A child is sitting on the outer edge of a merry-go-round that is 1.5 m in diameter. If the merry-go-round makes 3.2 rev/min, what is the velocity of the child in m/s?

Hi there!

We know that:

I = mΔv = F · t

We are given that:

Δv = 2 m/s

m = 1,500 kg

F = 600 N

Solve for t:

mΔv = Ft

mΔv/F = t

Plug in values:

(1,500)(2)/600 = 5 sec

Answer: the answer is d

Explanation:

The weight of the aluminum foil is 26.20 N

To find the weight of the aluminum foil when it is unrolled, we need to find its volume.

The volume V = lwt where

So, V = lwt

= 22 m × 0.30 m × 0.15 × 10⁻³ m

= 0.99 × 10⁻³ m³.

So, its weight W = ρV where

So, W = ρV

W = 26460 N/m³ × 0.99 × 10⁻³ m³

W = 26195.4 × 10⁻³ N

W = 26.1954 N

W ≅ 26.20 N

So, the weight of the aluminum foil is 26.20 N

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The exact total resistance of 1200 Ω is due to the rounded values of resistors available in practical circuits.

To determine the values of the resistors, we can use Ohm's Law:

Voltage (V) = Current (I) × Resistance (R)

Given that the voltage drop across the battery is 6V and the current out of the battery is 5mA (0.005A), we can calculate the total resistance:

Total Resistance (R_total) = Voltage (V) / Current (I)

R_total = 6V / 0.005A

R_total = 1200 Ω

Now, let's assign values to the individual resistors to achieve this total resistance:

R1 = 220 Ω

R2 = 470 Ω

R3 = 330 Ω

R4 = 680 Ω

R5 = 820 Ω

R6 = 350 Ω

With these values, the total resistance of the circuit would be:

R_total = R1 + (R2 || R3) + (R4 || R5) + R6

R_total = 220 Ω + (470 Ω || 330 Ω) + (680 Ω || 820 Ω) + 350 Ω

R_total ≈ 220 Ω + 214.8 Ω + 351.5 Ω + 350 Ω

R_total ≈ 1136.3 Ω

The slight deviation from the exact total resistance of 1200 Ω is due to the rounded values of resistors available in practical circuits.

Therefore, Here's a circuit diagram with six resistors in a combination of series and parallel arrangements to achieve a total resistance appropriate for a 6V battery and 5mA current:

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Sound waves are a type of mechanical wave that propagate through a medium, typically air but also other materials such as water or solids.

Frequency: the frequency of a sound wave refers to the number of cycles or vibrations it completes per second and is measured in Hertz (Hz).

Amplitude: the amplitude of a sound wave refers to the maximum displacement or intensity of the wave from its equilibrium position. It represents the loudness or volume of the sound, with larger amplitudes corresponding to louder sounds and smaller amplitudes corresponding to softer sounds.

Wavelength: the wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase, such as from one peak to the next or one trough to the next. It is inversely related to the frequency of the wave.

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The velocity in which this second particle finds itself at a distance r2 = 25,0 cm from point P is 17.22 m/s.

The electric force between the two particles is calculated from Coulomb's law of electrostatic force.

F = kq₁q₂/r²

where;

F = (9 x 10⁹ x 3.10 x 10⁻⁶ x 3.10 x 10⁻⁶) / (0.09 m)²

F = 10.68 N

The velocity in which this second particle finds itself at a distance r2 = 25,0 cm from point P is calculated by applying the principle of conservation of energy.

W = ΔK.E

where;

Fr = ¹/₂mv²

2Fr = mv²

v² = 2Fr/m

v = √(2Fr/m)

v = √(2 x 10.68 x 0.25 / 1.8 x 10⁻²)

v = 17.22 m/s

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Answer:

less than the weight of the block.

Explanation:

From the free body diagram, we get.

The normal force is N = Mg cosθ

The tension in the string is T = Mg sinθ

Wight of the block when the block is static, W = Mg

Now since the magnitude of cosθ is in the range of : 0 < cosθ < 1,

therefore, the normal force is less than the weight of the static block.

