer is (A) (mg)^1/2.

To find the tension in the string when an object of mass m is suspended from the center, we can use the formula for tension in a string:

T = (mg)/(2L)

Where T is the tension, m is the mass of the object, g is the acceleration due to gravity, and L is the length of the string.

Substituting the given values, the tension in the string is:

T = (m)(9.8)/(2L)

Therefore, the correct answer is (A) (mg)^1/2.

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Answer:

D. a cation that has a smaller radius than the atom.

Explanation:

When electrons are removed from the outermost shell of a calcium atom, the atom becomes a cation that has a smaller radius than the atom.

When electrons are removed from the outermost shell of a calcium atom, the atom becomes: D. a cation that has a smaller radius than the atom.

An ion can be defined as an atom or molecules (group of atoms) that has either lost or gained one or more of its valence electrons, thereby, making it to have a net positive or negative electrical charge respectively.

Basically, there are two (2) types of ion and these are:

A cation is a positive electrical charge which is formed when the atom of a chemical element losses an electron.

Hence, a cation is formed when an electron is removed from the atom of a chemical element.

Generally, the atomic size of a chemical element would increase when its number of electrons increase, thereby, increasing its atomic radius.

Consequently, the radius of a cation in comparison with the radius of its neutral atom becomes smaller because it losses more electron from the outermost shell of its atom.

In conclusion, when electrons are removed from the outermost shell of a calcium atom, the atom becomes a cation that has a smaller radius than its atom.

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(a) [tex]-1.5\cdot 10^6 N[/tex]

First of all, we need to calculate the acceleration of the person, by using the following SUVAT equation:

[tex]v^2 -u ^2 = 2ad[/tex]

where

v = 0 is the final velocity

u = 20.0 m/s is the initial velocity

a is the acceleration

d = 1.00 cm = 0.01 m is the displacement of the person

Solving for a,

[tex]a=\frac{v^2-u^2}{2d}=\frac{0-20.0^2}{2(0.01)}=-20000 m/s^2[/tex]

And the average force on the person is given by

[tex]F=ma[/tex]

with m = 75.0 kg being the mass of the person. Substituting,

[tex]F=(75)(-20000)=-1.5\cdot 10^6 N[/tex]

where the negative sign means the force is opposite to the direction of motion of the person.

b) [tex]-1.0\cdot 10^5 N[/tex]

In this case,

v = 0 is the final velocity

u = 20.0 m/s is the initial velocity

a is the acceleration

d  = 15.00 cm = 0.15 m is the displacement of the person with the air bag

So the acceleration is

[tex]a=\frac{v^2-u^2}{2d}=\frac{0-20.0^2}{2(0.15)}=-1333 m/s^2[/tex]

So the average force on the person is

[tex]F=ma=(75)(-1333)=-1.0\cdot 10^5 N[/tex]

The average force on the person if he is stopped by a padded dashboard is -1.5 x 10⁶ N.

The average force on the person if he is stopped by an air bag is -10,000 N.

The given parameters;

The deceleration of the car when the padded dashboard compresses an average of 1.00 cm.

s = 0.01 m

[tex]v^2 = u^2 + 2as\\\\0 = 20^2 + (2\times 0.01)a\\\\0 = 400 + 0.02a\\\\0.02a = -400\\\\a = \frac{-400}{0.02} \\\\a = -20,000 \ m/s^2[/tex]

The average force is calculated as;

F = ma

F = 75 x (-20,000)

F = -1.5 x 10⁶ N.

The deceleration of the car when the air bag compresses an average of 15 cm.

s = 0.15 m

[tex]v^2 = u^2 + 2as\\\\0 = u^2 + 2as\\\\-2as = u^2\\\\a = \frac{u^2}{-2s} = \frac{20^2}{-2\times 0.15} = -1,333.33 \ m/s^2[/tex]

The average force is calculated as follows;

F = ma

F = 75 x (-1,333.33)

F = -10,000 N.

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Answer: Nuclear energy

Explanation:

Nuclear energy (also called atomic energy) is the energy found in the nucleus of an atom.

