A certain spring is found not to obey Hooke’s law; it exerts a restoring force Fx(x)=−αx−βx2 if it is stretched or compressed, where α=60.0N/m and β=18.0N/m2. The mass of the spring is negligible. (a) Calculate the potential-energy function U(x) for this spring. Let U = 0 when x = 0. (b) An object with mass 0.900 kg on a frictionless, horizontal surface is attached to this spring, pulled a distance 1.00 m to the right (the +x-direction) to stretch the spring, and released. What is the speed of the object when it is 0.50 m to the right of the x = 0 equilibrium position?

Answer:

43.76%

Explanation:

The air density at the sea level ρ_s  = 1.25 kg/m^3.

also, air density at the top of the mountain where ρ_t = 0.547 kg/m^3.

taking temp as --50° C  and pressure as 1/3 of P_atm.

therefore,  t percent is the air density at the summit of Mount Everest relative to the air density at sea level

= [tex]\frac{\rho_t}{\rho_s}\times100[/tex]

=[tex]\frac{0.547}{1.25}\times100[/tex]

=43.76 %

Answer:

458.33 ft

Explanation:

We are given that

Wavelength of of an x- ray photon=1 in

Wavelength of of an x- ray photon==[tex]\frac{1}{12}[/tex]ft

1 in=[tex]\frac{1}{12}[/tex]feet

We have to find the  length of line (in feet) drawn by you to represent the wavelength of visible light.

According to question

Wavelength of visible light=[tex]5500\times \frac{1}{12}[/tex] ft

Wavelength of visible light[tex]=\frac{5500}{12}[/tex]ft

Wavelength of visible light=458.33 ft

Hence, the 458.33 ft line must drawn  by you to represent the wavelength of visible light.

Answer:

458.33 ft

Explanation:

I had the same question once

Answer:

Electric potential,  V = 40.68 volts

Explanation:

Given that,

Charge on the sphere, [tex]q=22.6\ pC=22.6\times 10^{-12}\ C[/tex]

Diameter of the plastic sphere, d = 1 cm

Radius, r = 0.5 cm

We need to find the electric potential at its surface. The potential at a surface is given by :

[tex]V=\dfrac{kq}{r}[/tex]

[tex]V=\dfrac{9\times 10^9\times 22.6\times 10^{-12}}{0.5\times 10^{-2}}[/tex]

V = 40.68 volts

So, the electric potential at its surface is 40.68 volts. Hence, this is the required solution.

Answer:

   2- 3 - 1- 4

Explanation:

Extracting energy from the wind is known as wind energy. Wind energy is are a renewable source of energy.

Energy can be extracted from the wind by following different steps.

1) Wind will turn the wind turbine blade.

2) Then the mechanical energy from the wind turbine blade is transferred to the generator.

3) The generator will convert mechanical energy into electrical energy.

4) the electrical energy produced is then transferred to the grid.

Hence, the sequence of Power generation is  

       2- 3 - 1- 4

Answer:

He lost $53,240.60

Explanation:

In order to solve this problem, we must start by determining how many dollars he spent for the [tex]500m^{2}[/tex] of cloth. We can determine this by doing the following conversion:

[tex]500m^{2}*\frac{400 tepizes}{m^{2}}*\frac{\$0.625}{1 tepiz}=\$125,000[/tex]

Next, we need to figure out what is the price of the [tex]500m^{2}[/tex] of coth is in New York:

[tex]500m^{2}*\frac{1yd^{2}}{(0.9144m)^{2}}*\frac{\$120}{1 yard^{2}}=\$71,759.40[/tex]

so now we subtract the two amounts so we get:

$125,000-$71,759.40=$53,240.60

Answer:

18Joules

Explanation:

Potential Energy = mass * gravity * height

PE = 0.6 * 10 * 3

PE = 18Joules

Answer: 9.0 atm

Explanation:

To calculate the new pressure, we use the equation given by Boyle's law. This law states that pressure is directly proportional to the volume of the gas at constant temperature.

