A billiard ball is moving in the x-direction at 30. 0 cm/s and strikes another billiard ball moving in the y-direction at 40. 0 cm/s. As a result of the collision, the first ball moves at 50. 0 cm/s, and the second ball stops. In what final direction does the first ball move?

Answer:

Range describes the upper and lower limits of a thermometers' measurement scale

Answer:

50 minutes / 3000 seconds

Explanation:

Energy = power x time

time = energy / power

time = 900,000 / 300

time = 3000s

This can also be written as 50 minutes

An athlete stretches a spring an extra 40.0 cm beyond its initial length. The amount of energy transferred to the spring is b) 4230 J, if the spring constant is 52.9 N/cm

We can calculate using the below formula,

E= 1/2 kΔx²

where E is the energy transferred, k is the spring constant, and Δx is the displacement from the equilibrium position.

The equation for energy stored in the spring is given as follows:

E = 1/2 k x²

where E is the energy, x is the displacement from the equilibrium position, and k is the spring constant of the spring.

The amount of energy transferred to the spring is determined using the formula for the energy stored in the spring.

E = 1/2 k Δx²

Where E is the energy, Δx is the displacement from the equilibrium position, and k is the spring constant of the spring.

Given that the displacement, Δx = 40.0 cm and the spring constant, k = 52.9 N/cm.

We will substitute these values into the equation for energy transferred:

E = 1/2 k Δx²= 1/2 (52.9 N/cm) (40.0 cm)²= 1/2 (52.9 N/cm) (1600 cm²)= 4230 J

Therefore, the amount of energy transferred to the spring is b) 4230 J

The Question was Incomplete, Find the full content below :

An athlete stretches a spring an extra 40.0 cm beyond its initial length. How much energy has he transferred to the spring, if the spring constant is 52.9 N/cm?

a) 4230 kJ

b) 4230 J

c) 423 kJ

d) 423 J

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The main-sequence option B star has the greatest surface temperature out of the given stars.

A main-sequence star is a star that emits energy by nuclear fusion, particularly helium into carbon. These stars are distinguished by the fact that they are burning hydrogen in their cores. Their temperature, luminosity, and lifetime are all directly related to their mass.

According to the Hertzsprung-Russell diagram, a B-star refers to a hot, bright, and blue star that falls on the main sequence of the chart. The surface temperature of a main-sequence B star is about 10,000 Kelvin. Giant K stars and supergiant A stars have much lower surface temperatures than main-sequence B stars.

A giant K star is a type of star with a radius between 10 and 100 times that of the Sun. They are often orange, reddish-orange, or reddish-yellow in color. Giant K stars are a type of cool star, with temperatures ranging from 3,900 K to 5,200 K.

A supergiant A star is a type of star with a mass of more than 10 times that of the Sun. They are bigger and more luminous than normal stars. Their surface temperature is between 7,500 and 9,000 Kelvin, and they have a life expectancy of around 10 million years.

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Differential partitioning between stationary and mobile phase refers to the separation of components in a mixture based on their differing affinities for a stationary phase (usually a solid or a liquid on a solid support) and a mobile phase (usually a liquid or a gas).

The components with higher affinity for the stationary phase move slower, while those with a higher affinity for the mobile phase move faster.

To clean a TLC spotting capillary, follow these steps:
1. Rinse the capillary with an appropriate solvent (e.g., acetone or methanol) several times.
2. After rinsing, blow air through the capillary to remove any remaining solvent.
3. Allow the capillary to air dry before using it again for spotting.

Regarding the order of increasing Rf values on thin-layer chromatography for octanoic acid, the original list of compounds was not provided in the student question.

However, Rf values are affected by factors like polarity, size, and solubility.

Generally, compounds with lower polarity and smaller size will have higher Rf values, as they have a greater affinity for the mobile phase and will move faster on the TLC plate.

