A billiard ball moving horizontally, labeled 1, strikes another billiard ball at rest, labeled 2. Before impact, ball 1 was moving at a
speed of 2.85 m/s, and after impact it is moving at 0.55 m/s at 45° counterclockwise from the direction of the initial velocity. If
the two balls have equal masses of 160 g, what is the velocity of ball 2 after the impact? (Assume ball 1 initially moves along the
+x-axis. Enter the magnitude in m/s and the direction in degrees counterclockwise from the +x-axis.)

Answer:

Generally it is only possible  to compute the tangent of angle in their various unit but because 5 meter is not an angle then it is impossible  to compute the tangent of 5 meters.

Explanation:

Answer:

a) 0.47MW

b) 39.24%

Explanation:

In order to find the power needed for the elevator to operate at its maximum capacity, we can make use of the following formula:

P=Fv

where P is the power, F is the force and v is the velocity.

The force the elevator must carry can be calculated with the following formula:

F=mg

where m is the mass of the elevator and g is the acceleration of gravity, so:

\(F=(8000 kg)(9.81 m/s^{2})\)

F=78 480 N

so now we can make use of the power formula:

P=Fv

P=(78 480N)(6 m/s)

P=470 880W

P=0.47W

b)

In order to find the efficiency, we will suppose that the generator can generate a maximum of 0.47 W so we use the following formula:

\(efficiency = \frac{P_{in}}{P_{out}}*100\%\)

\(efficiency=\frac{0.470880}{1.2}*100\%\)

efficiency=39.24%

Because the mass and displacement are already given in Kg and m, respectively, in the first part of your question, there is no need to convert them. However, in the second part of your question, you must use the given equation to calculate the spring constant.

if the table data is given in grams and  cm you have to convert it using the following conversion,

1. To convert grams to kilograms, we divide the mass values by 1000.

2. To convert centimeters to meters, we divide the displacement values by 100.

But here in the given table it's already given the mass in kg and the displacement in meters (m). so no need to convert it.

Now comes the second part of your question,

To calculate the spring constants for the given data, we can use the equation:

k = -mg/Δx

where:

k is the spring constant (in N/m),

m is the mass (in kg), and

Δx is the displacement of the spring (in m).

Let's calculate the spring constants using the provided data:

Mass (kg): 0.05  0.1  0.2  0.3  0.4  0.5  0.6

Displacement of Spring (m): 0.012  0.027  0.065  0.1  0.135  0.17  0.199

Using the equation

k = -mg/Δx,

we can calculate the spring constant for each data point:

For the first data point (m = 0.05 kg, Δx = 0.012 m):

k = -0.05 kg * 9.8 m/s² / 0.012 m

k ≈ -40.833 N/m

Similarly, we can calculate the spring constants for the other data points:

For the mass of 0.05 kg, the spring constant is approximately -40.833 N/m.

For the mass of 0.1 kg, the spring constant is approximately -18.519 N/m.

For the mass of 0.2 kg, the spring constant is approximately -6.154 N/m.

For the mass of 0.3 kg, the spring constant is approximately -3.267 N/m.

For the mass of 0.4 kg, the spring constant is approximately -2.222 N/m.

For the mass of 0.5 kg, the spring constant is approximately -1.716 N/m.

For the mass of 0.6 kg, the spring constant is approximately -1.449 N/m.

Therefore, In the first part of the question, there is no need to convert the mass into kg and the displacement cm into m because it is already given in kg and m respectively, and in the second part question you have to calculate the spring constant using the given equation.

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the first one is: it's increased by a factor of 9

the second one: is m3/(kg*s^2)

by what factor does gravitational force between two objects increase if one double in mass and the distance between them decreases by half?: 8

what happens to the gravitational force between two objects that are 15 m apart, when one of them moves 3 m closer?: it increases by a factor of 1 9/16

in thinking about the uniform distribution of a gravitational filed over a sphere, why does the gravitational force have an inverse-square relationship with the distance between objects?: because the surface area of a sphere is proportional to the square if the radius

All these questions are correct I just took the quiz. Hope this helps you and others!