The equation given by this law is:

[tex]P_1V_1=P_2V_2[/tex]

where,

[tex]P_1\text{ and }V_1[/tex] are initial pressure and volume.

[tex]P_2\text{ and }V_2[/tex] are final pressure and volume.

We are given:

[tex]P_1=3.0atm\\V_1=150mL\\P_2=?mmHg\\V_2=50mL[/tex]

Putting values in above equation, we get:

[tex]3.0\times 150mL=P_2\times 50mL\\\\P_2=9.0atm[/tex]

Thus new pressure of 150 ml of a gas that is compressed to 50 ml is 9.0 atm

To find the net torque, we multiply the radius by each force, and then add them taking the direction into account. Then, we divide the net torque by the moment of inertia (which we find by substituting the given mass and radius values into the formula for a uniform solid disk) to find the angular acceleration.

To solve this question, we need to calculate the net torque ('t') which is the product of the radius and the force applied perpendicular to it, and then use that value to find the angular acceleration ('a', represented as rad/s2). This involves the physics concept of Newton's second law applied to rotation.

Step 1: Calculate net torque. The applied forces are perpendicular to the radius and friction is negligible, so the torque due to each force is t = rF. The total torque is the sum of the torques due to the two forces applied, taking into account that the 90.0 N force is in the counterclockwise direction and the 125 N force is in the clockwise direction (-125 N). The net torque would therefore be t = r(90 N) - r(125 N) = 0.364m(90 N) - 0.364m(125 N).

Step 2: Calculate angular acceleration. Angular acceleration is the net torque divided by the moment of inertia ('I') of the disk. The moment of inertia for a uniform solid disk is 0.5mr2. We can substitute m = 24.3 kg and r =0.364 m to find I. The angular acceleration is therefore a = t/I.

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The net torque produced by the two forces is 12.74 N·m and the angular acceleration of the disk is 7.90 rad/s². The calculation involved determining the torque from each force and then using the moment of inertia for a solid disk to find the angular acceleration.

(a) Net Torque Calculation

To calculate the net torque, we use the formula:

Torque (τ) = Force (F) x Radius (r) x sin(θ)

Assuming both forces are applied tangentially (θ = 90° or sin(90°) = 1), we have:

Torque from 90.0 N force:

τ₁ = 90.0 N x 0.364 m x 1 = 32.76 N·m (clockwise, so negative)

Torque from 125 N force:

τ₂ = 125 N x 0.364 m x 1 = 45.5 N·m (counterclockwise, so positive)

The net torque is:

Net Torque = τ₂ - τ₁ = 45.5 N·m - 32.76 N·m = 12.74 N·m

(b) Angular Acceleration Calculation

First, we need the moment of inertia (I) for a solid disk, given by:

I = 0.5 x Mass (m) x Radius² (r²)

For this disk:

I = 0.5 x 24.3 kg x (0.364 m)² = 1.612 kg·m²

Next, using the net torque (τ) to find angular acceleration (α):

α = τ / I

Substituting the values:

α = 12.74 N·m / 1.612 kg·m² = 7.90 rad/s²

Conclusion:

The net torque produced by the two forces is 12.74 N·m, and the angular acceleration of the disk is 7.90 rad/s².

Answer:

A. P = 18.75 watts

B. P = 75 watts

Explanation:

V = 120 Volts

P = VI

I = P/V = 75/120 = 0.625 Amps

V = IR

R = V/I

R = 120/0.625 = 192 Ω

So the resistance of the bulb is 192 Ω and it does not change as it is given in the question.  

A. How much power is dissipated in a light bulb that is normally rated at 75 W, if instead we hook it up to a potential difference of 60 V?