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a)The total (equivalent) resistance of the circuit is 4.8 Ω

b) what is the total current in the circuit is 2.08 A

c) what is the voltage across r1 is 12.48 V

a) To determine the total (equivalent) resistance of the circuit, use the equation

R = 1/(1/R1 + 1/R2)

where R1 and R2 are the individual resistors.

The total resistance of the circuit is therefore R = 1/(1/R1 + 1/R2) = 1/(1/6 + 1/8) = 4.8 Ω

b) The total current in the circuit is determined by Ohm's Law:

I = V/R

where V is the voltage and R is the resistance.

In this circuit, V = 10 V and R = 4.8 Ω

so the total current is I = V/R = 10 V/4.8 Ω = 2.08 A.

c) The voltage across R1 is determined by Ohm's Law:

V = I * R

where I is the current and R is the resistance.

In this circuit, I = 2.08 A and R1 = 6 Ω

so the voltage across R1 is V = I * R = 2.08 A * 6 Ω = 12.48 V.

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The magnitude of the resultant displacement is 334.4 m and the direction of the resultant displacement is 53.1° North of East.

To draw the displacement vector diagram, we start at point A and draw a vector from A to B, representing the athlete's displacement of 120 m South.

We then draw a vector from the end of the first vector (B) to the end of the second vector (C), representing the athlete's displacement of 200 m East. Finally, we draw a vector from the end of the second vector (C) to point D, representing the athlete's displacement of 270 m North. The diagram should form a closed triangle.

To find the resultant displacement of the athlete, we use the Pythagorean theorem and trigonometry. Let's call the displacement from A to B "vector AB," the displacement from B to C "vector BC," and the displacement from C to D "vector CD." The magnitude of the resultant displacement (R) is given by:

R = √(AB² + BC² + CD²)

R = √(120² + 200² + 270²) = 334.4 m (rounded to one decimal place)

To find the direction of the resultant displacement, we use trigonometry. We can find the angle between the resultant displacement and the North direction using the following formula:

θ = tan⁻¹(CD/BC)

Where CD is the Northward component of the displacement vectors and BC is the Eastward component of the displacement vectors.

θ = tan⁻¹(270/200) = 53.1° (rounded to one decimal place)

Therefore, the magnitude of the resultant displacement is 334.4 m and the direction of the resultant displacement is 53.1° North of East.

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 An object is dropped from the top of a building and takes 7.2s to hit the ground, the height of the building is approximately 255.84m.

.When an object is dropped from the top of a building, it begins to accelerate at 9.8 m/s², the rate of acceleration due to gravity on earth. The final velocity is the rate at which the object hits the ground and is calculated with the formula;  V = gt  , Where V = Final velocity , t = Time taken to fall ,  g = Acceleration due to gravity on earth

Substituting values; V = 9.8 m/s² x 7.2 s = 70.56 m/s

The height of the building can be calculated using the formula; h = 1/2gt²

Substituting values; h = 1/2 x 9.8 m/s² x (7.2 s)² = 255.84 m

Therefore, the height of the building is approximately 255.84m.

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To determine the torque at which a DC motor will operate at maximum power,

Step 1: Convert the no-load speed to radians per second.
10 k r p m = 10,000 rpm
1 rpm = (2 * pi) rad/min
10,000 rpm = 10,000 * (2 * pi) rad/min = 62,831.85 rad/min
To convert rad/min to rad/s, divide by 60:
62,831.85 rad/min ÷ 60 = 1,047.20 rad/s

Step 2: Calculate the motor's constant (K) using stall torque and no-load speed.
K = Stall Torque / No-Load Speed
K = 100 mN-m / 1,047.20 rad/s
K = 0.0955 N-m / rad/s

Step 3: Calculate the torque at which the motor operates at maximum power.
At maximum power, the torque is half the stall torque.
Torque = 0.5 * Stall Torque
Torque = 0.5 * 100 mN-m
Torque = 50 mN-m

The motor will operate at maximum power at a torque of 50 mN-m.

