The law of reflection states that the angle of incidence and the angle of reflection are always A: greater than 45 degrees each B: less than 45 degrees each C: equal in measure D: different in measure

Final answer:

The final displacement of the weather balloon, considering its 6 km upward travel and the 10 km north and 8 km east wind displacement, is approximately 14.1 km from its starting point.

Explanation:

The student is asking to find the final displacement of a weather balloon that has been blown by the wind as it travels upwards. To solve this, we can use the Pythagorean theorem since the balloon's movement creates a three-dimensional right-angled triangle with the vertical ascent and the horizontal wind displacement as the perpendicular sides.

The displacement due to the wind is found by using the Pythagorean theorem for the horizontal components: √((10 km)² + (8 km)²) = √(164 km²) which is approximately 12.81 km to the northeast.

The overall displacement of the balloon is the three-dimensional resultant which can be calculated using the Pythagorean theorem again with the 6 km vertical component and the 12.81 km horizontal component:

√((6 km)² + (12.81 km)²) = √(200 km²) which is approximately 14.1 km. This is the balloon's straight-line distance from its starting point.

Answer:

fourth shell to the second shell

Explanation:

When an electron of an atom moves from a lower energy shell to a higher energy shell (such as 1st shell to the 3rd shell), it absorbs energy through a specific wavelength of electromagnetic wave equivalent to the difference in energy levels of the electron shells.

Conversely, when the electron jumps from a higher electron shell to a lower one (such as  in this case) it releases energy, in the form a specific wavelength of electromagnetic wave, equivalent to the difference in energy levels between the two electron shells.

Answer:

fourth shell to the second shell

Explanation:

Answer:

B. 3.75 meters/second2

Explanation:

The velocity of a car traveling in a straight line increases from 0 meters/second to 30 meters/second in 8 seconds. What is the average acceleration of the car;

acceleration = (change in velocity)/(change in time)

acceleration = ( 30 - 0)/(8)

acceleration = 3.75 meters/second2

The orbital period of a spacecraft in low Mars orbit can be calculated using Kepler's Third Law, taking into account the radius of Mars and its gravitational influence.

The orbital period of a spacecraft in a low orbit near the surface of Mars can be calculated using Kepler's Third Law, which connects the time period of a planet's orbit (T) with the semi major axis of its orbit (r). It is important to note that the mass of the spacecraft is much smaller than the mass of Mars, and therefore, the mass of the spacecraft can be ignored in the calculation.

The formula for the orbital period is: T = 2π√(r³/μ), where μ (the standard gravitational parameter) is G*M (the gravitational constant, G, times the mass of Mars, M). Substituting the given radius of Mars into the formula we will get the orbital period of a spacecraft in a low orbit near the surface of Mars.

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The answer is: [tex]1.6888 \, \text{hr}.[/tex]

The orbital period [tex]\( T \)[/tex] of a spacecraft in a low orbit near the surface of Mars can be estimated using Kepler's third law, which relates the square of the orbital period of a planet to the cube of the semi-major axis of its orbit. For a circular orbit, the semi-major axis is equal to the radius of the orbit, which in this case is approximately the radius of Mars. Kepler's third law is given by:

[tex]\[ T^2 = \frac{4\pi^2}{G(M + m)}a^3 \][/tex]

where:

- [tex]\( T \)[/tex] is the orbital period of the spacecraft,

- [tex]\( G \)[/tex] is the gravitational constant [tex](\(6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2\)),[/tex]

- [tex]\( M \)[/tex] is the mass of Mars [tex](\(6.417 \times 10^{23} \, \text{kg}\)),[/tex]

- [tex]\( m \)[/tex] is the mass of the spacecraft (which is negligible compared to the mass of Mars),

- [tex]\( a \)[/tex] is the semi-major axis of the orbit (approximately the radius of Mars, [tex]\(3.4 \times 10^6 \, \text{m}\))[/tex].