As P = VI and I = V/R

P = V*(V/R)

P = V²/R

P = (60)/192

P = 18.75 watts

As expected, it will dissipate less power (18.75 watts) than rated power due to not having rated voltage of 120 Volts.

I = V/R = 60/192 = 0.3125 Amps

or I = P/V = 18.75/60 = 0.3125 Amps

Since the resistance is being held constant, decreasing voltage will also decrease current as V = IR voltage is directly proportional to the current.

B. How much power is dissipated in a light bulb that is normally rated at 75 W, if instead we hook it up to a potential difference of 120 V?

P = V*(V/R)

P = V²/R

P = 120/192 = 75 watts

I = P/V = 75/120 = 0.625 Amps

As expected, it will dissipate rated power of 75 watts at rated voltage of 120 Volts.

For a light bulb rated at 75 W at 120 V, the power dissipated at 60 V is 18.75 Watts and at 120 V, it would dissipate its rated power of 75 Watts.

The power dissipated by a resistor (in this case, a light bulb) can be calculated using the formula P = V² / R, where P is the power, V is the potential difference (or voltage), and R is resistance.

A. With a potential difference of 60 V (half of its normal voltage), we expect the bulb to dissipate a quarter of its normal power. Hence, the power in this case would be (60V)²/R = 75W/4 = 18.75 Watts.  

B. The rating on the bulb is 75 W assuming a household voltage of 120 V. So, if we hook it up to a potential difference of 120 V, it should dissipate its normal rated power of 75 Watts.

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A.  Strong element of customer involvement

B.  Lack of​ computer-aided design

C.  Tangible products are more personalized

D.  More challenging inventory considerations

Answer:

A. Strong element of customer involvement

Explanation:

A service operation involves managing and performing the activities that are necessary to deliver services at a good level of quality to customers. Service operation tends to be more difficult than a successful design of a tangible product because the process involves high customer contact because customers are consumers of the product but in the case of the services, they are also part of its production and this is more difficult to control. According to this, the answer is that a successful service operation is more difficult because it has a strong element of customer involvement.

Answer : The mass of solute needed are, 40 grams.

Explanation :

As we are given that 40 % (w/v) solution of sodium bicarbonate (solute) that means 40 grams of sodium bicarbonate present in 100 mL of solution.

Now we have to calculate the mass of solute needed.

As, 100 mL of solution needs mass of solute = 10 g

So, 400 mL of solution needs mass of solute = [tex]\frac{400mL}{100mL}\times 10g=40g[/tex]

Thus, the mass of solute needed are, 40 grams.

To prepare a 400 ml of 40% (w/v) solution of sodium bicarbonate, multiply the percentage (40%) by the total volume (400 ml) and divide by 100. You will need 160 grams of sodium bicarbonate for this solution.

To prepare 400 ml of a 40% (w/v) solution of sodium bicarbonate, you need to understand the meaning of (w/v). It stands for weight/volume, and it means that for every 100 ml of solution, you have the given percentage in grams of the solute. So, for a 40% (w/v) solution, 100 ml of the solution will contain 40 grams of sodium bicarbonate. Therefore, we need to calculate the amount of sodium bicarbonate for 400 ml of solution:

To prepare a 400 ml of 40% (w/v) sodium bicarbonate solution, you would need 160 grams of sodium bicarbonate.

Answer:

force of tension in the left cable = 7.66N

force of tension in the right cable = 5.074N

Explanation:

The detailed step and calculation is as shown in the attachment.

Answer:

3. It has the same net charge as 11 protons.

Explanation:

An electrically neutral object contains the same number of protons and electrons. Therefore, if 11 electrons are removed from it, there will be 11 more protons compared to the number of electrons in the object. Thus, the object It has the same net charge as 11 protons.

Atoms are electrically neutral, but removing electrons results in a charged object with a net charge equivalent to the number of protons present.