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The force needed to bring the 950-kg car to rest from a speed of 25 m/s in a distance of 120 m is approximately 4959.5 N.

To calculate the force needed to bring the car to rest, we can use the equation, F = ma, where, F = force, m = mass of the car and a = acceleration.

We can also use the equation for acceleration,

a = (v_f^2 - v_i^2)/2d, where, v_f = final velocity (0 m/s since the car is brought to rest), v_i = initial velocity (25 m/s) and d = distance traveled during braking (120 m).

Substituting the given values,

a = (0^2 - 25^2)/(2 x 120) = -5.21 m/s^2

The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, which is necessary to bring the car to rest.

Substituting the value of acceleration into the equation for force,

F = ma = (950 kg) x (-5.21 m/s^2) = -4959.5 N

Again, the negative sign indicates that the force is in the opposite direction to the initial velocity.

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The net impulse on the cabinet during the 2-second time interval when a 100 lb force is applied is 200 lb·s.

The net impulse on an object is equal to the change in its momentum, which can be calculated using the equation,

Impulse = Force x Time

In this case, a force of 100 lb is applied to the cabinet for 2 s. Since the surface is smooth, there is no frictional force acting on the cabinet, and it will move with a constant velocity after the force is applied.

The initial momentum of the cabinet is zero, since it is initially at rest. The final momentum of the cabinet can be calculated using the equation:

Final Momentum = Mass x Velocity

Since the mass of the cabinet is 100 lb, and it moves with a constant velocity after the force is applied, its final momentum is:

Final Momentum = 100 lb x v

where v is the velocity of the cabinet.

Since the force is applied for 2 s, the impulse on the cabinet is:

Impulse = Force x Time = 100 lb x 2 s = 200 lb·s

Since there are no external forces acting on the cabinet, the net impulse on the cabinet during this time interval is equal to the impulse calculated above:

Net Impulse = Impulse = 200 lb·s

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It took 1.82 seconds for the rock to come to a stop when the force of -1.1 N was applied.

What is force?

We can use the formula:

force = mass x acceleration

To find the acceleration of the rock when the force is applied. Since we know the mass of the rock is 1kg, we can rearrange the formula to solve for acceleration:

acceleration = force / mass

We know that the force applied to the rock is -1.1 Newtons (N), since it is bringing the rock to a stop. Thus:

acceleration = -1.1 N / 1 kg = -1.1 m/s²

The negative sign indicates that the acceleration is in the opposite direction of the motion of the rock.

Next, we can use the formula:

velocity = initial velocity + acceleration x time

To find the time it takes for the rock to come to a stop. We know the initial velocity of the rock is 2 m/s and the final velocity is 0 m/s (since it comes to a stop). Thus:

0 m/s = 2 m/s + (-1.1 m/s²) x time

Solving for time:

time = (0 m/s - 2 m/s) / (-1.1 m/s²) = 1.82 seconds

Therefore, it took 1.82 seconds for the rock to come to a stop when the force of -1.1 N was applied.

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The kinetic energy lost in this collision is 1.07 J. The negative sign indicates that the kinetic energy is lost during the collision.

Mass of 1st object = 2 kg, Velocity of 1st object = 7 m/s. Mass of 2nd object = 5 kg, Velocity of 2nd object = 3 m/s. We need to calculate the kinetic energy lost in this collision. As both the objects are moving in the same direction, we can apply the conservation of momentum equation for this type of collisions. Let us apply the equation for conservation of momentum before and after the collision:

Initial momentum = m1v1 + m2v2= (2 kg) (7 m/s) + (5 kg) (3 m/s)= 14 kg m/s + 15 kg m/s= 29 kg m/s. Final momentum = (m1 + m2) vf= (2 kg + 5 kg) vf= 7 kg vf. According to the conservation of momentum equation, Initial momentum = Final momentum29 kg m/s = 7 kg vfvf = 4.143 m/s. Now, we can apply the equation for kinetic energy to find out how much kinetic energy is lost in this collision.