Since the mass of the spacecraft [tex]\( m \)[/tex] is much smaller than the mass of Mars [tex]\( M \)[/tex], we can ignore [tex]\( m \)[/tex] in the calculation. The equation simplifies to:

[tex]\[ T^2 = \frac{4\pi^2}{GM}a^3 \][/tex]

Now we can solve for [tex]\( T \)[/tex]:

[tex]\[ T = \sqrt{\frac{4\pi^2}{GM}a^3} \][/tex]

Plugging in the values:

[tex]\[ T = \sqrt{\frac{4\pi^2}{(6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2)(6.417 \times 10^{23} \, \text{kg})}(3.4 \times 10^6 \, \text{m})^3} \][/tex]

[tex]\[ T = \sqrt{\frac{4\pi^2}{(6.674 \times 10^{-11})(6.417 \times 10^{23})}(3.4 \times 10^6)^3} \][/tex]

[tex]\[ T = \sqrt{\frac{4\pi^2}{4.276 \times 10^{13}}(3.4 \times 10^6)^3} \][/tex]

[tex]\[ T = \sqrt{\frac{4\pi^2}{4.276 \times 10^{13}}(3.93 \times 10^{19})} \][/tex]

[tex]\[ T = \sqrt{\frac{4\pi^2(3.93 \times 10^{19})}{4.276 \times 10^{13}}} \][/tex]

[tex]\[ T = \sqrt{\frac{4\pi^2 \times 3.93 \times 10^{19}}{4.276 \times 10^{13}}} \][/tex]

[tex]\[ T = \sqrt{\frac{4\pi^2 \times 3.93}{4.276} \times 10^6} \][/tex]

[tex]\[ T = \sqrt{\pi^2 \times \frac{4 \times 3.93}{4.276}} \times 10^3 \][/tex]

[tex]\[ T = \pi \sqrt{\frac{4 \times 3.93}{4.276}} \times 10^3 \][/tex]

[tex]\[ T \approx \pi \sqrt{3.77} \times 10^3 \][/tex]

[tex]\[ T \approx 3.1416 \times 1.94 \times 10^3 \][/tex]

[tex]\[ T \approx 6.08 \times 10^3 \, \text{s} \][/tex]

To convert seconds to minutes, divide by 60:

[tex]\[ T \approx \frac{6.08 \times 10^3 \, \text{s}}{60 \, \text{s/min}} \][/tex]

[tex]\[ T \approx 101.33 \, \text{min} \][/tex]

And to convert minutes to hours, divide by 60 again:

[tex]\[ T \approx \frac{101.33 \, \text{min}}{60 \, \text{min/hr}} \][/tex]

[tex]\[ T \approx 1.6888 \, \text{hr} \][/tex]

Answer: 4.33°

Explanation:

The formula to calculate the standard deviation for a uniform distribution for interval [a,b] is given by :-

[tex]\text{Standard deviation}:\sigma=\sqrt{\dfrac{(b-a)^2}{12}}[/tex]

Given : The amount that the water temperature is raised has a uniform distribution over the interval = [tex][10^{\circ},25^{\circ}][/tex]

Then , the standard deviation of the temperature increase is given by :-

[tex]\sigma=\sqrt{\dfrac{(25-10)^2}{12}}\\\\\Rightarrow\sigma=4.33012701892\approx4.33[/tex]

Hence, the standard deviation of the temperature increase is 4.33°.

For a uniformly distributed random variable, calculate the standard deviation using the formula sqrt((b - a)^2 / 12). In this case, the standard deviation of the temperature increase is approximately 4.33 degrees Celsius.

In statistics, the standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of values. This question deals with the uniform distribution, so it's a topic in probability and statistics.

For a uniform distribution on the interval [a, b], the standard deviation can be calculated using the formula: sqrt((b - a)^2 / 12). In this case, a = 10 degrees and b = 25 degrees. So, the standard deviation of the temperature increase is sqrt((25 - 10)^2 / 12) = sqrt(225 / 12) = sqrt(18.75) which is approximately 4.33 degrees Celsius.