Atoms are electrically neutral, meaning that the overall electric charge is zero because the number of protons (positive charge) equals the number of electrons (negative charge). When an atom loses electrons, it becomes positively charged, and when it gains electrons, it becomes negatively charged. In this case, removing 11 electrons from a neutrally charged object will result in a net charge equivalent to having the same net charge as 11 protons.

Explanation:

The given  frequency of tuning fork is 440 Hz . It produces 5 beats with trumpet wire . That means , the frequency of wire can be 440 ± 5

It can be either 445 or 435

Now the length of wire is increased , by which its frequency decreases . Because frequency is inversely proportional to length of wire .

If we decrease the frequency in 435 , the difference between tuning fork frequency and wire frequency will become greater than 5 even . So it cannot produce 3 beats with it .

If we decrease frequency from 445 , it can become 443 Hz . It gives 3 beat with the tuning fork as given .

Thus the initial frequency of wire is 445 Hz

To find the initial frequency of the trumpet player, we can use the concept of beat frequency. The initial frequency is either 442 Hz or 438 Hz.

To find the initial frequency of the trumpet player, we can use the concept of beat frequency. The beat frequency is the difference between the frequencies of two sounds, in this case, the trumpet player's note and the tuning fork. Initially, the trumpet player hears 5 beats per second. After adjusting the length of her trumpet, she hears 3 beats per second. The change in beat frequency is 5 - 3 = 2 Hz. Since the tuning fork remains at 440 Hz, the initial frequency of the trumpet player can be calculated by adding or subtracting the beat frequency from the tuning fork frequency. In this case, the initial frequency is either 440 + 2 = 442 Hz or 440 - 2 = 438 Hz.

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Answer:

a. FTh = 30 N

b. Fw = 30 N

c. a = 200 m/s2

Explanation:

See full explanation in the picture. Please rate as brainliest

The magnitude of squid thrust force, magnitude of force on the water and the acceleration experienced by the water is required.

The magnitude of squid thrust force and magnitude of force on the water is 30 N.

The acceleration is [tex]200\ \text{m/s}^2[/tex]

m = Mass

a = Acceleration

m = 1.5 kg

a = [tex]20\ \text{m/s}^2[/tex]

Thrust force

[tex]F=ma\\\Rightarrow F=1.5\times 20\\\Rightarrow F=30\ \text{N}[/tex]

The magnitude of squid thrust force will be equal to the magnitude of force on the water from the third law of motion.

F = 30 N

m = 0.15 kg

Acceleration is given by

[tex]a=\dfrac{F}{m}\\\Rightarrow a=\dfrac{30}{0.15}\\\Rightarrow a=200\ \text{m/s}^2[/tex]

Learn more about Newton's law:

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Answer: a. gamma rays

Explanation:

Scientists are able to use gamma rays to determine the composition of planets and other celestial bodies.

Special equipment exists that can measure gamma rays emitted by atoms on a planet's surface when it is struck by cosmic rays thus enabling us (humans) to understand more of the universe.

Answer:

Wrong its actually radio waves

Explanation:

Answer:

We need 4 times more force to keep the car in circular motion if the velocity gets double.

Explanation:

Lets take the mass of the car = m

The radius of the arc = r

[tex]F=\frac{m\times v^2}{r}[/tex]

Given that speed of the car gets double ,v' = 2 v

Then the force on the car = F'

[tex]F'=\frac{m\times v'^2}{r}[/tex]  ( radius of the arc is constant)

[tex]F'=\frac{m\times (2v)^2}{r} [/tex]

[tex]F'=4\times \frac{m\times v^2}{r}[/tex]

We know that [tex]F=\frac{m\times v^2}{r}[/tex]

Therefore F' = 4 F

So we can say that we need 4 times more force to keep the car in circular motion if the velocity gets double.

The magnitude of centripetal force will become four times with the twice the greater speed of car.

Given data:

The magnitude of centripetal force on car is, Fc.