This energy is released spontaneously (within the stars and the sun) or artificially (in nuclear reactors built by humans) in nuclear reactions, which are divided into two types:

-Fission (separation of the components of the atom nucleous)

-Fusion (joining two light nuclei to form a heavier nucleous)

In the case of the Sun, the nuclear reactions that occur are due fusion, in which the hydrogen is converted into helium.

Answer:

No

Explanation:

The amount of energy transferred out of battery will not be the same as given during charging.

A battery has its internal resistance as well which will draw some energy, through this internal resistance energy is lost

                                         P = I² R

                where P is energy, I is current passing and R is resistance.

As per law of conservation energy will be saved as it is the sum of drawn energy and energy wasted in internal  resistance. But the total energy transferred out will not be same.

Answer:

149 m

Explanation:

The distances across the lake is forming a triangle.  

let the distance between the point and the left side be 'x'

and the distance between the point and the right be 'y'

and the distance across the lake be 'z' and the angle opposite to 'z' be 'Z' given:

∠Z = 83°

x = 105 m

y = 119 m

Now, applying the Law of Cosines, we get  

z² = x² + y² - 2xycos(Z)  

Substituting the values in the above equation, we get

z² = 105² + 119² - 2×105×119×cos(83°)

or

z = √22140.48

or

z = 148.796 m ≈ 149 m

The point is 149 m across the lake

Answer:

The speed of sound in this gas is 409.6 m/s.

Explanation:

The length of the column changes from 20 cm from resonance to resonance. Thus,

[tex]L=\frac {(2n+1)\lambda}{4}[/tex]

The length change from one resonance to resonance. so, there is 1 loop change. So,

ΔL = 1 loop = λ/2

ΔL = 20 cm (given)

Also, 1 cm = 0.01 m

So,

ΔL = 0.2 cm (given)

The wavelength is:

λ = ΔL×2

λ = 2x0.2 = 0.4 m

Given:

Frequency (ν) = 1024 Hz

Velocity of the sound in the gas = ν×λ = 1024×0.4 m/s = 409.6 m/s

Answer:

[tex]\theta = 50.5 degree[/tex]

Explanation:

As we know that the refractive index of the water is

[tex]\mu_w = \mu_1[/tex]

also we know that refractive index of the glass is

[tex]\mu_g = \mu_2[/tex]

now we know by Snell's law

[tex]\mu_1 sin\theta_1 = \mu_2 sin\theta_2[/tex]

so we have

[tex]\mu_1 sin36 = \mu_2 sin49.6[/tex]

[tex]\frac{\mu_1}{\mu_2} = 1.2956[/tex]

now if no light will refract into the water then in that case

[tex]\mu_1 sin\theta = \mu_2 sin90[/tex]

now we have

[tex](1.2956) sin\theta = 1[/tex]

[tex]sin\theta = 0.77[/tex]

[tex]\theta = 50.52 degree[/tex]

A) The net unbalanced force acting on the wagon is; F_net = 50 N

B) The forces acting on the wagon are;

Applied Force = 50 N

Frictional Force = 50 N

C) What will happen if mass is increase is that;

frictional force will increase.

Formula for force is;

Force = mass x acceleration

F = ma

A) We are told that the speed is constant and at constant speed, acceleration is zero. Thus; F_net = 0 N

B) We are told that the force required to push the wagon at constant speed is 50 N.

Now, from newtons third law of motion, it states that to every action, there is an equal and opposite reaction.

Thus, there will be an equal opposite reaction which will be the frictional force. Thus; F_f = 50 N

C) Frictional force has the formula;

F_f = μmg

So if the mass is increased, the frictional force will also increase.

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(a) The net force acting on the wagon is zero (0).

(b) The forces acting on the wagon are, the applied horizontal force on the wagon and frictional force between the wagon and the sidewalk.

(c) As the mass increases, the applied force should increase by equal amount to keep the moving at constant speed.

The given parameters;

The net horizontal force acting on the wagon is given as;

[tex]\Sigma F_x = 0\\\\F - F_k = ma[/tex]

where;

At constant speed, the acceleration of the wagon = 0

[tex]F - F_k = m(0)\\\\F- F_k = 0\\\\[/tex]

Thus, the net force acting on the wagon is zero (0).