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Answer: Electrons are the smallest of the three particles that make up atoms. Electrons are found in shells or orbitals that surround the nucleus of an atom

Explanation: hope this helps

Answer:

3099 J

Explanation:

While the fireman  slides down, his initial gravitational potential energy is converted partially into kinetic energy, partially into thermal energy, so we can write:

[tex]\Delta U = K + E_t[/tex] (1)

where

[tex]\Delta U [\tex] is the change in gravitational potential energy

K is the kinetic energy gained

Et is the thermal energy

The variation in gravitational potential energy is

[tex] U = mg \Delta h = (80 kg)(9.8 m/s^2)(4.2 m)=3293 J [/tex]

where m=80 kg is the mass of the fireman, g=9.8 m/s^2 is the acceleration of gravity, [tex]\Delta h=4.2 m[/tex] is the change in height of the fireman.

The kinetic energy gained is

[tex] K=\frac{1}{2}mv^2=\frac{1}{2}(80 kg)(2.2 m/s)^2=194 J[/tex]

where v = 2.2 m/s is the speed reached by the fireman at the bottom of the slide

So now solving eq.(1) we find the increase in thermal energy :

[tex] E_t = \Delta U - K = 3293 J - 194 J = 3099 J[/tex]

Answer:

3100 J

Explanation:

Because this scenario using three forms of energy (kinetic, gravitational potential, thermal), we use the conservation of energy formula:

0=ΔKe + Δ Ug + ΔEth

Keep in mind we want to find change in thermal energy, so:

ΔEth = -(ΔKe + ΔUg)

Change in kinetic energy:

ΔKe = Kf - Ki = [tex]\frac{1}{2}(0)^{2} -\frac{1}{2}(80)(2.2)^{2} = 190 J[/tex]

Change in Gravitational potential energy:

[tex]mgy_{f} - mgy_{i} = 0 - (80)(9.80)(4.2) = - 3300 J[/tex]

ΔEth = [tex]-(190 -3300) = 3100 J[/tex]

Change in thermal energy = 3100 J

Answer:

D 60°

Explanation:

Using trigonometry:

- The new speed (v/2) of the particle corresponds to the hypothenuse

- The component of v/4 represents the side adjacent  to the angle that we want fo find, [tex]\theta[/tex]

So we can write:

[tex]cos \theta = \frac{adjacent}{hypothenuse}=\frac{v/4}{v/2}=\frac{1}{2}[/tex]

So we find the angle

[tex]\theta= cos^{-1} (\frac{1}{2})=60^{\circ}[/tex]

Answer:

D 60°

Explanation:

Using trigonometry in the attached image:

[tex]cos\alpha =\frac{v/4}{v/2}[/tex]

[tex]cos\alpha =\frac{1}{2}[/tex]

[tex]\alpha =cos^{-1} \frac{1}{2}[/tex]

Angle=60°

Answer:

[tex]2.0\cdot 10^2 N[/tex]

Explanation:

The cabinet does not move: this means that the net force acting on it is zero.

Along the horizontal direction, we have two forces:

- The push exerted by Bob, F = 200 N, forward

- The frictional force, [tex]F_f[/tex], which acts in the opposite direction (backward)

Since the net force must be zero, we have:

[tex]F-F_f = 0[/tex]

So solving the equation we can find the magnitude of the friction force:

[tex]F_f = F = 200 N=2.0 \cdot 10^2 N[/tex]

Answer:

A) 24.7 m, B) 28.9 m/s²

Explanation:

Hooke's law states the force of a spring is equal to the spring constant times the change in length:

F = k ΔL

Solving for k:

k = F / ΔL

The spring constant is inversely proportional to the length:

k ∝ 1/L

Therefore:

k₁ L₁ = k₂ L₂

(F₁ / ΔL₁) L₁ = k₂ L₂

(mg / 1.30) (5.00) = k L

k = (5.00/1.30) (mg / L)

Initial energy = final energy

Initial gravitational energy = final gravitational energy + elastic energy

mgH = mgh + 1/2 k (ΔL)²

mg(H - h) = 1/2 k (ΔL)²

mg(60.0 - 10.0) = 1/2 k (ΔL)²

50mg = 1/2 k (ΔL)²

100mg = k (ΔL)²

The stuntman will fall a distance L and then an additional distance ΔL.  We know this distance is equal to 60-10 = 50 m.  L + ΔL = 50, so ΔL = 50 - L.