The force acting on any object undergoing the motion around the circular path, such that the motion is balanced is known as centripetal force. It is also known as the center-seeking force. And the expression for the centripetal force is given as,

Fc = mv²/r

Here,

m is the mass of car.

v is the speed of car.

r is the radius of circular track.

If the speed of car is twice as great, then the new centripetal force is given as,

F'c = m(2v)²/r

F'c = 4 × mv²/r

F'c = 4 × Fc

Thus, we can conclude that the magnitude of centripetal force will become four times with the twice the greater speed of car.

Learn more about the centripetal force here:

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Answer:

Overload current, short-circuit current and short circuit

Explanation:

Overload current is an excessive current relative to normal operating current, but one that is confined to the normal conductive path provided by the conductors, circuit components, and loads of the distribution system.

A short-circuit current is a current that flows outside the normal conducting path.

One generally accepted definition of short circuit is when a phase or ungrounded conductor comes in contact with, or arcing current flows between, another phase conductor, neutral, or ground.

Answer :

I think it is A. Distance

Answer:

A. Distance

Explanation:

Velocity, Acceleration, and displacement all require a magnitude and direction to be measured.

Explanation:

(A) Electric field for the parallel plate capacitor is given by :

[tex]E=\dfrac{\sigma}{2\epsilon_o}[/tex]

It is clear that the electric field does not depend on the separation of the plates.

(B) The relation between the electric field and the electric potential is given by :

[tex]V=Ed[/tex]

d is the separation between plates. So, if the separation of the plates is increased, the potential difference increases.

(C) The capacitance of the parallel plate capacitor is given by :

[tex]C=\dfrac{A\epsilon_o}{d}[/tex]

So, the capacitance decreases when the separation of the plates is increased.

(D) The energy stored in the capacitor is given by :

[tex]E=\dfrac{1}{2}CV^2[/tex]

[tex]E=\dfrac{1}{2}C(Ed)^2[/tex]

So, the energy stored in the capacitor  is increased when the separation of the plates is increased.

Answer:

a)constant

b)constant

c)constant

d) constant

Explanation:

a)

The electric field between the plates remain constant. The Electric field between the plates is given as:

[tex]E=\frac{\sigma}{\epsilon}[/tex]

where:

[tex]\sigma=[/tex] surface charge density

[tex]\epsilon=[/tex] permittivity of the material between the plates

b)

The potential difference between the plates is related as:

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

and

[tex]E=\frac{V}{d}[/tex]

where:

d = distance between the plates

Therefore the potential difference remains constant when the capacitor plates distance remains constant.

c)

the capacitance:

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

When the charge and potential difference is constant then the capacitance also remains constant.

d)

Energy stored in a capacitor:

[tex]U=\frac{1}{2} C.V^2[/tex]

Since capacitance and potential difference are constant therefore potential difference is also constant.

Explanation:

We know from newton's 2nd law that F= m/a. That is force directly proportional to mass and inversely proportional to acceleration. F is same for the skier and Earth but mass is different for both. m for earth is way larger than the m for skier. So, for constant Force , a of Earth must very small as compared with a of the skier.

Skiers and skateboarders accelerate due to action-reaction force pairs in accordance with Newton's third law, but the Earth's immense mass leads to negligible acceleration, rendering its movement imperceptible.

Understanding Force and Acceleration

When discussing the action-reaction force pair between the Earth and a skier, Newton's third law of motion is essential. This law states that for every action, there is an equal and opposite reaction. When the skier accelerates, the force exerted on them by the Earth (gravity) is met with an equal and opposite force exerted by the skier back onto the Earth. The reason the Earth does not seem to move while the skier accelerates is due to the massive difference in mass between the Earth and the skier. Since acceleration is calculated as force divided by mass (F = ma), the much larger mass of the Earth compared to the skier results in a negligible acceleration of the Earth. This is similar to why stationary skater A does not move when pushing skater B; if skater A has more contact with the surface or better frictional grip, they may not move significantly despite exerting force.