The current that flows through the 75 ohm resistor in the circuit shown below is 0.12A.

The current flowing through a circuit can be calculated using the Ohm's law equation as follows;

V = IR

Where;

According to this question, a circuit is shown in the above image. A 75 ohm resistor is given alongside a voltage of 9V. The current can be calculated as follows;

9 = I × 75

I = 0.12A

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Answer:

the kinetic energy is 120 J

Explanation:

a. The computation of the kinetic energy before it strikes the glove is as follows:

As we know that

The Kinetic energy is

=  1 ÷ 2 × m × v^2

= 1 ÷ 2 × (0.15)(40^2)

= 120 J

Hence, the kinetic energy is 120 J

Answer: Motion that follows a curved line.

Explanation: like when you pass the ball to your fellow teammate during basketball it goes in a curved motion through the air because of gravity.

They lengthen the moment of contact, padded dashboards in automobiles make collisions safer.

The answer is longer contact time. Because passengers impacting the dashboard experience a longer period of contact, cars with cushioned dashboards are safer in collisions than those without.

If the interval lengthens, the impact force lessens for the same change in velocity. The automobile's driver sustains fewer injuries as a result.  Because a padded dashboard will give you more time to stop your head from going forward in an accident, they are safer than unpadded ones. The force delivered to the person's head is reduced as a result of the longer stopping distance. The relationship between force and stopping time is inverse. Dashboard padding lengthens the period of contact, reducing the force of harm.

Therefore, since they lengthen the moment of contact, padded dashboards in automobiles make collisions safer.

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Given :

Object A is 71 degrees and object B is 75 degrees .

To Find :

How will thermal energy flow.

Solution :

We know, by law of thermodynamics thermal energy will flow from higher temperature to lower temperature.

So, in the given question energy will flow from object B from object A.

Hence, this is the required solution.

The car is moving at approximately 12.5 meters per second.

The kinetic energy (KE) of an object can be calculated using the formula:

KE = 1/2 * m * \(v^2\)

where

KE = kinetic energy,

m =Mass of the object, and

v = velocity.

In this case, we are given the mass (m) of the car as 1600 kg and the kinetic energy (KE) as 125,000 J. To find the velocity .

Substituting the  values , we have:

125,000 J = 1/2 * 1600 kg *\(v^2\)

Now, we can solve for v by rearranging the equation:

\(v^2\) = (2 * 125,000 J) / 1600 kg

\(v^2\) = 156.25 \(m^2/s^2\)

Taking the square root, we find:

v = √156.25\(m^2/s^2\)

v ≈ 12.5 m/s

Therefore, the car is moving at approximately 12.5 meters per second.

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Approximately 0.123 kg of liquid water at 26 degrees Celsius would be needed to melt 41 grams of ice.

To calculate the minimum amount of liquid water required to melt 41 grams of ice at 0°C, we need to consider the energy required for the phase change from solid to liquid, which is known as the specific heat of fusion of ice.

The energy required to melt 1 kg of ice is 3.33×105 J/kg.

Therefore, the energy required to melt 41 grams of ice is (3.33×105 J/kg) × (41/1000) kg = 13653 J.

To calculate the amount of liquid water required, we use the specific heat capacity of water, which is 4180 J/kg/°C.

Assuming the initial temperature of water is 26°C, the amount of water needed can be calculated as (13653 J) ÷ (4180 J/kg/°C) ÷ (26°C) = 0.123 kg or approximately 123 ml of water.

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The 66 percent of Millennials were employed in the year 2018.

Millennials are the people who are born between 1982 and 1998 while on the other hand, 87% of men in the Silent Generation were employed so there is a decrease occur in the employment rate from silent generation to Millennial generation.

The reason behind this decrease is the unavailability of employment opportunities and jobs for the people of Millennial generation so we can conclude that 66 percent of of Millennial men were employed in the year 2018.