100mg = k (50 - L)²

100mg = k (2500 - 100L + L²)

100mg = (5.00/1.30) (mg / L) (2500 - 100L + L²)

26L = 2500 - 100L + L²

0 = L² - 126L + 2500

L = (126 ± √5876) / 2

L = 63 ± √1469

L ≈ 24.7 m, 101 m

Obviously L can't be more than 50.0 m, so L = 24.7 m.

As a mass on a spring, the stuntman will follow simple harmonic motion, so his maximum acceleration will be experienced at his minimum velocity, or at the very bottom.

∑F = ma

k ΔL - mg = ma

(5.00/1.30) (mg / L) ΔL - mg = ma

(5.00/1.30) (g / L) ΔL - g = a

(5.00/1.30) (9.81 / 24.7) (50.0 - 24.7) - 9.81 = a

a = 28.9 m/s²

Answer:

2 x 10⁻¹²F

Explanation:

Capacitance is defined as the ration of charge (q) on either plates to the potential difference V between them.

                        C = [tex]\frac{q}{V}[/tex]

Where  q is the charge on the plates

             V is the potential difference

From the given parameters:

Charge on plate, q = 2.0 x 10⁻¹⁰C

Potential difference across the plate = 100V

Unknown parameter:

Capacitance of the system = ? = C

Solution

        Capacitance = 2.0 x 10⁻¹⁰/100 = 2 x 10⁻¹²F

Answer:

Covalent bond between two atoms with unequal electronegativities results in unequal sharing of electrons.

Explanation:

Unequal sharing of electrons between two atoms results in polar covalent bonds, characterized by partial charges on the atoms, due to different electronegativities.

When unequal sharing of electrons occurs between two atoms, it results in a polar covalent bond. This type of bond is characterized by the partial charges that develop on the atoms involved. Atoms with higher electronegativities attract the bonding electrons more strongly, leading to a partial negative charge on the more electronegative atom and a partial positive charge on the less electronegative one.

The unequal sharing of electrons and the resulting polar covalent bonds are crucial concepts because they influence molecular structure, physical properties, and reactivity.

For example, water (H₂O) has polar covalent bonds between hydrogen and oxygen, with the oxygen atom having a partial negative charge and the hydrogen atoms having partial positive charges. This polarity allows water to dissolve various substances, making it an excellent solvent.

Answer:

An object is in static equilibrium if the following is true:

+ the sum of the forces on it in each direction is zero.

+ the sum of the forces on it in each direction is zero.+ the sum of the torques on it in each direction is zero.

+ the sum of the forces on it in each direction is zero.+ the sum of the torques on it in each direction is zero.+ it's linear momentum is zero (i.e. it's not moving).

An object in static equilibrium will have these attributes;

Therefore, when an object is in static equilibrium, the summation of forces on it will be zero.

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Answer:

5000 N/m

Explanation:

Hooke's law for the spring is

[tex] F = k \Delta x[/tex]

where here we have

F = 100 N is the force applied to the spring

k is the spring constant

[tex]\Delta x = 22 cm - 20 cm = 2 cm = 0.02 m[/tex] is the stretching of the spring with respect to its equilibrium position

Solving the equation for k, we find the spring constant:

[tex]k=\frac{F}{\Delta x}=\frac{100 N}{0.02 m}=5000 N/m[/tex]

Hawaii Volcanoes National Park was established as part of the process wherein Hawaii transitioned from an independent kingdom to a U.S. territory and state. The park is significant for tourism and the study of volcanic activity in Hawaii, representing a critical part of the island's modern development pattern.