(b) The forces acting on the wagon are;

(c) The Newton's second law of motion is given as;

F = ma

[tex]F = \frac{m(\Delta v)}{t} \\\\\Delta v =\frac{Ft}{m} \\\\\frac{F_1}{m_1} = \frac{2F_1}{2m_1}[/tex]

Thus, as the mass increases, the applied force should increase by equal amount to keep the moving at constant speed.

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Explanation:

This sentence is the description of a specific type of energy: the mechanical energy.

To unerstand it better:

The mechanical energy of a body, a system or a substance is that which is obtained from the speed of its movement (kinetic energy) or its specific position (potential energy), in order to produce a mechanical work.   This means mechanical energy involves both the kinetic energy and the potential energy (which can be elastic or gravitational, for example).  

In addition, it should be noted that mechanical energy is conserved in conservative fields and is a scalar magnitude.

Therefore:

The sum of potential and kinetic energies in the particles of a substance is called Mechanical Energy

Answer:

Explanation:

internal!!!!!!!!

Answer:

The frog's horizontal velocity is 0.2 m/s.

Explanation:

To solve this problem, we must first remember what velocity is and how we solve for it.  Velocity can be solved for using the formula x/t, where x represents horizontal distance and t represents time (in seconds), that it takes to travel this distance.  If we plug in the given numbers for these variables and solve, we get the following:

v = x/t

v = 0.8m/4s

v = 0.2 m/s

Therefore, the correct answer is 0.2 m/s.  We can verify that these units are correct because the formula calls for distance divided by time, so meters per second is a sensible answer.

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Answer:

1) Recollapsing universe

2) critical universe

3) Coasting universe

Explanation:

According to the smallest ration (ratio actual mass density to current density) to largest ration, rank of models for expansion of universe are

1) Recollapsing universe -in this, metric expansion of space is reverse and universe recollapses.

2) critical universe - in this, expansion of universe is very low.

3) Coasting universe -  in this, expansion of universe is steady and uniform

Answer:

The maximum power available from the water fall is 239.568 kWh/week.

Explanation:

Given:

Flow rate = 0.15 × 10² m³/h

now the mass of water flowing per hour will be = flow rate × mass density of water(i.e 1000 kg/m³)

mass of water flowing per hour will be = 0.15 × 10² m³/h × 1000 kg/m³ = 15000 kg/h

The gravitational potential energy of the falling water = mgh = 15000 × 9.8 × 35 = 5145000 J/h

or

5145000/3600 = 1426.166 J/s (as 1 h = 3600 seconds)

or

1426.166 W = 1.426 kW

Now, the number of hours in a week = 7 × 24 = 168 hours

Now the energy produce in a week = 1.426 kW × 168 hr = 239.568 kWh/week.

No it is not sufficient to meet the needs

The maximum hydraulic power generated by the waterfall is around 14.35 kW, which is more than the required energy for weekly consumption (2.28 kW). Therefore, the waterfall can especially serve as a power source.

The problem involves the calculation of hydraulic power, which is given by the formula Power = p * g * h * Q, where p is the density of water (around 1000 kg/m³ in standard conditions), g is the gravitational acceleration (approximated as 9.8 m/s²), h is the waterfall height (in meters), and Q is the flow rate (in m³/s). First, we need to convert the flow rate from m³/h to m³/s. We get Q = 0.150 * 10² m³/h = 0.04167 m³/s.

After substituting the figures into the formula, we get: Power = 1000 kg/m³ * 9.8 m/s² * 35.0 m * 0.04167 m³/s = 14350.5 Watts, or about 14.35 kW.

Given the energy requirement per week is 1750 kWh, let's convert it to the energy required per second. That is 1750 kWh/wk = (1750 * 1000) / (7 * 24 * 60 * 60) = 2.28 kW. This means, the maximum power available from the waterfall is more than enough to meet your requirements.

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To determine the magnitude and direction of the electric field when an electron is released in a uniform electric field, we use the displacement formula and compare the acceleration due to the electric field with the acceleration due to gravity.

(a) To determine the magnitude of the electric field, we can use the formula E = delta V / delta x. The electron experiences constant acceleration, so the displacement equation is given by x = (1/2)at^2, where x is the displacement, a is the acceleration, and t is the time. Plugging in the given values, we find that the acceleration is 5.00 x 10^11 m/s^2 (upward).