Furthermore, when objects like a skateboarder jump off a building, both the Earth and the skateboarder exert mutual forces on each other. Despite experiencing the same total change of momentum, the Earth's massive size means its acceleration is imperceptible, while the skateboarder moves considerably more.

Answer:

The correct answer is option a.

Explanation:

Conservation of momentum :

[tex]m_1u_1+m_2u_2=m_1v_1+m_1v_2[/tex]

Where :

[tex]m_1, m_2[/tex] = masses of object collided

[tex]u_1,u_2[/tex] = initial velocity before collision

[tex]v_1,v_2[/tex] = final velocity after collision

We have :

Two equal-mass carts roll towards each other.

[tex]m_1=m_2=M[/tex]

Initial velocity of [tex]m_1=u_1=2 m/s[/tex]

Initial velocity of [tex]m_2=u_2=-1 m/s[/tex] (opposite direction)

Final velocity of [tex]m_1=v_1=v[/tex] (same direction )

Final velocity of [tex]m_2=v_2=v[/tex]  (same direction)

[tex]M\times 2 m/s+M(-1 m/s)=Mv+Mv[/tex]

[tex]1 m/s=2v[/tex]

v = 0.5 m/s

rg135

The speed of the carts after their collision is 0.5 m/s.

Using the principle of conservation of momentum, the combined carts will have a speed of 0.5 m/s after their collision. This is because their total momentum prior to the collision is conserved during the collision and is equal to their total momentum post the collision.

This is a question about the principle of conservation of linear momentum in physics. Before the collision, the total momentum of the system (two carts) is the sum of their individual momenta. Since they have equal mass, we can write the total momentum as momentum of cart 1 + momentum of cart 2 = total momentum, or (mass x velocity of cart 1) + (mass x -velocity of cart 2) = total momentum. Since one cart is moving rightward and the other is moving leftward, we take the velocity of the leftward moving cart, cart 2, as negative. Thus, we have (mass x 2 m/s) - (mass x 1 m/s) = total momentum, hence the total momentum comes out to be mass x 1 m/s.

After the collision, the two carts couple and move with a common speed which we denoted as V. According to the conservation of linear momentum law, the total momentum before collision must be equal to the total momentum after the collision, which gives us mass x 1 m/s = 2 x mass x V (since the total mass after the collision becomes 2 times the mass of one cart), solving this gives V = 0.5 m/s.

Therefore, the combined carts will have a speed of 0.5 m/s after the collision. So, the answer to your question is a. 0.5 m/s.

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Answer:

c. as it was 1,000 years ago

Explanation:

since the object is one thousand light years away, it means what ever light is comes from the object (is reflected off the object) would take 1,000 years to get to us, meaning we would be seeing the object as it was 1,000 years ago.

Answer:

force on the proton = 5.96 × [tex]10^{-14}[/tex] N

Explanation:

given data

kinetic energy = 1.16 ×[tex]10^{5}[/tex]  eV

charge density of σ = +6.60 μC/m²

solution

we get here force on the proton that is express as

F = qE  ....................1

here q is charge on proton i.e = 1.6 × [tex]10^{-19}[/tex] C

and E is electric field due to charge i.e E = [tex]\frac{\sigma }{2*\epsilon_o }[/tex]

so put the value in equation 1 we get

force on the proton = 1.6 × [tex]10^{-19}[/tex] × [tex]\frac{6.60*10^{-6}}{2*8.85*10^{-12}}[/tex]  

force on the proton = 5.96 × [tex]10^{-14}[/tex] N

Final answer:

The magnitude of the force on the proton is 1.19 × 10-13 N.

Explanation:

In order to find the magnitude of the force on the proton, we can use the formula F = qE, where F is the force, q is the charge of the proton, and E is the electric field. First, we need to convert the charge density from μC/m² to C/m², which gives us σ = 6.60 × 10-6 C/m². Since the electric field is uniform, we can use the equation E = σ/ε₀, where ε₀ is the electric constant.