Hawaii Volcanoes National Park was established to preserve the natural setting of the volcanic landscapes on the island of Hawaii. As part of the United States, Hawaii's history encompasses a period where it was an independent kingdom, later becoming a U.S. territory, and eventually the 50th state in 1959. The park itself is a hub for tourists and plays an important role in the modern development pattern of Hawaii, which relies heavily on tourism and military presence.

Volcanic activity is a key feature of Hawaii's geography, with eruptions such as the destructive volcanic eruption that occurred in May 2018, offering a reminder of the dynamic and ever-changing natural forces shaping the island. The islands are known for their diverse ecosystems, which are protected and studied within areas like Hawaii Volcanoes National Park and other national monuments such as Kilauea.

Answer:

(3) 3.2 × 10–19 C

Explanation:

The charge of a subatomic particle can only be an integer multiple of the fundamental charge, which is

[tex]q=1.6\cdot 10^{-19} C[/tex]

So, let's analyze the 4 options:

(1) 5.0 × 10–20 C

[tex]\frac{5.0\cdot 10^{-20}C}{1.6\cdot 10^{-19} C}=0.31[/tex] --> not an integer number

(2) 8.0 × 10–20 C

[tex]\frac{8.0\cdot 10^{-20}C}{1.6\cdot 10^{-19} C}=0.5[/tex] --> not an integer number

(3) 3.2 × 10–19 C

[tex]\frac{3.2\cdot 10^{-19}C}{1.6\cdot 10^{-19} C}=2[/tex] --> integer number

(4) 5.0 × 10–19 C

[tex]\frac{5.0\cdot 10^{-19}C}{1.6\cdot 10^{-19}C}=3.13[/tex] --> not an integer number

So, the only option which is correct is (3).

Answer:

(1) 5.0 × 10–20 C (2) 8.0 × 10–20 C (3) 3.2 × 10–19 C (4) 5.0 × 10–19 C

Explanation:

3.2 × 10–19 C

Answer:

Voltage-gated calcium ion channels open, and calcium ions diffuse into the cell

The arrival of an action potential at the presynaptic terminal triggers a depolarization of the membrane and the opening of Na+ channels and Ca2+ channels. This leads to the fusion of synaptic vesicles with the presynaptic membrane and the release of neurotransmitters into the synapse.

When an action potential arrives at the presynaptic terminal, the membrane gets depolarized and opens voltage-gated Na+ channels. This allows Na+ ions to enter the cell and further depolarize the presynaptic membrane. As a result, voltage-gated Ca2+ channels open and allow Calcium ions into the cell. This, in turn, triggers a signaling cascade leading to the fusion of small, membrane-bound vesicles known as synaptic vesicles that contain neurotransmitter molecules with the presynaptic membrane. Finally, the neurotransmitter is released into the synapse, where it can bind to receptors on the postsynaptic cell and induce chemical reactions that will affect the cell's membrane potential.

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Explanation:

This sentence is the description of the mechanical energy.

In this sense, the mechanical energy of a body or a system 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.

That is to say: The 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:

Answer:

[tex]1.7\cdot 10^3 N[/tex]

Explanation:

The impulse theorem states that the product between the force and the time interval of the collision is equal to the change in momentum:

[tex]F \Delta t = m \Delta v[/tex]

where

F is the force

[tex]\Delta t[/tex] is the time interval

m is the mass

[tex]\Delta v[/tex] is the change in velocity

Here we have

m = 84 kg

[tex]\Delta t = 1.2 s[/tex]

[tex]\Delta v = 24 m/s[/tex]

So we can solve the equation to find the force:

[tex]F= \frac{m \Delta v}{\Delta t }=\frac{(84 kg)(24 m/s)}{1.2 s}=1680 N \sim 1.7\cdot 10^3 N[/tex]

i sorry i thought of geocentric as something else it appears that the earth was the center

Answer: Earth

Explanation: edge2022

The correct description of water is that it has a high specific heat and strong cohesive forces between molecules, which means it requires a large amount of energy to increase its temperature.