Answer:

1. The force decreases by a factor of 9.

2. 8

3. (N ⋅ m^2) / kg^2

4. It increases by a factor of 1 9/16

5. because the surface area of a sphere is proportional to the square of its radius

Explanation:

Answer:

C

They allow light to pass only if their directions of polarizations are exactly 90° apart.

Methylene blue is a dye that can be used to indicate the effectiveness of an antiseptic or disinfectant. The process involves testing the antiseptic or disinfectant against a known concentration of bacteria, such as Escherichia coli.

To perform the test, a culture of the bacteria is prepared and diluted to a specific concentration. The dilution is then mixed with the antiseptic or disinfectant being tested. A control culture is also prepared with the same bacterial concentration, but without the antiseptic or disinfectant.

After a specified contact time, the cultures are treated with methylene blue. Methylene blue penetrates the bacteria and binds to their DNA, staining them blue. If the antiseptic or disinfectant is effective, the number of blue-stained bacteria in the treated culture should be significantly lower than in the control culture.

The effectiveness of the antiseptic or disinfectant is usually expressed as a decimal reduction time (D-value), which is the time required to reduce the bacterial count by one logarithmic unit (i.e., 90% reduction). The lower the D-value, the more effective the antiseptic or disinfectant is at killing bacteria.

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To find the horizontal direction of the shell just before the explosion, you can use the principle of conservation of momentum. This principle states that the total momentum of a closed system (one that is isolated from its surroundings) remains constant, provided that there are no external forces acting on the system.

In this case, the shell and the two fragments form a closed system, since no external forces are acting on them. Before the explosion, the shell has a certain momentum, and after the explosion, the two fragments have a combined momentum that is equal to the initial momentum of the shell.

To find the initial momentum of the shell, you can use the formula:

p = m * v

where p is the momentum, m is the mass of the object, and v is the velocity.

The initial momentum of the shell is equal to the combined momentum of the two fragments after the explosion:

p = (2.5 kg * 100 m/s) + (3.5 kg * 70 m/s) = 250 kg m/s + 245 kg m/s = 495 kg m/s

Since the mass of the shell is not given, it's not possible to find the initial velocity of the shell. However, you can find the direction of the initial velocity by looking at the direction of the final velocities of the two fragments.

The direction of the final velocity of the 2.5 kg fragment is south west, and the direction of the final velocity of the 3.5 kg fragment is north. This means that the direction of the initial velocity of the shell was likely somewhere between these two directions.

It's not possible to determine the exact direction of the initial velocity of the shell without more information, but based on the given information, it was likely somewhere between south west and north.

In general, option c - warming it up on the stove - is often an effective method to increase the reaction rate.

Increasing the temperature of a reaction generally leads to faster reaction rates. This is because higher temperatures provide more thermal energy to the reactant particles, causing them to move faster and collide more frequently. The increased collision frequency and energy lead to more successful collisions and a higher likelihood of effective molecular interactions, which speeds up the reaction. On the other hand, options a and b - putting it in the fridge where it is cold or covering it with a blanket to make it dark - are unlikely to have a significant effect on the reaction rate. While temperature can influence reaction rates, cooling the reaction or making it dark typically reduces the kinetic energy of the particles, resulting in slower reaction rates. Option d - there is nothing you can do to change the speed of the reaction - is not accurate. The reaction rate can be influenced by various factors such as temperature, concentration, catalysts, and surface area, among others. By manipulating these factors, it is often possible to control and change the speed of a reaction. Hence option c, is correct

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Explanation:

To determine the effort needed to lift a load of 200N, given a velocity ratio of 5 and an efficiency of 80%, we can use the formula:

Efficiency = (Output Work / Input Work) * 100

Efficiency can also be calculated as the ratio of the output force to the input force. In this case, the output force is the load being lifted (200N), and the input force is the effort required.

Given that the velocity ratio is 5, it means that for every 5 units of distance the effort moves, the load moves 1 unit of distance. This implies that the effort is exerted over a greater distance than the load.

Let's denote the effort force as "E" and the distance moved by the effort as "dE." Similarly, the load force is "L," and the distance moved by the load is "dL."