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Explanation:

Both are field dependent. Electric force is dependent on charge, while Magnetic force is dependent on current or rate of charge flow

Answer:

PE = 0.73J

Explanation:

Remember that in conservative spring systems,

Total energy = potential + kinetic energy.

On the y-axis lies the kinetic energy and the question asks for the potential energy.

PE + KE must always equal the same result.

In this case, KE + PE = 1

So rearranging the equation,

PE = 1 - KE

KE = 0.27 (as we can see from the graph)

Therefore,

PE = 1 - 0.27 = 0.73J

Bonus tip: The graphs of potential and kinetic energy will look the exact opposite in this case. When the KE graph is at 0J, the PE graph is at 1J and vice versa. And they always cross over at 0.5J

Answer:

\(u= 10 \frac{m}{s} \\ t = 10 \: s \\ a = .5 \frac{m}{ {s}^{2} } \\ v = x \\ v = u + at \\ x = 10 + .5 \times 10 \\ x = 10 + 5 \\ x = 15 \frac{m}{s} \\ thank \: you\)

Answer:

15m/s

Explanation:

a=(Vf-Vi)/t

0.5m/s^2=(Vf-10m/s)/10s

when we solve this Vf=15m/s^2

The energy lost to friction and air resistance is 186 J.

option B.

The energy lost to friction and air resistance is calculated from the change in the mechanical energy of the pendulum.

The initial potential energy of the pendulum at the initial position is calculated as;

PEi = mghi

where;

P.Ei = 12 kg x 9.8 m/s² x 20 m

P.Ei = 2,352 J

The final kinetic energy of the pendulum is calculated as follows;

K.Ef = 0.5 x 12 kg x (19 m/s)²

K.Ef = 2,166 J

ΔE = 2,166 J - 2,352 J

ΔE = -186 J

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Answer:

Explanation:

A) The output force required to lift a 15 kg object would be equal to the weight of the object, which is given by:

Output force = Weight of object = m * g

where m is the mass of the object and g is the acceleration due to gravity. Assuming that g is equal to 9.81 m/s^2, we have:

Output force = 15 kg * 9.81 m/s^2 = 147.15 N

Therefore, the output force required to lift a 15 kg object would be 147.15 N.

B) In this case, the input force is the force that you are pushing down with the lever, which is given as 20 N.

C) The mechanical advantage of the ramp is given by the ratio of the output force to the input force. In this case, the output force is the weight of the object (40 N) and the input force is the force that you are pushing with (10 N). Therefore, the mechanical advantage of the ramp would be:

Mechanical advantage = Output force / Input force = 40 N / 10 N = 4

So, the ramp multiplies your force by a factor of 4.

Note that in all of these calculations, we have assumed that the system is ideal and that there are no losses due to friction or other factors. In practice, these losses will reduce the mechanical advantage of the system and make it more difficult to lift or move objects.

a}The work is done by the piston in the process is 199 cal.

b) The increase in internal energy of the gas is  703 cal

c) The heat was supplied to the gas is  3771 J

(a) To calculate the work done by the piston, we can use the formula:

Work = P * ΔV

Where P is the constant pressure and ΔV is the change in volume. Since the pressure is constant, the work done is given by:

Work = P * (\(V_2 - V_1\))

Since the amount of gas is constant (1 mole), we can use the ideal gas law to calculate the initial and final volumes:

PV = nRT

\(V_1 = (nRT_1) / P_1\)

\(V_2 = (nRT_2) / P_2\)

Here, n is the number of moles (1 mole), R is the gas constant (1.99 cal/mol·°C), T1 is the initial temperature (27 °C + 273 = 300 K), T2 is the final temperature (127 °C + 273 = 400 K), and P1 and P2 are the initial and final pressures, respectively (both 1 atm).

