The height of a typical playground slide is about 6 ft and it rises at an angle of 30 ∘ above the horizontal.

a.)Some children like to slide down while sitting on a sheet of wax paper. This makes the friction force exerted by the slide very small. If a child starts from rest and we take the friction force to be zero, what is the speed of the child when he reaches the bottom of the slide?

b.)If the child doesn't use the wax paper, his speed at the bottom is half the value calculated in part A. What is the coefficient of kinetic friction between the child and the slide when wax paper isn't used? μk = ?

I found the answer to part a, it is 3m/s, but I need part b. Please show all steps, thank you!

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]

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:

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.

Hydraulic fracturing involves several of Earth's system spheres including the geosphere (with drilling into rock formations), the hydrosphere (with extensive use of water), and the biosphere (potential impacts on ecosystems).

The scientific investigation on hydraulic fracturing involves several of Earth's systems, specifically the biosphere, the hydrosphere, and the geosphere. The geosphere is involved as hydraulic fracturing involves the extraction of natural gas from deep underground rock formations. The hydrosphere is engaged as large quantities of water are used in the process, potentially affecting water resources. Finally, the biosphere is implicated as there could possibly be impacts on local ecosystems and wildlife from the operation and waste produced from the process.

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Answer:

1keff=1k1+1k2

see further explanation

Explanation:for clarification

Show that the effective force constant of a series combination is given by 1keff=1k1+1k2. (Hint: For a given force, the total distance stretched by the equivalent single spring is the sum of the distances stretched by the springs in combination. Also, each spring must exert the same force. Do you see why?

From Hooke's law , we know that the force exerted on an elastic object is directly proportional to the extension provided that the elastic limit is not exceeded.

Now the spring is in series combination

F[tex]\alpha[/tex]e

F=ke

k=f/e.........*

where k is the force constant or the constant of proportionality

k=f/e

[tex]f_{eff} =f_{1} +f_{2}[/tex]............................1

also for effective force constant

divide all through by extension

1) Total force is

Ft=F1+F2

Ft=k1e1+k2e2

F = k(e1+e2) 2)

Since force on the 2 springs is the same, so

k1e1=k2e2

e1=F/k1 and e2=F/k2,

and e1+e2=F/keq

Substituting e1 and e2, you get

1/keq=1/k1+1/k2

Hint: For a given force, the total distance stretched by the equivalent single spring is the sum of the distances stretched by the springs in combination.

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.

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: Option A : Technician A

Explanation:

The statement/observation, "that the starter motor used to crank diesel engines can draw up to 400 amps of current" made by Technician A is correct.

A diesel engine uses up to 400+ Amperes of electricity to start up a diesel engine in the ignition chamber of motor engine.

Answer: 5m/L^2

Explanation:

Inertial I = mr^2 where r = distance from axis of rotation, while m is the mass of the object.

I = 2[m(1L/2)^2] + 2[m(3L/2)^2] = 2m×. 25/L^2+ 3m×2. 25/L^2= 0. 5m/l^2 +4. 5m/l^2

= 5m/l^2.

Answer:

The Total Momentum before and after collision remains the same.

Explanation:

Note that the balls have the same masses.

A moving cue ball has an initial momentum. After every collision with another stationary ball, the momentum, which is the product of their mass and velocity, of the balls is conserved. This simply means that the total momentum before the collision is the same as the total momentum after the collision.

This also means that the energy must be conserved as well. The balls cannot fling away from each other with more energy than you give them.

Answer:

Total momentum is conserved before and after collusion and it's elastic.

Explanation:

For two colliding balls, the general vector equation for conservation of linear momentum is giving as

Ma*V1a = Ma*V2a + Mb*V2b

Where Ma=mass of que ball = Mb = mass of billiard ball so therefore

V1a= velocity of que ball before impact, V2a = velocity of que ball after impact, V2b = velocity of billiard ball after impact.

So therefore:

V1a = V2a + V2b

Answer:

Earth attract the Moon with a force that is greater.

Explanation:

According to the law of gravitation, the gravitational force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Mathematically, F1 = Gm1m2/r²... 1

Let m1 be the mass of the earth and m2 be that of the moon

If the Earth is much more massive than is the Moon, the new force of attraction between them will become;

F2= G(2m1)m2/r²

F2 = 2Gm1m2/r² ... (2)

Dividing eqn 1 by 2 we have;

F1/F2 = (Gm1m2/r²)÷(2Gm1m2/r²)

F1/F2 = Gm1m2/r²×r²/2Gm1m2

F1/F2 = 1/2

F2=2F1

This shows that that the earth will attract the moon by a force 2times the initial force of the masses(i.e a much greater force)

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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When a hammer drives a nail into a board, it does work on the nail, resulting in the hammer's mechanical energy being less after the impact due to the transfer of kinetic energy. The correct answer is C. Less, because the hammer has done work.

The question relates to mechanical energy and work in a physics context, specifically during the interaction between a hammer and a nail. When a hammer drives a nail into a board, it transfers some of its kinetic energy to the nail, doing work on the nail. As the kinetic energy is transferred from the hammer to the nail, the hammer's mechanical energy decreases. Therefore, the correct answer is C. Less, because the hammer has done work. This is due to an inelastic collision where some of the kinetic energy is not conserved in form of kinetic energy but could be converted into other forms such as thermal energy or energy needed to deform the nail and the wood.