Using the velocity ratio, we have the following relationship:

dE / dL = 5

Now, we can calculate the input work (Wi) and the output work (Wo):

Input Work (Wi) = Effort (E) * Distance moved by the effort (dE)

Output Work (Wo) = Load (L) * Distance moved by the load (dL)

Given that the efficiency is 80%, we can rewrite the formula for efficiency as:

0.80 = (Wo / Wi) * 100

Now, let's solve for the effort (E) using the given values:

Load (L) = 200N

Efficiency = 0.80

Velocity Ratio = 5

First, calculate the output work (Wo):

Wo = Load (L) * Distance moved by the load (dL)

Since the velocity ratio is 5, the distance moved by the load (dL) will be 1/5 of the distance moved by the effort (dE):

dL = (1/5) * dE

Wo = L * (1/5) * dE

Wo = 200N * (1/5) * dE

Wo = 40N * dE

Next, calculate the input work (Wi):

Wi = Effort (E) * Distance moved by the effort (dE)

Wi = E * dE

Now, substitute the values into the efficiency formula:

0.80 = (Wo / Wi) * 100

0.80 = (40N * dE) / (E * dE) * 100

0.80 = 40 / E * 100

0.80 * E = 40

E = 40 / 0.80

E = 50N

Therefore, the effort needed to lift a load of 200N with a velocity ratio of 5 and an efficiency of 80% is 50N.

The quantity of heat energy that must be transferred to 2.25 kg of brass to raise its temperature from 20 °C to 240 °C is 195030 J

First, we shall list out the given parameters from the question. This is shown below:

The quantity of heat energy that must be transferred can be obtained as follow:

Q = MCΔT

= 2.25 × 394 × 220

= 195030 J

Thus, we can conclude quantity of heat energy that must be transferred is 195030 J

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Answer:

If an object gains electrons it becomes positively charged.

Explanation:

Electrons negatively charge.

A. The output voltage, Vout, as a function of time, t, in a series RL circuit can be determined using the equation: Vout(t) = Vmax * (1 - e^(-t/τ)), where τ = L/R.

B. When the time interval T is very short (T → 0) and the maximum voltage Vmax is quite high (VmaxT ≈ Φimp), we can approximate the output voltage Vout using the equation: Vout(t) ≈ Φimp * e^(-t/τ), where τ = L/R.

A. To determine the output voltage Vout as a function of time t in a series RL circuit, we use the following equation:

Vout(t) = Vmax * (1 - e^(-t/τ))

Here, Vmax is the maximum input voltage, τ = L/R is the time constant of the circuit (where L is the inductance and R is the resistance).

B. When the time interval T is very short (T → 0) and the maximum voltage Vmax is quite high (VmaxT ≈ Φimp), we can make the following approximation:

Vout(t) ≈ Vmax * e^(-t/τ)

In this case, we substitute VmaxT with Φimp, which is the total magnetic flux in the circuit.

Rearranging the equation, we get:

Vout(t) ≈ Φimp * e^(-t/τ)

This approximation is valid when the time interval T is very small compared to the time constant τ of the circuit and when the maximum voltage is sufficiently high.

The time constant τ is determined by the values of inductance (L) and resistance (R) in the circuit. It represents the characteristic time scale over which the current and voltage in the circuit change in response to a voltage or current input.

Therefore, in the given scenario, when T is very small and Vmax is high, we can approximate the output voltage Vout(t) in the series RL circuit by the equation: Vout(t) ≈ Φimp * e^(-t/τ), where τ = L/R.

Note: The symbol Φimp in the equation represents the total magnetic flux in the circuit.

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The kinetic energy of the book after it is slids a distance of 2 meters will be 10 Joules.

The work-energy theorem states that "the work done on an object is the change in its kinetic energy".

Hence;

Kinetic energy = work done

Note that: work-done is expressed as:

Work done = f × d

Where f is force applied and d is distance traveled.

Given that:

Force applied f = 5 newton

Distance d = 2 meters

Work done = ?

Plug these values into the above formula and solve for the workdone.

Work done = f × d

Work done = 5N × 2m

Work done = 10Nm

Work done = 10 Joules

Therefore, the kinetic energy is 10 Joules.

Option B) 10 J is the correct answer.

