A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If a timer is started when its displacement is a maximum (hence x = 8 cm when t = 0), what is the displacement of the mass when t = 3.7 s?

The actual rotor speed of the motor is 1140 rpm, which is the answer given in option C.

The speed of a synchronous motor is given by the formula:

Ns = 120f / p

where:

Ns = synchronous speed of the motor in revolutions per minute (rpm)

f = frequency of the power supply in hertz (Hz)

p = number of poles of the motor

For a 6-pole motor supplied at 60 Hz, the synchronous speed is:

Ns = 120 * 60 / 6 = 1200 rpm

However, due to various losses, the actual speed of a motor is always less than the synchronous speed. The difference between the synchronous speed and the actual speed is known as the slip. The slip is usually expressed as a percentage of the synchronous speed.

The formula for calculating the actual rotor speed of a motor is:

Nr = (1 - s) * Ns

where:

Nr = actual rotor speed of the motor in rpm

s = slip of the motor as a fraction of the synchronous speed

Ns = synchronous speed of the motor in rpm

In this case, the slip is given as 5% of the synchronous speed. Therefore:

s = 0.05

Ns = 1200 rpm

Substituting these values in the formula for actual rotor speed, we get:

Nr = (1 - 0.05) * 1200 = 1140 rpm

Hence, the actual rotor speed of the motor is 1140 rpm, which is the answer given in option C.

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The rolling object and the surface it's rolling on also contribute to the decrease in velocity.

A rolling object travels slower the further away it gets from the base of the ramp. This is due to the conservation of energy, where the initial potential energy of the object at the top of the ramp is converted to both kinetic energy and potential energy as the object rolls down the ramp. As the object moves away from the base of the ramp, it gains height and therefore potential energy, causing a reduction in kinetic energy and thus a decrease in velocity. Additionally, frictional forces between the rolling object and the surface it's rolling on also contribute to the decrease in velocity.

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Yes, it would be possible to place a non-reflective coating on an airplane to cancel radar waves of wavelength 3 cm.

The process of canceling radar waves is called stealth technology. In stealth technology, materials with a low radar cross-section are used to make an object less visible to radar. This means that the object will not reflect radar waves and will therefore be less visible on radar screens.

To achieve stealth technology, a non-reflective coating is applied to the surface of the airplane. This coating is made up of a combination of materials that have the ability to absorb radar waves of the 3 cm wavelength. When the radar waves hit the surface of the coating, they are absorbed instead of being reflected back to the radar station.

In conclusion, placing a non-reflective coating on an airplane to cancel radar waves of wavelength 3 cm is possible through the use of stealth technology. This involves using materials with a low radar cross-section, a non-reflective coating, and designing the shape of the airplane to deflect radar waves away from the radar station.

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Linear speed of the tip of the minute hand of regular clock whose hand is 7.2 cm in length is : 1.25 x 10⁻⁴ m/s.

Minute hand of any regular clock completes one full revolution in 60 minutes ( 3600 seconds) and linear speed of the tip of minute hand can be calculated as follows:

Distance traveled by the tip of minute hand = Circumference of the circular path traced by tip of the minute hand

= 2πr, where r is length of the minute hand

Therefore, distance traveled by the tip of the minute hand = 2π(7.2 cm) = 45.12 cm

Time taken to travel this distance = Time taken for one revolution = 3600 seconds

Therefore, the linear speed of the tip of the minute hand = Distance traveled ÷ Time taken

= 45.12 cm ÷ 3600 seconds

= 0.01253333 cm/s

= 1.25 x 10⁻⁴ m/s.

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The average horsepower output of the engine is 46.74 hp.

Heat energy given by burning gasoline, Q = 46000 J/g = 46 x 10⁶ J/kg

Rate of fuel usage = 13 kg/h = 3.61 x 10⁻³ kg/s

Fuel efficiency, η = 21% = 0.21

Therefore, the average output of the engine,

P = Rate of fuel usage x Q x η

P = 3.61 x 10⁻³x 46 x 10⁶x 0.21

P = 34.9 x 10³ W

P = 34.9 x 10³/746

P = 46.74 hp

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No, the mechanical energy is not constant during the time the mass falls toward the Earth.