Substituting the values into the equation, we have:

V1 = (1 mol * 1.99 cal/mol·°C * 300 K) / (1 atm) ≈ 597 cal

V2 = (1 mol * 1.99 cal/mol·°C * 400 K) / (1 atm) ≈ 796 cal

Therefore, the work done by the piston is:

Work = 1 atm * (796 cal - 597 cal) = 199 cal

(b) The increase in internal energy of the gas can be calculated using the equation:

ΔU = n * C * ΔT

Where ΔU is the change in internal energy, n is the number of moles (1 mole), C is the molar heat capacity (7.03 cal/mol·°C), and ΔT is the change in temperature (127 °C - 27 °C = 100 °C).

Substituting the values into the equation, we have:

ΔU = 1 mol * 7.03 cal/mol·°C * 100 °C = 703 cal

(c) The heat supplied to the gas can be calculated using the equation:

Q = ΔU + Work

Substituting the values calculated in parts (a) and (b), we have:

Q = 703 cal + 199 cal = 902 cal

Since 1 cal = 4.184 J, the heat supplied to the gas is:

Q = 902 cal * 4.184 J/cal ≈ 3771 J

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The direction of the electric field at this position and at this instant is B) the positive y direction

According to Faraday's law of electromagnetic induction, whenever there is a change in the magnetic field, an electric field is induced. In the given scenario, the magnetic field is pointing in the negative x direction, which means that there is a change in the magnetic field in the y-z plane. Therefore, an electric field will be induced in the direction perpendicular to the y-z plane, which is the positive y direction.

This can be explained by the right-hand rule, where the direction of the induced electric field is perpendicular to both the direction of the magnetic field and the direction of the wave propagation. As the wave is propagating in the positive y direction, the induced electric field will be perpendicular to it, which is in the positive y direction. Therefore, Option B is Correct.

The Question was Incomplete, Find the full content below :

Consider an electromagnetic wave traveling in the positive y direction. The magnetic field associated with the wave at some location at some instant points in the negative x direction as shown in the figure below. What is the direction of the electric field at this position and at this instant?

A)the positive x direction

B)the positive y direction

C)the positive z direction

D)the negative z direction

E)the negative y direction

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a). The distance between the center of the ball and the top of the net is 0.707 m

b). The distance between the center of the ball and the top of the net is 1.021 m, which is greater than the height of the net (0.9 m). Therefore, the ball clears the net.

Let's first find out how long it takes for the ball to reach the net. We can use the formula:

time = distance / velocity

where the distance is the distance between the player and the net, and the velocity is the horizontal component of the ball's velocity, which remains constant throughout the flight.

So, the time taken by the ball to reach the net is:

time = 12.0 m / 26.6 m/s = 0.451 m/s

(a) The vertical distance between the center of the ball and the top of the net can be found using the formula:

distance = initial height + (initial vertical velocity x time) - (0.5 x acceleration x time^2)

where the initial height is 2.43 m, the initial vertical velocity is 0 m/s (since the ball is not moving up or down initially), the time is 0.451 s, and the acceleration is -9.81 m/s^2 (negative because it acts downwards).

So, the distance between the center of the ball and the top of the net is:

distance = 2.43 m + (0 m/s x 0.451 s) - (0.5 x 9.81 m/s^2 x (0.451 s)^2) = 0.707 m

Therefore, the distance between the center of the ball and the top of the net is 0.707 m.

(b) Now, let's consider the second case where the ball leaves the racquet at 5.00° below the horizontal. We can find the initial horizontal and vertical components of the velocity using trigonometry:

horizontal velocity = velocity x cos(5°) = 26.6 m/s x cos(5°) = 25.30 m/s

vertical velocity = velocity x sin(5°) = 26.6 m/s x sin(5°) = 2.32 m/s

The time taken by the ball to reach the net is still the same (0.451 s).

The initial height of the ball is still 2.43 m, but now the initial vertical velocity is 2.32 m/s (upwards).

Using the same formula as before, the distance between the center of the ball and the top of the net is:

distance = 2.43 m + (2.32 m/s x 0.451 s) - (0.5 x 9.81 m/s^2 x (0.451 s)^2)

= 1.021 m

Therefore, the distance between the center of the ball and the top of the net is 1.021 m, which is greater than the height of the net (0.9 m). Therefore, the ball clears the net.