Plugging in the values, we have E = (6.60 × 10-6 C/m²) / (8.85 × 10-12 C²/N·m²), which gives us E = 7.46 × 10^5 N/C. Now, we can find the force using F = qE.

F = (1.60 × 10-19 C)(7.46 × 10^5 N/C) = 1.19 × 10-13 N.

Answer:

Technician A is right.                                                    

Explanation:

Given that,

Voltage of circuit, V = 12 volt

Current in the circuit, I = 3 A

Technician A says the electric power in this circuit is 36 watts. Technician B says the electric power in this circuit is 4 watts. We need to say that which technician is correct.

The power of any circuit is given by :

[tex]P=V\times I[/tex]

[tex]P=12\ V\times 3\ A[/tex]

P = 36 watts

So, technician A is right. Hence, this is the required solution.

The power in an electric circuit is calculated by multiplying the voltage by the current. Therefore, in a 12-volt circuit with a current of 3 amps, the power would be 36 watts. This confirms the statement made by Technician A, making him correct.

In the context of electric circuits, the power is determined by multiplying the voltage across the circuit by the current flowing through it. This relationship is captured in the formula P = IV, where P represents power, I represents current, and V represents voltage.

In this particular case, given a 12-volt circuit with a current of 3 amps, the calculation becomes P=12V * 3A. Accordingly, the power in this circuit would be 36 watts, validating Technician A's statement. Therefore, in this instance, Technician A is correct and Technician B is incorrect.

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Answer:

2 m/s

Explanation:

From the law of conservation of momentum,

Total momentum before collision = total momentum after collision

mu+m'u' = V(m+m') .................................Equation 1

Where m = mass of the first player, u = initial speed of the first player, m' = mass of the second player, u' = initial speed of the second player, V = combined speed of both players.

Making V the subject of the equation,

V = (mu+m'u')/(m+m')................ Equation 2

Note: Taking the direction of the first player as positive.

Given: m = 75 kg, m' = 100 kg, u = 6 m/s, u' = -8 m/s (opposite the first player),

Substituting into equation 2

V = [(75×6)+(100×(--8))]/(75+100)

V = (450-800)/175

V = 350/175

V = - 2 m/s.

Note: The negative signs tells that the combined speed is in the direction of the second player.

Hence the combined speed of the two players = 2 m/s

Final answer:

The question involves using the conservation of momentum to calculate the combined speed of two football players after they collide and cling together. By applying the formula (m1*v1 + m2*v2) / (m1 + m2), the resulting velocity can be obtained, considering the direction of the players' velocities.

Explanation:

The question involves a physical interaction between two football players, which is described by the conservation of momentum, a fundamental concept in physics. When two objects, in this case football players, collide and stick together, the total momentum before the collision equals the total momentum after the collision, provided no external forces act on the system. The formula to find the combined velocity just after the collision is derived from the conservation of momentum principle: (m1*v1 + m2*v2) / (m1 + m2), where m1 and m2 are the masses and v1 and v2 are the velocities of the two players respectively.

Therefore, to find the combined speed of the two players just after the collision, we would use their given masses and initial speeds: (75kg*6m/s + 100kg*-8m/s) / (75kg + 100kg). The negative sign indicates that the second player is running in the opposite direction. After solving, we'd get the resulting velocity, which represents the speed and direction of the two players immediately after the collision.

Answer:

a) 0.15 μC b) 9.4*10¹¹ electrons.