This is because as the mass falls, it loses potential energy due to the decrease in its height, and gains kinetic energy due to its increase in speed. This means that the total mechanical energy, which is the sum of the potential and kinetic energies, is conserved only if there is no external work done on the mass.

However, in reality, there are several factors that can cause the mechanical energy to change, such as air resistance, friction, and the deformation of the mass and the Earth's surface upon impact. Air resistance, for example, can cause the mechanical energy to decrease as some of the energy is dissipated as heat due to the resistance of the air. Friction and deformation can also cause the mechanical energy to decrease by converting some of the energy into other forms, such as heat or sound.

Therefore, the conservation of mechanical energy is an idealized concept that assumes an isolated system with no external work done on it. In reality, mechanical energy is often not conserved due to various factors that can cause energy to be converted into other forms.

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The cause of acoustic speckle is:c. interference of tiny acoustic wavelets.

Acoustic speckle occurs due to the interference of acoustic wavelets that scatter and reflect from different structures or interfaces within a medium. This interference creates constructive and destructive patterns that result in the speckled appearance of acoustic images. Refraction and attenuation can affect the propagation of acoustic waves, but they are not the primary cause of acoustic speckle. Similarly, the resonance of particles in the near field can lead to acoustic scattering, but it is not directly related to the formation of speckle patterns.

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Radioactive tritium (3H) labeled guanine is indeed used to measure the rate of biochemical processes that involve its binding or incorporation.

In this context, the best site for tritium labeling would be at the C8 position of the guanine molecule. This is because the C8 position is less likely to undergo exchange with the solvent (water) and maintains the integrity of the labeled guanine throughout the experiment. The best site for tritium labeling in this type of experiment would be the 8th position of the guanine molecule. This is because the 8th position is involved in biochemical processes such as base-pairing and is also solvent-accessible, allowing for efficient incorporation of the radioactive tritium.

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We can see that the angular acceleration of the object is given as 20 m/s^2. Option B

We have to know that the formula that we can use to obtain the angular acceleration in the case of the problem that we have here is;

a = -ω^2x

where a is the acceleration, ω is the angular frequency, and x is the displacement from the equilibrium position.

But we have to recall that we have;

ω= √(k/m)

We can now obtain the angular velocity as;

ω= √80/0.4

= 14.14 rad/s

Thus we have the angular acceleration as;

a = - (14.14)^2 * 0.1

a = - 20 m/s^2

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The total energy of the system  total energy , willincreases. Option A is correct.

The total energy of a simple harmonic motion system is equal to the sum of kinetic energy and potential energy. The kinetic energy is directly proportional to the mass of the object, while the potential energy is directly proportional to the square of the amplitude of the oscillation.
If the mass of the system is doubled while the amplitude remains the same, the potential energy of the system will remain unchanged. However, the kinetic energy of the system will increase by a factor of two due to the doubling of the mass.
Therefore, the total energy of the system will increase after the mass is doubled but the amplitude is not changed. This can be explained by the fact that the increased kinetic energy is more than enough to compensate for the unchanged potential energy.
In conclusion, the answer is (a) the total energy of the system will increase. It is important to note that this is true only if the amplitude is not changed. If the amplitude is changed as well, the result may be different.

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If 0.00259 kg of ice is melted, and the density of the mystery material is [tex]2500 kg/m^3[/tex].