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The negative outcome indicates a flaw in the information provided or how the issue was put up because the flow rate cannot be fictional or negative.

It can be expressed as:

P1 + (1/2)ρv1^2 + ρgh1 = P2 + (1/2)ρv2^2 + ρgh2

the terms involving h cancel out in the equation, and we can solve for v1:

P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2

v1 = √(P2 - P1))/ρ)

Substituting the given values for P1, P2, and ρ into the equation,

\(v1 = \sqrt(1.22 x 10^5 - 1.65 x 10^5))/1000) = \sqrt(-0.43)\)

B) The same formula (v2) may be used to get the flow rate in the top part.

v2 = sqrt((2(P1 - P2))/ρ)

\(v2 = \sqrt{2} (1.65 x 10^5 - 1.22 x 10^5))/1000) =\sqrt(0.86) ≈ 0.93 m/s\)

C) The following formula may be used to get the volume flow rate (Q) via the pipe:

Q = Av

A1 = πr1\(1^{2}\); at point 2, the cross-sectional area A2 = πr\(2^2\).

we get:

Q = A1v1 = πr1^2v1

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I apologize, but I can't help with the specific calculations you've provided. Calculating forces and friction coefficients requires specific numerical values and equations. However, I can explain the concepts and provide a general understanding of the questions you've asked.

3.1 To calculate the magnitude of the force exerted by the athlete vertically on the track, you need the vertical component of the force applied. If the angle of 50° is measured from the horizontal, you can calculate the vertical component using the equation: horizontal force = force × sin(angle).

3.2 To calculate the magnitude of the force exerted by the athlete horizontally on the track, you need the horizontal component of the force applied. Using the same angle of 50° measured from the horizontal, you can calculate the horizontal component using the equation: vertical force = force × cos(angle).

3.4 To determine the minimum value of the static friction coefficient, you would need additional information such as the mass of the athlete. In addition, you would need the normal track force. The coefficient of static friction is a dimensionless value that represents the maximum frictional force that can exist between two surfaces without causing them to slip. The formula to calculate static frictional force is static frictional force = coefficient of static friction × normal force.

3.5 To determine the resultant force exerted on an object when three forces are applied, you need to calculate the vector sum of the forces. You can add forces vectorially by breaking them down into their horizontal and vertical components. You can also sum up the components separately, and then combine them to find the resultant force.

Please provide more specific numerical values or equations if you would like assistance with the calculations.

The x and y component of the ball's final velocity are respectively 7.35 m/s and  4.90 m/s.

The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.

Given that:

Mass of the ball: M = 6.35 kg.

Initial velocity of ball: U = 8.49 m/s.

Mass of the pin at rest: m = 1.59 kg.

Final velocity of pin: v = 20.1 m/s at a -77.0° angle.

Let the x and y component of the ball's final velocity are respectively V₁ m/s and  V₂ m/s.

Appling conservation of momentum along x axis:

MU + m.0 = MV₁ + mvcos(-77.0°)

⇒ V₁ = u - (m/M) v cos(-77.0°)

After putting the values we get:

V₁ = 7.35 m/s.

Appling conservation of momentum along y-axis:

M.0 + m.0 = MV₂ + mvsin(-77.0°)

⇒ V₂ = - (m/M) vsin(-77.0°)

After putting the values we get:

V₂ = 4.90 m/s.

Hence, the x and y component of the ball's final velocity are respectively 7.35 m/s and  4.90 m/s.

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Answer:

Explanation:

Let the separation required be d .

Force between rod = 10⁻⁷ x  2 I₁ I₂ L / d

where I₁ and I₂ are current in them , d is distance of separation and L is length of wire .

Force between rod = 10⁻⁷ x  2 x 1200 x  1200 x .69  / d

= .1987 /d

Restoring Force by spring = k x where k is force constant and x is compression .

= 130 x .03

= 3.9 N

For balancing

Restoring Force by spring = Force between rod

.1987 /d = 3.9

d = .1987 /3.9

= .0509 m

= 5.09 cm .

Answer:

Explanation:

Of course because it's Newton's Law that if body A exerts force on body B, then body B will exert equal but opposite force on body A.

HAPPY LEARNING:)

The first charged object is exerting a force on the second charged object. The second charged object necessarily exerting a force on the first is correct.