Initial kinetic energy of the system = (1/2) m1v12 + (1/2) m2v22= (1/2) (2 kg) (7 m/s)2 + (1/2) (5 kg) (3 m/s)2= 49 J + 22.5 J= 71.5 J. Final kinetic energy of the system = (1/2) (m1 + m2) vf2= (1/2) (7 kg) (4.143 m/s)2= 72.57 J. Therefore, the kinetic energy lost in this collision is: Kinetic energy lost = Initial kinetic energy - Final kinetic energy= 71.5 J - 72.57 J= -1.07 J

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Kinetic energy of a gas molecule depends on temperature. The correct answer is option C.

The kinetic energy of a molecule is the energy that it possesses due to its motion. This kinetic energy depends on temperature. Hence, the correct option is C: Temperature.

When we raise the temperature of a gas, we increase the kinetic energy of the gas molecules. When the temperature of a gas increases, the gas molecules start moving with more speed. As a result, the average kinetic energy of the gas molecules increases.

Kinetic energy is the energy that is associated with the motion of an object. Kinetic energy is a scalar quantity, and it depends on the mass and speed of the object. The formula for kinetic energy is given by

K = 1/2mv²

Where

K represents the kinetic energy of the object,

m represents the mass of the object,

v represents the speed of the object.

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Answer:

The statement is True, waves propagate faster in a less dense medium if the stiffness is the same.

Waves can be defined as a disturbance that travels through space or matter, transferring energy from one point to another without transporting matter.

There are various kinds of waves, and they all exhibit similar properties.

Waves propagate faster in a less dense medium if the stiffness is the same .

Waves move at various speeds in different media. The speed of a wave is determined by the nature of the medium and the frequency and wavelength of the wave.

In general, waves propagate faster in less dense media than in denser ones.

This holds true if the stiffness is constant. For example, sound waves travel quicker in air than in water because air is less dense than water. In brief, waves propagate faster in a less dense medium if the stiffness is constant.

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Answer:

To determine how much the height of the Washington Monument changes due to the increase in temperature, we can use the formula:

ΔL = αLΔT

where ΔL is the change in length, α is the coefficient of linear thermal expansion, L is the original length, and ΔT is the change in temperature.

In this case, we want to find the change in height, which is the same as the change in length along the vertical direction. Therefore, we can use the same formula to find the change in height:

Δh = αhΔT

where Δh is the change in height, α is the coefficient of linear thermal expansion, h is the original height, and ΔT is the change in temperature.

Substituting the given values, we get:

Δh = (2.5 × 10^-6/°C) × (170 m) × (35.0°C)

Δh ≈ 0.15 m

Therefore, the height of the Washington Monument increases by approximately 0.15 m when the temperature increases from 0°C to 35.0°C.

Answer:

These are called Sankey Diagrams.

These summarise all the energy transfers taking place in a process. Sankey diagrams are drawn to scale - the thicker the line or arrow, the greater the amount of energy involved. Usually, the top line/arrow shows the amount of useful energy transferred from the total input and the one which curves shows the wasted/dissipated energy of the total input energy. It helps to show efficiency in this manner.

Hope this helps!!!

Due to their free fall, the two balls are falling at the same acceleration. Gravity has an effect on the two balls that are thrown downward from the top of the structure. Because of gravity, both balls fall freely.

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New scientific terms in the physical sciences are most likely to be coined from Greek or Latin. Physical science is the branch of natural science that deals with nonliving things, as well as their interactions and phenomena. The two main branches of physical science are physics and chemistry.

Latin is the language that gave birth to modern scientific vocabulary. Scientists use Latin to name organisms and describe anatomy, among other things. For example, in the human anatomy, the femur is a large, strong bone that is commonly referred to as the thigh bone. Greek is used to coin new words in various sciences, including physics, because of the country's historical and cultural influence.