(b) We can justify ignoring the effects of gravity by comparing the acceleration due to the electric field with the acceleration due to gravity. For an electron in a uniform electric field, the acceleration is much greater than the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the effects of gravity can be ignored in this scenario.

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The magnitude and direction of the electric field can be determined by calculating the electric field strength. Gravity can be ignored in this situation because the electric field is much stronger.

(a) To find the magnitude and direction of the electric field, we can use the equation:

Electric field strength (E) = Force (F) / Charge (q)

Given that the electron is accelerating upward, the direction of the electric field is downward. Using the formula, we can rearrange it to find the electric field strength:

Electric field strength = Force / Charge = mass x acceleration / charge = (9.11 x 10^-31 kg) x (9.8 m/s^2) / (1.6 x 10^-19 C) = 5.67 x 10^11 N/C

The magnitude of the electric field is 5.67 x 10^11 N/C, and the direction is downward.

(b) We can justify ignoring the effects of gravity by comparing the magnitude of the electric field to the gravitational field strength. The gravitational field strength near the surface of the Earth is approximately 9.8 N/kg. Comparing this to the electric field strength of 5.67 x 10^11 N/C, we can see that the electric field is much stronger than the gravitational field. Therefore, the effects of gravity can be ignored.

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Answer:

a). T = 1.64 hr

b). v = 7.503 km/s

Explanation:

Given :

NASA launched the Aura spacecraft to study the earth's climate and atmosphere.

 Height of the satellite orbit from the earth's surface, h = 705 km

                                                                                            = 705000 m

Therefore we know that,

a).Time period of the space craft is

[tex]T = 2\pi \sqrt{\frac{(R+h)^{3}}{G\times M}}[/tex]

where, G = Universal Gravitational constant

               = [tex]6.67 \times 10^{-11} N-m^{2}/kg^{2}[/tex]

          M = Mass of the earth

               = 5.98 x [tex]10^{24}[/tex] kg

          R = Radius of the earth

             = 6.38 x [tex]10^{6}[/tex] m

∴[tex]T = 2\pi \sqrt{\frac{(R+h)^{3}}{G\times M}}[/tex]

 [tex]T = 2\pi \sqrt{\frac{((6.36\times 10^{6})+705000)^{3}}{6.67\times 10^{-11}\times 5398\times 10^{24}}}[/tex]

[tex]T = 5933[/tex] s

           = 1.64 hr

Thus, the satellite will take 1.64 hr to make one orbit.

b). We know velocity of the spacecraft is given by

[tex]v=\sqrt{\frac{G\times M}{R+h}}[/tex]

[tex]v=\sqrt{\frac{6.67\times 10^{-11}\times 5.98\times 10^{24}}{(6.38\times 10^{6})+705000}}[/tex]

v = 7503 m/s

  = 7.503 km/s

Thus, the Aura satellite is moving with velocity v = 7.503 km/s

A) The number of hours it takes for the satellite to make one orbit ( h ) = 1.64 hours

b) The speed of the Aura spacecraft = 7.5 Km/s

Given data

Height of satellite Orbit ( h ) = 705 km ≈ 705000 m

A) Determine the time taken in hours for the satellite to make a single orbit

T = [tex]2\pi \sqrt{\frac{(R+h)^3}{GM} }[/tex]  -------- ( 1 )

where ; G = 6.67 * 10⁻¹¹ N-m²/kg²,     M ( mass of earth ) = 5.98 * 10²⁴,

R = 6.38 * 10⁶ m ,     h = 705000 m

Insert the values into equation ( 1 )

T = 5933 secs  

   = 1.64 hours   ( time taken to complete one orbit )

B) Determine how fast Aura spacecraft is moving

V = [tex]\sqrt{\frac{GM}{R+h} }[/tex]   -------- ( 2 )

where ; G = 6.67 * 10⁻¹¹ N-m²/kg²,     M ( mass of earth ) = 5.98 * 10²⁴,

R = 6.38 * 10⁶ m ,     h = 705000 m

Insert values into equation ( 2 )

∴ V = 7503 m/s

       = 7.5 km/s

Hence we can conclude that the  number of hours it takes for the satellite to make one orbit ( h ) = 1.64 hours and The speed of the Aura spacecraft = 7.5 Km/s