Among the options provided in the question, the correct answer regarding the properties of water is D. Water is a special substance with many unique characteristics due to its structure and interactions. One of its key features is that it requires a large amount of energy per gram to raise its temperature. This property is known as water’s high specific heat, and it is because the hydrogen bonds between water molecules must be broken to increase motion (temperature), which takes a considerable amount of energy. Additionally, water has strong cohesive forces between its molecules, which lead to a high degree of cohesion and contribute to its high boiling point compared to molecules of similar size.

Answer:  The air gets warmer and rises then it goes back toward the poles

Explanation: Hope this helps, tell me if it didn't.

Answer:

Towards the right

Explanation:

The equator is the region which receives maximum amount of sunlight. Due to this, the area experiences more heat and the air in this region becomes warm, and less dense. It then slowly rises up, forming a low pressure zone. This air is then carried by the wind towards both the poles. The wind that carries the air towards the north gets slightly deflected towards the right side because of a force known as the Coriolis force. This force is created due to the rotation of the earth.

Answer:

Zero

Explanation:

The work done by a force is given by:

[tex]W=Fd cos \theta[/tex]

where

F is the magnitude of the force

d is the displacement of the object

[tex]\theta[/tex] is the direction between the force and the displacement

In this problem, the force is the tension in the string, while the object is the ball. The tension is always radial (towards the centre of the circle), while the ball moves tangentially to the circle: this means that the tension and the displacement are always perpendicular to each other, so

[tex]\theta=90^{\circ}, cos \theta = 0[/tex]

and so the work done is zero.

The work done on the ball swung on a string in a horizontal circle due to the tension force of 10 N in the string during one revolution of the ball is zero.  

The work done by the tension force on the ball is given by:

[tex] W = F*d*cos(\theta) [/tex]   (1)

Where:

F: is the tension force = 10 N

d: is the displacement

θ: is the angle between the force and the displacement

The displacement is given by the circular path of circumference 6 meters.

In one point of the circular path, the direction of the tension force is to the center of the circumference and the displacement is orthogonal to this direction, so the angle between them is 90° (see the picture below).  

The work is then (eq 1):

[tex] W = F*d*cos(\theta) = 10 N*6 m*cos(90) = 0 [/tex]

Therefore, the work done on the ball by the tension force is 0 (zero).

Find more about work here:

I hope it helps you!                      

Answer:

Market participation allows individuals to specialize and, with trade, ultimately consume more.

People benefit from participating in the market as it leads to better or less expensive products for consumers, higher profits for businesses, and increased income for employees. This process is also beneficial to society overall, yielding positive social results defined as the 'invisible hand' by Adam Smith.

People benefit from participating in the market for several reasons. Consumers usually get access to better or less expensive products as businesses constantly compete against each other to provide the best products or services. This competition leads to innovation and pushes businesses to find ways to decrease costs and increase the quality of their goods or products.

From the businesses' perspective, the ones able to provide better or cost-effective products realize an increase in their profits. Their employees also benefit through increased income. It is primarily a win-win for all parties involved - consumers, businesses, and employees. The total gains from such market participation usually outweigh the losses, leading to overall economic welfare in the nation.

Furthermore, self-interested behavior in a market can yield positive social results, termed as 'the invisible hand' by the economist Adam Smith. When persons work hard to earn, they contribute to the economic output. Consumers looking for the best deals motivate businesses to offer goods and services catering to their needs, which in turn, tends to benefit the overall society.

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The most accepted theory so far, in relation to the formation of our solar system is that it was originated by the contraction of a cloud of interstellar gas due to its own gravity.

To understand it better:

According to this theory, a cloud of gas and interstellar dust began to shrink due to its own gravity. This led to the increase in the temperature of the system, which began to rotate forming a large gas sphere in the center (the Sun) with a flat disk around it.

This is how the Sun formed from the sphere in the center and the planets formed from the disk orbiting in the same plane.