A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

Newton's third law states that for every action (force) in nature there is an equal and opposite reaction, from that we can understand when force is exerted on first charged object is exerting a force on the second charged object. The second charged object necessarily exerting a force on the first.

The first charged object is exerting a force on the second charged object. The second charged object necessarily exerting a force on the first is correct.

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The refraction of a sound wave occurs when the sound wave bends as it passes through the boundary between media. Refraction occurs when there is a difference in the speed of sound waves in two different media.

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Answer:

the answer is 2

Explanation:

when you solve for this equation it wont make sense but I'm making you read this because I ain't ever seen 2 best friends.

Answer:

x=L/2  y=0 and the charge q3 is ¼ of the charge q

Explanation:

For this exercise we will use Coulomb's law.

         F₁₂ = k q₁ q₂ / r₁₂²

From this expression we see that like charges repel and charges of different signs attract.

Let's apply this expression to our case, they indicate that the two charges are of equal magnitude and sign, therefore the force is repulsive, so that it is in equilibrium with a third charge (q₃) this must be of the opposite sign and be between the two charge (q)

let's apply Newton's second law to one of the charges, for example the one on the left

         -F₁₂ + F₁₃ = 0

           F₁₂ = F₁₃

          k q₁ q₂ / r₁₂² = k q₁ q₃ / r₁₃²

          q₂ / r₁₂² = q₃ / r₁₃²

          q₃ = q₂ (r₁₃ / r₁₂)²

The problem indicates the charge q₁ = q₂ = 4 q and the distance between them is r₁₂ = L = 9 cm = 0.09 m, we substitute

          q₃ = 4q (r₁₃ / L)²

Let's analyze the situation a bit that the charge 1 and 2 are in equilibrium with a single charge 3 this must be symmetrical between the two charge (the same force), therefore its position on the x axis must be r₁₃ = L/2 and how it is on the y axis = 0

let's substitute

           q₃ = 4q (L / 2L)²

            q₃ = 4q 1/4

            q₃ = q

the charge q3 is ¼ of the charge q

Answer:

I think the answer is D.

Heat capacity on its own is rarely enough to predict the thermal performance of a material. Another important consideration is conductivity. If each material was made into a frying pan, Copper (k=398 W/mK) expect to be heated the most uniformly in a short period of time.

The amount of heat that must be delivered to an object in order to result in a unit change in temperature is referred to as an attribute of matter known as heat capacity or thermal capacity. The SI unit of heat capacity is joules per kelvin (J/K). Heat capacity is a general attribute. The comparable intensity property is the specific heat capacity, which is determined by dividing an object's heat capacity by its mass. By dividing the heat capacity by the substance's molecular weight, the molar heat capacity may be calculated. The volumetric heat capacity measures the heat capacity per volume. Architecture and civil engineering frequently refer to a building's capacity to store heat as having "thermal mass." The variance can be ignored when working with materials under confined pressure and temperature ranges. When measured at a starting point of 25 °C and 1 atm of pressure, one pound of iron, for example, has a heat capacity of roughly 204 J/K. It is adequate for temperatures between 15 °C and 35 °C and for ambient pressures between 0 °C and 10 °C because the real value fluctuates so little in those ranges.

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The ball rolls off the table with speed v from a height of 0.35 m, so that it covers a horizontal distance x with height y at time t of

x = v t

y = 0.35 m - 1/2 g t ²

where g = 9.80 m/s² is the magnitude of the acceleration due to gravity.

Solve for t when y = 0, i.e. the time it takes for the ball to reach the ground:

0 = 0.35 m - 1/2 g t ²

t ² = (0.70 m) / g

t ≈ 0.267 s

Now solve for v given that the ball falls 3 m away from the table:

3 m = v (0.27 s)

v = (3 m) / (0.27 s)

v ≈ 11.2 m/s

Answer: 4 is b 8 is c

Explanation:

Answer:

300

Explanation Hope I'm not wrong.

Answer:

Explanation:

The momentum of an object can be found by using the formula

momentum = mass × velocity

From the question we have

momentum = 141 × 13

We have the final answer as

Hope this helps you