Many new scientific terms in physics, for example, have Greek roots. For example, "photovoltaic" is a term used to describe the generation of electricity from light, while "thermodynamics" is a term used to describe the study of heat and temperature change in a system.

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Photovoltaic cells use solar energy to produce electricity. The correct option is D.

Photovoltaic cells convert sunlight into electrical energy by converting the energy of photons, which are particles of light. The photovoltaic cell works by separating electric charges in a solid state using the photoelectric effect.

The electric field inside the cell causes the separated charges to flow through the circuit, providing electrical power to the load. Silicon is the most widely utilized material for solar cells.

The photovoltaic effect was initially observed by Edmond Becquerel in 1839, and it was first exploited in the 1950s when photovoltaic silicon was made into semiconductors, which was a technology that had already been in use in the semiconductor industry for over a decade.

In conclusion, solar energy is a renewable and clean source of energy that is produced by photovoltaic cells that convert sunlight into electrical energy using the photovoltaic effect.

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The height of a parallelogram with an area of 375cm² and a base of 25cm is 15cm.

We can use the formula for the area of a parallelogram, which is A = bh, where A is the area, b is the base, and h is the height. Substitute the given values of the area and the base in the formula, we get: A = bh375 = 25h Divide both sides by 25 to get the value of h, and we get: h = 15 Therefore, the height of the parallelogram is 15cm.
To find the height of the parallelogram, you can use the formula for the area: Area = base × height. You are given the area (375 cm²) and the base (25 cm).

375 cm² = 25 cm × height

To find the height, divide both sides by 25 cm:

height = 375 cm² / 25 cm

height = 15 cm

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5.45 cm to the right of the second lens is where the final image is created.

The image will get smaller and smaller as we move the object further and further away. The focal point will draw the image's location ever-closer. The light would be concentrated at the focal point if the object were extremely far away, such as the sun.

Using the thin lens equation, we have: 1/f = 1/di + 1/do

For the first lens, we have:

f1 = -6.00 cm (negative because the lens is diverging)

do1 = -10.0 cm (negative because the object is to the left of the lens)

Solving for di1, we get: 1/di1 = 1/f1 - 1/do1

di1 = -15.0 cm (negative because the image is to the left of the lens)

The first lens creates a virtual, upright image whose magnification is determined by: m1 = -di1/do1 = 1.50

As there are 4.50 cm between the first and second lenses, the location of the thing that the second lens sees is:

do2 = di1 - 4.50 cm = -19.5 cm

For the second lens, we have:

f2 = 6.00 cm (positive because the lens is converging)

do2 = -19.5 cm (negative because the object is to the left of the lens)

Solving for di2, we get:

1/di2 = 1/f2 - 1/do2

di2 = 5.45 cm

The final image is real and inverted, and its magnification is given by:

m = -di2/do2 = 0.279

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The block rises to a maximum height of 9.98 m above the point of release.

The maximum height above the point of release to which the block rises after it is released from rest can be calculated as follows:

Step 1: Determine the potential energy stored in the spring U = 1/2 kx² Where, U is the potential energy of the spring, k is the force constant, and x is the compression in meters U = 1/2 × 4975 N/m × (0.099 m)²U = 24.52 J

Step 2: The potential energy stored in the spring is converted into kinetic energy, which is then converted into gravitational potential energy.
Thus, U = K.E. = 1/2 mv²Where, K.E. is the kinetic energy of the block, m is the mass of the block, and v is the velocity of the block just after leaving the spring. Rearrange the above formula to calculate the velocity of the block as it leaves the spring: v = √(2U/m)v = √[2(24.52 J)/0.259 kg]v = 5.60 m/s

Step 3: At the maximum height above the point of release, the block has zero kinetic energy and a maximum potential energy. Thus, the gravitational potential energy of the block can be calculated as follows: mgh = U
Where, m is the mass of the block, g is the acceleration due to gravity, h is the maximum height above the point of release, and U is the potential energy stored in the spring. h = U/mg= U/(mg) = (24.52 J)/(0.259 kg × 9.81 m/s²)h = 9.98 m

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The time taken by the rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s² is 5.30 s. Hence, option (b) is the correct answer.