To calculate the quantity of ice melted, we first need to determine the heat generated by the lead bullet. The heat generated can be calculated using the formula:
[tex]Q = 0.5 * m * v^2[/tex]
where Q is the heat generated, m is the mass of the bullet (0.003 kg), and v is its speed (240 m/s).
[tex]Q = 0.5 * 0.003 * (240^2) = 86.4 J[/tex]
Now, we can determine the mass of ice melted using the formula:
[tex]mass_ice = Q / (L_f * 4.186)[/tex]
where L_f is the latent heat of fusion (80 kcal/kg), and 4.186 is the conversion factor from kcal to J.
[tex]mass_ice = 86.4 / (80 * 4.186) = 0.00259 kg[/tex]
To find the density of the mystery material, use the formula:
density = mass / volume
First, find the volume of the block:
[tex]volume = length * width * height = 0.12 m * 0.11 m * 0.035 m = 0.000462 m^3[/tex]
Now, convert the mass of the mystery material to kg:
[tex]mass = 1155 g * (1 kg / 1000 g) = 1.155 kg[/tex]
Finally, calculate the density:
[tex]density = 1.155 kg / 0.000462 m^3 = 2500 kg/m^3[/tex]

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The man should stand 0.465 m away from the mirror to form an upright image of his chin that is twice the chin's actual size.

To form an upright image that is twice the chin's actual size using a concave shaving mirror, the man should stand at the focal point of the mirror. The mirror equation can be used to find the required distance:
1/f = 1/u + 1/v
where f is the focal length, u is the object distance, and v is the image distance.

Given that, u = -1.50 m and v = -0.184 m (inverted image is formed on the same side as the object). We can find the focal length:

1/f = 1/(-1.50) + 1/(-0.184)
1/f = -0.667 - 5.435
f = -0.155 m

Since he wants an upright image that is twice the chin's actual size, the magnification should be -2. The magnification formula is:

M = -v/u

So, -2 = -v/(-0.155) => v = 0.31 m

Now we can use the mirror equation again to find the new object distance (u'):

1/(-0.155) = 1/u' + 1/0.31
u' = 0.465 m

The man should stand 0.465 m away from the mirror to form an upright image of his chin that is twice the chin's actual size.

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The gun applies 100 N of force to the bullet. Force = mass x acceleration, where F = 0.01 x 10000 and N = 100. The gun applies 100 N of force to the bullet.

The pace at which a person's velocity changes is known as acceleration. acceleration (a) is the change in velocity over time. As a result, every change in velocity will result in acceleration whenever the speed or direction changes.

Most likely, you picture something racing up when you think about acceleration. But a moving thing accelerates as it slows down. A change in speed is what acceleration is, so keep that in mind. The speed of a car that would be slowing down decreases.

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If the Hubble constant has been constant since the Big Bang, the age of the universe would be between 14 billion and 28 billion years.

If we assume that the Hubble constant has been constant since the Big Bang, then we can use the Hubble time, which is the reciprocal of the Hubble constant, to estimate the age of the universe.

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Option (b.) 51°C

Explanation:
First, we need to calculate the amount of heat energy supplied to the water by the immersion heater using the formula:

Q = Pt

where Q is the heat energy (in joules), P is the power of the immersion heater (in watts), and t is the time (in seconds).

We need to convert 10 minutes to seconds:

t = 10 min x 60 s/min = 600 s

Now we can calculate Q:

Q = 800 W x 600 s = 480,000 J

Next, we can use the formula for specific heat capacity:

Q = mcΔT

where m is the mass of the water (in kilograms), c is the specific heat capacity of water (4,186 J/kg°C), and ΔT is the temperature increase (in °C).

We can rearrange this formula to solve for ΔT:

ΔT = Q / (mc)

Substituting the values we have:

ΔT = 480,000 J / (4.0 kg x 4,186 J/kg°C)

ΔT = 28.8°C

Therefore, the temperature increase of the water is 28.8°C.

But remember, the question asks for the temperature increase of the water, not the final temperature. So we need to add the initial temperature of the water to ΔT:

Initial temperature of the water is not given, but assuming it is 20°C (room temperature),

Temperature increase = 28.8°C + 20°C = 48.8°C ≈ 51°C

Therefore, the answer is b. 51°C.

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The angular velocity of the merry-go-round after the child gets onto it is 2.34 rad/s.