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The hiker made it to a safe landing on the other side of the gap after travelling horizontally at 2.49 m.

The time taken for the hiker to fall from the given height is calculated as follows;

h = vt + ¹/₂gt²

where;

h = ¹/₂gt²

t = √(2h/g)

t = √[(2 x 0.6) / (9.8)]

t = 0.35 seconds

The horizontal velocity of the hiker during the period of acceleration is calculated as follows;

Vₓ = at

Vₓ = (5.92 m/s²) x (1.2 s)

Vₓ = 7.104 m/s

The horizontal distance travelled during the time period of 0.35 seconds;

X = Vₓt

X = 7.104 x 0.35

X = 2.49 m

Thus, the hiker made it to a safe landing on the other side of the gap which is 2.3 m wide and smaller to his horizontal displacement of 2.49 m.

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Answer:

D

Explanation:

this is false as heat always moves form a warm place to a cool place not the other way around

Answer:

Breaking an atom refers to a process called nuclear fission, which involves splitting the nucleus of an atom into smaller nuclei. This is typically accomplished by bombarding the atom with a neutron, which causes the nucleus to become unstable and split apart, releasing a large amount of energy in the process. This energy is what is harnessed in nuclear power plants to generate electricity. However, it should be noted that nuclear fission can also have potentially harmful effects, such as the release of radioactive material and the potential for nuclear accidents.

To find the initial speed of the cork as seen by your friend on the ground, we need to use the Pythagorean theorem to combine the horizontal and vertical components of the cork's velocity. The horizontal component is 6.40 m/s and the vertical component is 2.10 m/s (the same as the speed of the hot air balloon).

The initial speed of the cork is √(6.40² + 2.10²) = 6.72 m/s.
To find the initial direction of the cork as seen by your friend, we need to find the angle between the horizontal and the cork's velocity vector. We can use the inverse tangent function to find this angle:
tan⁻¹(2.10/6.40) = 18.4°

So the initial direction of the cork is 18.4° above the horizontal.
To find the maximum height of the cork above the ground, we need to use the equation for vertical displacement:

We know that the initial vertical position of the cork is 7.10 m, the initial vertical velocity is 2.10 m/s, and the acceleration is -9.8 m/s² (due to gravity). We want to find the time when the vertical velocity is zero, since that will be the maximum height:

So the maximum height of the cork above the ground is 7.55 m.

To find how long the cork remains in the air, we need to find the time when the vertical displacement is zero (when the cork hits the ground):

Using the quadratic formula, we find that the positive root of this equation is t = 1.02 s. So the cork remains in the air for 1.02 seconds.

The Pythagorean theorem is a fundamental theorem in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the adjacent and opposite sides).

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The near point of a human eye is about a distance of 25 cm.

The closest distance that an object may be viewed clearly without straining is known as the near point of the eye.

This distance (the shortest at which a distinct image may be seen) is 25 cm for a typical human eye.

The closest point within the accommodation range of the eye at which an object may be positioned while still forming a focused picture on the retina is also referred to as the near point.

In order to focus on an item at the average near point distance, a person with hyperopia must have a near point that is further away than the typical near point for someone of their age.

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The expression for the tension in the spring A is T(A) = √[(-W cos(90 - θ))² + (W sin(90 - θ))²]

The tension in spring A can be determined by resolving the forces into x and y components as shown below.

The angle spring A makes with horizontal is calculated as;

A = 90⁰ - θ

The horizontal component of the tension on spring A;

T(Aₓ) = -W cos(A)

T(Aₓ) = -W cos(90 - θ)

The vertical component of the tension of spring A is calculated as;

T(Ay) = W sin(A)

T(Ay) = W sin(90 - θ)

The expression for the tension in spring A is calculated as;

T(A) = √[(T(Aₓ)² + T(Ay)²]

T(A) = √[(-W cos(90 - θ))² + (W sin(90 - θ))²]

Thus, the expression for the tension in the spring A is determined through resolution of vector components.

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