Series Circuit.

There is only one path in which electrons can flow in a circuit.

Algebraic Formulas (for n number of components)

I = I1 = I2 = I3 =In

V= V1 + V2 + V3 + - - -  + Vn

Req = R1 + R2 + R3 + - - -  + Rn

Vn = I Rn                

Parallel Circuit.

There is more than one path in which electrons can flow in a circuit.

Algebraic Formulas

I = I1 + I2 + I3 = - - - - - +In

V= V1 = V2 = V3 + - - - - - = Vn  

1/Req = 1/R1 + 1/R2 + 1/R3 + - - - - - + 1/Rn

V = In Rn  

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:

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. 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:

Tension in the string will be 19.293 N

Explanation:

We have given length of the string r = 42.1 cm = 0.421 m

Mass of the stone m = 1000 gram

We know that 1000 gram = 1 kg

Velocity in the circular path v = 2.85 m/sec

We have to find the tension in the string

Tension in the string will be equal to centripetal force

So tension [tex]T=\frac{mv^2}{r}[/tex], here m is mass, v is velocity and r is length of the string

So tension in the string [tex]T=\frac{1\times 2.85^2}{0.421}=19.293N[/tex]

So tension in the string will be equal to 19.293 N

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:

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:

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.

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 : 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.

The object's weight on the other planet is determined by the force of gravity on that planet, which depends on the planet's mass and radius. The object's weight can be found by plugging these values into the formula for gravitational force, once the actual mass of the object is obtained by dividing its weight on Earth by the Earth's gravitational acceleration.

To find the weight of the object on the other planet, we need to calculate the gravitational pull on that planet. The force of gravity is given by the formula F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the centers of the two objects (which in this case is the radius of the planet).

On Earth, the object weighs 100 lbs. This is its mass times the gravity of Earth, which is roughly 9.8 m/s^2. So we can find the mass of the object by dividing the weight (100 lbs) by the acceleration due to gravity (9.8 m/s^2).

The planet in question is stated to have 3 times the Earth's radius and 5 times its mass. So we substitute these values into the formula along with the mass of the object we calculated, and solve for F, the force, which will be the weight of the object on the other planet.

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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.

Answer:

The Sun's temperature were doubled, it would give off 16X more energy.

Explanation:

The Stefan's law gives the relationship between total energy radiated per unit surface area of a black body and the temperature. It is given by :

[tex]j\propto T^4[/tex]

[tex]j=\sigma T^4[/tex]

[tex]\sigma[/tex] is the constant of proportionality called the Stefan–Boltzmann constant

T is temperature

So, the correct statement regarding Stefan's Law is that if the Sun's temperature were doubled, it would give off 16 X more energy. Hence, the correct option is (C).

Final answer:

Stefan's Law, or the Stefan-Boltzmann law, indicates the power output of a black body like the Sun would increase by a factor of 16 (C) if its temperature were to double, due to the relationship where energy flux is proportional to the fourth power of temperature. Hence, (C) is the correct option.

Explanation:

The correct answer to the statement 'Stefan's Law says' is that if the Sun's temperature were doubled, it would give off 16X more energy.

This relationship is known as the Stefan-Boltzmann law and states that the total energy flux (energy radiated per square meter) from a black body, such as a star, is proportional to the fourth power of its absolute temperature, as expressed in the formula [tex]F = \sigma\T4[/tex] (with sigma being the Stefan-Boltzmann constant).

Therefore, if the temperature of the Sun were to double from its current temperature (approximately 5800 K to 11600 K), its power output, or radiated energy, would increase by a factor of 24 or 16.

Answer :

I think it is A. Distance

Answer:

A. Distance

Explanation:

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

The ice in first container melts fastly because the container is made of material with low specific heat capacity. The material is a poor insulator.

The heat energy required to raise the temperature of a substance by one degree Celsius per one gram of that substance is called its specific heat capacity. It is an intensive property.

Less the specific heat, heat energy required by the material is less to increase the temperature. If a substance is having higher specific heat it requires more heat energy and it is a poor conductor.

To melt a substance heat energy is required to absorb by the substances to weaken the intermolecular forces. If the ice in container melts easily than the ice in other container, the material of the first container is made with material of less specific heat.

The material with less specific heat is a thermal conductor. Therefore, option A is correct.

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Answer:

-433 MJ of work

Explanation:

Given:

Displacement of the sailboat is, [tex]d=10.00\ km[/tex] towards north

Force applied by the wind is, [tex]F_w=5.00\times 10^4\ N[/tex]

Direction of the force is, [tex]\theta=30(Towards\ East\ of\ South)[/tex]

The vector diagram representing the given scenario is shown below.

We know that, work done by a force is the dot product of force and displacement and is given as:

[tex]W=F\cdot d=Fd\cos x[/tex]

Where, 'x' is the angle between the tails of the vectors 'F' and 'd'.

Now, from the figure below, we can find 'x'.

[tex]x=180-\theta=180-30=150[/tex]

Now, plug in all the given values and solve for 'W'.

[tex]W=(5.00\times 10^4\ N)(10.00\times 10^3\ m)(\cos 150)\\\\W=-433012702\ J =-433\ MJ[/tex]

Therefore, the work done by the wind is nearly 433 MJ. The negative sign implies that the force acts in the direction opposite to the displacement.