Answer: 59 seconds

Explanation:

Answer:59 seconds

Explanation:

(a) 18717 N

There are two forces acting on the elevator:

- The tension in the cable, T, upward

- The weight of the elevator+passenger, downward, which is given by

W = mg

where m=1700 kg is the mass and g=9.81 m/s^2 is the acceleration of gravity

According to Newton's second law, the resultant of these forces must be equal to the product between mass and acceleration:

T - mg = ma

where

a = 1.20 m/s^2 is the acceleration, also upward

Solving the equation for T, we find the tension in the cable:

[tex]T=mg+ma=m(g+a)=(1700 kg)(9.81 m/s^2)(1.20 m/s^2)=18717 N[/tex]

(b) 16677 N

In this second part of the trip, the elevator continues at constant velocity. This means that the acceleration is zero:

a = 0

So Newton's second law becomes:

T - mg = ma = 0

Therefore, the tension in the cable will be equal to the weight of the elevator+passenger:

T = mg = (1700 kg)(9.81 m/s^2)=16677 N

(c) 15657 N

In this third part of the trip, the elevator has a deceleration of

a = -0.60 m/s^2

and we use a negative sign since the acceleration is now downward.

Therefore, Newton's second law is

T - mg = ma

And substituting all the data, we find the new tension in the cable:

[tex] T=mg+ma=m(g+a)=(1700 kg)(9.81 m/s^2-0.60 m/s^2)=15657 N[/tex]

(d) 19.35 m, 0 m/s

The distance covered by the elevator in part a) of the trip is

[tex]d_1 = \frac{1}{2}at^2 = \frac{1}{2}(1.20 m/s^2)(1.50 s)^2=1.35 m[/tex]

The final velocity reached in this part is

[tex]v_1 = at=(1.20 m/s^2)(1.50 s)=1.8 m/s[/tex]

In the second part, the elevator moves at constant velocity of

[tex]v_2 = v_1 = 1.8 m/s[/tex]

so the distance covered is

[tex]d_2 = v_2 t = (1.8 m/s)(8.50 s)=15.3 m[/tex]

The distance covered in the third part will be

[tex]d_3 = v_2 t + \frac{1}{2}at^2 = (1.8 m/s)(3.0 s) + \frac{1}{2}(-0.6 m/s^2)(3.0 s)^2=2.7 m[/tex]

While the final velocity is

[tex]v_3 = v_2 + at = 1.8 m/s + (-0.6 m/s^2)(3.0 s)=0[/tex]

and the total distance covered (so, the heigth of the elevator above the ground) is

[tex]d = d_1 + d_2 + d_3 = 1.35 m +15.30 m+2.70 m=19.35 m[/tex]

To calculate the tension in the cable, use the equation Tension = mass x acceleration + weight. To find the height the elevator moved, use the equations of motion.

To calculate the tension in the cable, we need to consider the forces acting on the elevator. When the elevator accelerates upward, two forces are acting on it - the force due to its weight and the tension in the cable. The tension in the cable is given by the equation:

Tension = mass x acceleration + weight

Using this equation, we can calculate the tension in the cable for each scenario:

(a) Tension during acceleration = (1700 kg x 1.20 m/s^2) + (1700 kg x 9.8 m/s^2)

(b) Tension during constant velocity = 1700 kg x 9.8 m/s^2

(c) Tension during deceleration = (1700 kg x -0.600 m/s^2) + (1700 kg x 9.8 m/s^2)

To find how high the elevator has moved above its original starting point, we can use the equations of motion. The final velocity of the elevator can be found using the equation:

Final velocity = initial velocity + (acceleration x time)

The displacement can be found by using the equation:

Displacement = (initial velocity x time) + (0.5 x acceleration x time^2)

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Potential energy or stored energy, and kinetic energy, the energy due to motion can be balanced in the process of converting kinetic energy to potential energy during an uphill motion

The correct option for, which situation shows potential energy and kinetic energy are balanced is option;

A roller coaster car going uphill

The reason the selected option is correct is as follows:

Potential energy is the energy that is due to the relative position of an item in relation to a ground or zero state. The formula for potential energy due to the elevation is given as follows;

Potential energy, P.E. = m·g·h

Kinetic energy is the energy that is due to motion. The kinetic energy of an item is given as follows;