We are given the initial angular velocity, ω1 = 15.0 rad/s, final angular velocity, ω2 = 33.3 rad/s, and angular acceleration, α = 3.45 rad/s². We are supposed to find the time, t, taken by the rotating object to speed up from ω1 to ω2.

We can use the following kinematic equation to solve this problem:

ω2 = ω1 + αt

Rearranging this equation, we get:

t = (ω2 - ω1) / α

Substituting the given values in the above equation, we get:

t = (33.3 - 15.0) / 3.45

t = 5.30 s

So, the correct option is B.

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The measure of exterior angle is 130 degrees. Option D is correct.

Since triangle jkl is equilateral, all its interior angles have a measure of 60 degrees. The sum of an exterior angle and an interior angle of a triangle is always 180 degrees. Therefore, the measure of exterior angle 1 is the sum of angle j and angle k. Since angle j is 60 degrees, angle k must be 180 - 60 = 120 degrees, because the sum of angles in a triangle is always 180 degrees.

Therefore, the measure of exterior angle 1 is 60 + 120 = 180 degrees. However, an exterior angle is defined as the angle formed by a side of a triangle and the extension of an adjacent side. Therefore, the actual exterior angle 1 is the supplement of 180 degrees, which is 180 - 1 = 179 degrees. So the answer is (D) 130 degrees.

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Answer:

Approximately [tex]73.6\; {\rm m\cdot s^{-1}}[/tex].

([tex]v = (1/2)\, g\, t[/tex], assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].)

Explanation:

Assume that the air resistance on the ball is negligible. Let [tex]v[/tex] denote the initial velocity of the ball.

The kinetic energy of the ball will be conserved. Hence, when the ball returns to the starting position, the ball will be travelling at the same speed but in the opposite direction (downwards.) The velocity will become [tex](-v)[/tex].

The change in the velocity of the ball would be [tex]\Delta v = ((-v) - v) = (-2\, v)[/tex].

Change in velocity is also equal to [tex]a\, t[/tex], where [tex]a[/tex] is acceleration and [tex]t[/tex] is the time required to achieve such change. Under the assumptions, acceleration of the ball will be constantly [tex]a = (-g)[/tex]. Hence:

[tex]\Delta v = a\, t = (-g)\, t[/tex].

Since [tex]\Delta v = ((-v) - v) = (-2\, v)[/tex]:

[tex](-2\, v) = \Delta v = (-g)\, t[/tex].

[tex]\begin{aligned}v &= \frac{(-g)\, t}{(-2)} = \frac{g\, t}{2}\end{aligned}[/tex].

Substitute in [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] and [tex]t = 15.0\; {\rm s}[/tex] to obtain:

[tex]\begin{aligned}v &= \frac{g\, t}{2} \\ &= \frac{(9.81)\, (15.0)}{2}\; {\rm m\cdot s^{-1}} \\ &\approx 73.6\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].

If the box slides forward another meter, the amount of work the person does is 1600 joules.

The work done by the person can be calculated as the product of the applied force and the distance moved by the box in the direction of the force:

W = Fd

where W is the work done, F is the applied force, and d is the distance moved in the direction of the force.

In this case, the person applies a force of 400 newtons and pushes the box for a distance of 4 meters. After he stops pushing, the box slides forward another meter, but since the person is not applying any force at that point, no work is done by him.