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Answer:

v = 4.17 m/s

Explanation:

as we know that block is moving towards the end of the rod

so let say just after the collision the block is moving with speed v' and rod is rotating with speed "w"

so we have angular momentum conservation about the hinge point

[tex]mvL = mv'L + I\omega[/tex]

[tex](2.2)(12)L = (2.2)v'(L) + (\frac{3.6 L^2}{3}) \omega[/tex]

[tex]12 = v' + 0.545(\omega L)[/tex]

now by the equation of coefficient of restitution we can say

[tex]0.85 = \frac{(\omega L) - v'}{12}[/tex]

now we have

[tex]\omega L - v' = 10.2[/tex]

now we have

[tex]\omega L = 14.37  [/tex]

[tex]v' = 4.17 m/s[/tex]

so velocity of block just after collision is 4.17 m/s

To find the velocity of the block after the collision, we can use the principle of conservation of momentum and the coefficient of restitution.

First, we need to calculate the velocity of the 3.6-lb rod AB after the collision with the 2.2-lb block.

To do this, we can use the principle of conservation of momentum. The momentum before the collision is given by the sum of the momentums of the rod and the block: (3.6 lb) x (0 ft/s) + (2.2 lb) x (12 ft/s) = 26.4 lb-ft/s.

The coefficient of restitution (e) is defined as the ratio of the relative velocity of separation to the relative velocity of approach. In this case, the relative velocity of approach is 12 ft/s, and the relative velocity of separation is the sought-after velocity of the block immediately after the collision.

Answer:

I believe the answer is C.) actually, both ways

hope this helps! (:

Explanation:

Answer:

 [tex]\omega_f = 0.0067\ rad/s[/tex]

Explanation:

Given:

Initial angular velocity of the disc, [tex]\omega_o[/tex] = 0.067 rad/s

Initial moment of inertia of the disc, [tex]I_o[/tex]  = 0.10 kg.m²

Distance of sand ring from the axis, r = 0.40m

Mass of the sand ring = 0.50 kg

Now, no external torque is applied to the rotating disk.

Thus, the angular momentum of the system will remain conserved.

Also,from the properties of moment of inertia, the addition of the sand ring will increase the initial moment of inertia by an amount Mr²

thus, we have

Initial Angular Momentum = Final Angular Momentum

or

[tex]I_o\omega_o = I_f\times\omega_f[/tex]

[tex]I_o\omega_o = (I_o + Mr^2)\times\omega_f[/tex]

Where,

[tex]I_f[/tex] = Final moment of inertia

[tex]\omega_f[/tex] = Final angular velocity

substituting the values, we get

 [tex]0.10\times0.067 = (0.10 + 0.50\times 0.40^2)\times\omega_f[/tex]

or

 [tex]0.0067 = (0.18)\times\omega_f[/tex]

or

 [tex]\omega_f = 0.0067\ rad/s[/tex]

The rate of change of angular displacement is defined as angular velocity. After all the sand is in place the angular velocity of the disk will be 0.067 rad/sec.

The rate of change of angular displacement is defined as angular velocity, and it is stated as follows:

ω = θ t

Where,

θ is the angle of rotation,

t is the time

ω is the angular speed

ω₀ is the initial angular velocity of the disc = 0.067 rad/s

I₀ is the initial moment of inertia of the disc,  = 0.10 kg.m²

r is the distance of sand ring from the axis = 0.40m

m is the mass of the sand ring = 0.50 kg

If the net external torque is applied to the rotating disk is zero

According to the angular momentum conservation principle;

Initial Angular Momentum = Final Angular Momentum

[tex]\rm I_0 \omega_0= I_f \omega_f \\\\[/tex]

According to parallel axis theorem ;

[tex]\\\\ I_f = I_0 + mr^2[/tex]

[tex]\rm I_0 \omega_0= (I_0 + mr^2 ) \omega_f[/tex]

[tex]\rm 0.10 \times 0.067= (0.10 + 1020 \times 0.40^2 ) \omega_f \\\\ \rm \omega_f=0.0067\ rad/sec[/tex]

Hence the angular velocity of the disk will be 0.067 rad/sec.