Kinetic energy, K.E. = (1/2) × m × v²

The potential and kinetic energy of a body is balanced when we have;

P.E. = m·g·h = K.E. = (1/2)·m·v²

Which gives;

g·h = (1/2)·v²

Therefore, a point is reached as the an body moves up a heal, where the potential energy (the energy due to height of the object) and the kinetic energy (the energy due to current speed) of the object are equal

The correct situation which shows potential energy and kinetic energy are balanced is therefore; A roller coaster car going uphill

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Final answer:

Potential energy and kinetic energy are balanced when a roller coaster car is going uphill, where potential energy increases and kinetic energy decreases as the car ascends. At the peak, the two energies balance out due to the law of conservation of energy, ensuring total mechanical energy remains constant in a closed system.

Explanation:

The situation where potential energy (PE) and kinetic energy (KE) are balanced is when a roller coaster car is going uphill. As the roller coaster car ascends, its PE increases while its KE decreases as it slows down. At the peak of the hill, there's a moment where the car's velocity is zero and all of the KE has been converted into PE. If we assume no energy is lost to friction and we're dealing with a closed system, the law of conservation of energy states that the total mechanical energy (the sum of KE and PE) remains constant. Thus, the roller coaster at the top of the first rise has a certain amount of total mechanical energy, which balances out as it ascends and descends, converting between KE and PE.

For example, if a roller coaster descends 20 m and starts with an initial speed of 5 m/s, whether it was moving uphill or downhill, it will have the same final speed when it reaches a point 20 m below its starting height. This is consistent with the conservation of energy principle, as the total amount of mechanical energy remains the same throughout the ride, despite the continuous conversion between PE and KE.

Explanation:

It is given that,

Mass of Millersburg Ferry, m = 13000 kg

Velocity, v = 11 m/s

Applied force, F = 10⁶ N

Time period, t = 20 seconds

(a) Impulse is given by the product of force and time taken i.e.

[tex]J=F.\Delta t[/tex]

[tex]J=10^6\ N\times 20\ s[/tex]

[tex]J=2\times 10^7\ N-s[/tex]

(b) Impulse is also given by the change in momentum i.e.

[tex]J=\Delta p=p_f-p_i[/tex]

[tex]J=p_f-p_i[/tex]

[tex]p_f=J+p_i[/tex]

[tex]p_f=2\times 10^7\ N-s+13000\ kg\times 11\ m/s[/tex]

[tex]p_f=20143000\ kg-m/s[/tex]

(c) For new velocity,

[tex]v_f=\dfrac{p_f}{m}[/tex]

[tex]v_f=\dfrac{20143000\ kg-m/s}{13000\ kg}[/tex]

[tex]v_f=1549.46\ m/s[/tex]

Hence, this is the required solution.

Answer:

(a) Impulse of the engine = 20*10^6 N.s

(b) New momentum of the ferry =  1985700 kgm/s

(c) The new velocity of the ferry = 1527.5 m/s

Explanation:

In the given problem, we have:

mass (m) = 13000 kg; velocity (v) = 11 m/s; Force (F) = 1.0*10^6 N; period (t) = 20 s.

From the Newton's law of motion, it is know that:

force*time = mass*velocity; and impulse = force*time

Thus:

(a) the magnitude of the impulse from the engine is:

Impulse = 1.0*10^6 * 20 = 20*10^6 N.s

(b) The new momentum of the ferry is equivalent to the difference between the engine momentum and the ferry momentum. Therefore, we have:

New momentum = Engine momentum - Ferry momentum

Ferry momentum = mass*velocity = 13000*11 =143000 kgm/s

Engine momentum = 1.0*10^6 * 20 = 20*10^6 N.s = 20*10^6 (kgm/s^2 *s) = 20*10^6 kgm/s

Therefore:

New momentum = 20*10^6 - 143000 =  1985700 kgm/s

(c) The new velocity of the ferry is:

v = new momentum/mass = 1985700/13000 = 1527.5 m/s