Explanation:

As the total charge must be conserved, the total charge on the spheres, after being brought to contact each other, and then separated, must be equal to the total charge present in the spheres prior to be put in contact:

Q = +8.2μC +9.0 μC +(-7.8 μC) + (-8.8 μC) = +0.6 μC

As the spheres are assumed perfect conductors, as they are identical, once in contact each other, the excess charge spreads evenly on each sphere, so the final charge, on each of them, is just the fourth part of the total charge:

Qs = Qt/4 = 0.6 μC / 4 = 0.15 μC.

b) As the charge has a positive sign, this means that each sphere has a defect of electrons.

In order to know how many electrons are absent in each sphere, we can divide the total charge by the charge of one electron, which is the elementary charge e, as follows:

[tex]N =\frac{0.15e-6C}{1.6e-19C} = 9.4e11 electrons[/tex]

700 makes the maximum output power.

Explanation:

In physics, power is the rate of doing work or of transferring heat, i.e. the amount of energy transferred or converted per unit time. The output power of a motor is the product of the torque that the motor generates and the angular velocity of its output shaft.

A joule is equal to one Newton-meter, which is the amount of work needed to move a 1 Newton force a distance of 1 meter. When you divide work by time, you get power, measured in units of joules per second. This is also called a Watt. 1 Watt = 1 Joule Sec. This is the formula to calculate output power.

The maximum output power of a 700W dual rail power supply is 700W. 'Dual rail' refers to how the power is distributed, it does not increase the total output.

Having determined that the power supply is a 700W dual rail, this refers to the maximum amount of power that the power supply can output. The power supply's maximum output power is its total capacity, which in this case is 700W. It's important to remember that 'dual rail' refers to the way the power is distributed and doesn't increase the overall power. Simply put, a dual rail power supply divides its power between two ‘rails’ or circuits, but the maximum output power remains 700W.

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Answer:

(a). The total charge of this system is 10 C.

(b). The charges of the spheres before the connection is 5 C and 4.2 C.

Explanation:

Given that,

Distance [tex]r= 1.00\times10^{5}\ m[/tex]

Force = 22.5 N

The two spheres are connected for a moment by a wire. After this, charge is re-distributed equally, and each sphere now has a charge

We need to calculate the charge

Using formula of electric force

[tex]F=\dfrac{kq_{1}q_{2}}{r^2}[/tex]

Here, charge is equal

Put the value into the formula

[tex]22.5=\dfrac{9\times10^{9}\times q^2}{(1.00\times10^{5})}[/tex]

[tex]q^2=\dfrac{22.5\times(1.00\times10^{5})^2}{9\times10^{9}}[/tex]

[tex]q=\sqrt{\dfrac{22.5\times(1.00\times10^{5})^2}{9\times10^{9}}}[/tex]

[tex]q=5\ C[/tex]

(a). We need to calculate the total charge of this system

We have the charge of each sphere after re-distribution.

We know that the charge is distributed equally.

Therefore, the total charge of the system is

[tex]q+Q=2q=2\times5=10\ C[/tex]

(b). We need to calculate the charge of the spheres before the connection

Using formula of electric force

[tex]F=\dfrac{kq_{1}q_{2}}{r^2}[/tex]

Put the value into the formula

[tex]18.9=\dfrac{9\times10^{9}\times q_{1}\times q_{2}}{(1.00\times10^{5})}[/tex]

[tex]q_{2}=\dfrac{18.9\times(1.00\times10^{5})^2}{9\times10^{9}\times5}[/tex]

[tex]q_{2}=4.2\ C[/tex]

Hence, (a). The total charge of this system is 10 C.

(b). The charges of the spheres before the connection is 5 C and 4.2 C.

Answer:

[tex]\theta=15.70^\circ[/tex]

Explanation:

A right triangle is formed, in which the vertical elevation is the opposite cathetus and the horizontal distance is the adjacent cathetus, since we know these two values, we can calculate the angle of inclination using the definition of tangent:

[tex]tan\theta=\frac{opp}{adj}\\\theta=arctan(\frac{opp}{adj})\\\theta=arctan(\frac{28.1m}{100m})\\\theta=15.70^\circ[/tex]