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Answer:

0.29[tex]\text{m}\text{s}^{2}[/tex]

Explanation:

Given: Haley is driving down a straight highway at 73 mph. A construction sign warns that the speed limit will drop to 55 mph in 0.50 mi.

To Find: constant acceleration (in [tex]\text{m}\text{s}^{2}[/tex]) that will bring Haley to this lower speed in the distance available

Solution:

we know that,

[tex]1[/tex] mile=[tex]1.609[/tex]km

[tex]1[/tex] km[tex]\setminus[/tex]h = [tex]5\setminus18 m\setminus s[/tex]

Initial Speed of Haley(u)=[tex]73[/tex] mph

                                     [tex]73\times 1.609\times 5\setminus 18[/tex]

                                     [tex]32.63[/tex][tex]\text{m}\setminus\text{s}[/tex]

Final Speed of Haley(v)= [tex]55[/tex] mph

                                     [tex]55\times 1.609\times 5\setminus 18[/tex]

                                     [tex]24.58[/tex][tex]\text{m}\setminus\text{s}[/tex]

The distance to be travelled  while lowering the speed(S)=[tex]0.5[/tex] mile

                                     [tex]0.805[/tex] km

                                     [tex]805[/tex] m

according to third equation of motion,

                     [tex]\text{v}^{2}-\text{u}^{2}=2\text{a}\text{S}[/tex]

as speed is lowering down the acceleration will be in the opposite direction of motion, hence acceleration will be negative, equation will become

                    [tex]\text{u}^{2} -\text{v}^{2}=2a\text{S}[/tex]

putting values,

                     [tex]32.63^{2}[/tex]-[tex]24.58^{2}[/tex]=[tex]2a\times805[/tex]

                     a=[tex]460.55\setminus1610[/tex]

                     a≅[tex]0.29[/tex][tex]\text{m}\text{s}^{2}[/tex]

the constant acceleration that will drop speed to [tex]55 \text{mph}[/tex] is [tex]0.29[/tex][tex]\text{m}\text{s}^{2}[/tex]

The constant acceleration of the driver is -0.286 m/s²

The given parameters;

initial velocity of the driver, v = 73 mph

final velocity of the driver, v = 55 mph

distance available, d = 0.5 mile

The constant acceleration of the driver is calculated as follows;

[tex]v^2 = u^2 + 2as\\\\2as = v^2 - u^2\\\\a = \frac{v^2 - u^2}{2s} \\\\a = \frac{55^2 - 73^2}{2(0.5)} \\\\a = -2,304\ mi/h^2[/tex]

The acceleration in m/s²

1 mile = 1609 m

[tex]a = \frac{-2304 \ mi}{hr^2} \times \frac{1609 \ m}{1 \ mile} \times \frac{1 \ hr^2}{(3600)^2 \ s^2} \\\\a = -0.286 \ m/s^2[/tex]

Thus, the constant acceleration of the driver is -0.286 m/s²

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Answer:

F1= 196 N

F2= 392 N  

Explanation:

Given:

length of the plank = 2 m

mass of the plank = 20 kg

Weight of the plank = 20 x 9.8 =196 N  

Torque due to the weight of the plank with respect to the pivoted end (i.e the end held by the hand) Counter clockwise torque  = 196 x cog of wood

= 196 x 1 = 196 Nm

Clockwise torque = F2 x 0.5

for the balanced case  

F2 x 0.5 = 196  

F2 = 196/ 0.5

F2= 392 N  

now,

the net force

Net downward force  =Net upward force

F1 + weight of plank = F2

F1 + 196 = 392N

F1 = 392 – 196

F1= 196 N

To find the forces F1 and F2 exerted on the plank, we can use the principle of equilibrium. The sum of the forces acting on the plank must be zero, and the sum of the torques must also be zero. By solving the equations derived from these conditions, we can determine the values of F1 and F2.

To find the forces F1 and F2, we can use the principle of equilibrium. According to the principle, the sum of the forces acting on an object in equilibrium must be zero, and the sum of the torques must also be zero.

For the vertical forces:

F1 + F2 - mg = 0

Where m is the mass of the plank and g is the acceleration due to gravity.

For the torques:

F1 * 2m = F2 * 0.5m

Solving these equations will give us the values for F1 and F2.

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