Therefore, the work done by the person is:

W = Fd = (400 N)(4 m) = 1600 J

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If the Sun takes 233 million years to orbit once around the Milky Way, how many orbits had the Sun made when it was 1.1 billion years old

To determine how many orbits the Sun had made when it was 1.1 billion years old,

1. Convert 1.1 billion years to million years: 1.1 billion years = 1100 million years.
2. Divide the age of the Sun by the time it takes to complete one orbit around the Milky Way: 1100 million years / 233 million years = 4.72 orbits.

Since the Sun cannot complete a partial orbit, it had made 4 orbits around the Milky Way when it was 1.1 billion years old.

Regarding how many times the Sun has orbited around the Milky Way since it first formed, we need to know the current age of the Sun. The Sun is approximately 4.6 billion years old.

Following the same steps as above:
1. Convert 4.6 billion years to million years: 4.6 billion years = 4600 million years.
2. Divide the age of the Sun by the time it takes to complete one orbit around the Milky Way: 4600 million years / 233 million years = 19.74 orbits.

Similar to the previous case, the Sun cannot complete a partial orbit, so it has made 19 orbits around the Milky Way since it first formed.

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Equations/Concepts Used:

Kinetic Energy => [tex]K=\frac{1}{2}mv^2[/tex]

Gravitational Potential Energy => [tex]U_{g}=mgy[/tex]

Mechanical Energy => [tex]E_{Mech.}=U+K[/tex]

Conservation of Energy => [tex]E_{0}=E_{f}[/tex]

At point 1

[tex]m=60 \ kg[/tex]

[tex]v=8 \ m/s[/tex]

PE ==> [tex]U_{g}=mgy \Rightarrow =(60)(9.8)(0) \Rightarrow U_{g}= 0 \ J[/tex]

KE ==> [tex]K=\frac{1}{2}mv^2 \Rightarrow =\frac{1}{2}(60)(8)^2 \Rightarrow K=1920 \ J[/tex]

ME==> [tex]E_{Mech.}=U+K \Rightarrow = 0+1920 \Rightarrow E_{Mech.}=1920 \ J[/tex]

At point 2

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

Find the velocity of the skater at point 2 using conservation of energy.

We already found the total energy at point 1, which was 1920 Joules.

==> [tex]E_{1}=E_{2} \Rightarrow 1920=U_{g_{2}}+K_2 \Rightarrow 1920=(60)(9.8)(1)+\frac{1}{2}(60)v^2[/tex]

[tex]\Rightarrow 1920=588+30v^2 \Rightarrow 1332=30v^2 \Rightarrow v^2=44.4 \Rightarrow v=6.66 \ m/s[/tex]

From the equation above we answered the following,

[tex]v=6.66 \ m/s[/tex]

[tex]U_g=588 \ J[/tex]

We know the velocity at point 2, find KE then ME.

[tex]K=\frac{1}{2}(60)(6.66)^2 \Rightarrow K=1331 \ J[/tex]

[tex]E_{Mech.}=588+1331 \Rightarrow E_{Mech.}= 1919 \ J[/tex]

Notice how mechanical energy remains constant, this is because energy is a conserved quantity.

At point 3

Use conservation of energy again, using points 1 and 3.

==> [tex]E_1=E_3 \Rightarrow 1920=U_{g_3}+K_3 \Rightarrow 1920=(60)(9.8)h+0[/tex]

At point 3 the skaters velocity will go to 0 and all energy will be potential.

So, [tex]v=0 \ m/s[/tex]

[tex]\Rightarrow 1920=588h \Rightarrow h=3.27 \ m[/tex]

==> [tex]U_g=(60)(9.8)(3.27) \Rightarrow U_g=1923 \ J[/tex]

Answers:

Point 1, PE=0 J, KE=1920 J, ME=1920J

Point 2, PE=588 J, KE= 1331 J, ME= 1919 J, v=6.66 m/s

Point 3, PE=1923 J, KE=0 J ,ME= 1923 J, v=0 m/s, h=3.27 m