Before the child gets onto the merry-go-round, its angular momentum is given by:

L = Iω

where I is the moment of inertia and ω is the angular velocity. The moment of inertia of a solid disk is I = (1/2)M[tex]R^2[/tex], where M is the mass of the merry-go-round and R is the radius. Substituting the given values, we have:

I = (1/2)(120 kg)(1.80 m[tex])^2[/tex] = 194.4 kg·[tex]m^2[/tex]

The initial angular velocity is given as ω = 2πf = 2π(0.500 rev/s) = 3.14 rad/s.

When the child gets onto the merry-go-round, the system becomes a combination of the child and the merry-go-round, and the moment of inertia of the system changes. The new moment of inertia is:

I' = I + M[tex]R^2[/tex]

where M is the mass of the child. Substituting the given values, we have:

I' = (1/2)(120 kg)(1.80 m[tex])^2[/tex] + (22.0 kg)(1.80 m[tex])^2[/tex] = 259.2 kg·[tex]m^2[/tex]

The angular momentum of the system is conserved, so we have:

L = I'ω'

where ω' is the new angular velocity. Solving for ω', we get:

ω' = L/I' = (Iω)/I' = (I/I')ω

Substituting the given values, we have:

ω' = (194.4 kg·[tex]m^2[/tex]/259.2 kg·[tex]m^2[/tex])(3.14 rad/s) = 2.34 rad/s

Therefore, the angular velocity of the merry-go-round after the child gets onto it is 2.34 rad/s.

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Yes. originally Newton did not use the concept of acceleration or velocity in his laws, he used the terms instead cause it was already known.

Force(F) applied on the body is mass(m) times its acceleration(a). i.e. F=ma according to this equation we get acceleration as a = F/m this equation says that when we apply more force to the body, more acceleration it gets. When more is the mass of the body, greater force is needed to accelerate with same amount to that less mass.

when newton was sitting under the apple tree, an apple felled on his head where he got idea about law of gravitation.

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The tension in the string is 49 N, which is option 1.

When an object is suspended by a string, the tension in the string is equal to the weight of the object. The weight of the object can be calculated as follows:

Weight = mass x acceleration due to gravity

where mass is the mass of the object and acceleration due to gravity is the acceleration experienced by an object due to the Earth's gravitational force, which is approximately 9.8 m/s^2.

In this problem, the elevator is accelerating downwards at a rate of 2.6 m/s^2. Since the object is suspended by a string, its acceleration will also be 2.6 m/s^2 downwards, which means that the net acceleration of the object will be:

Net acceleration = acceleration due to gravity - acceleration of the elevator

Net acceleration = 9.8 m/s^2 - 2.6 m/s^2

Net acceleration = 7.2 m/s^2 downwards

Now we can calculate the weight of the object:

Weight = mass x acceleration due to gravity

Weight = 5.0 kg x 9.8 m/s^2

Weight = 49 N

Therefore, the tension in the string is 49 N, which is option 1.

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If a collapsing interstellar cloud formed only a protostar without an accretion disk around it.

When an interstellar cloud collapses under its own gravity, it can form a protostar. However, the protostar is often surrounded by a rotating disk of gas and dust called an accretion disk. This disk is important because it allows material to fall onto the protostar, increasing its mass and causing it to grow in size.

If a collapsing interstellar cloud formed only a protostar without an accretion disk around it, the protostar would not be able to accrete additional material as effectively. This would limit its growth and could result in a smaller final size than if it had an accretion disk.

Without an accretion disk, the protostar would also not be able to form planets or other objects in orbit around it. Planets form from the leftover material in the accretion disk that orbits the protostar. Without an accretion disk, there would be no material available to form planets.

Additionally, the lack of an accretion disk could affect the rotation of the protostar. The accretion disk is responsible for transferring angular momentum away from the protostar, allowing it to spin faster. Without an accretion disk, the protostar may not be able to shed its excess angular momentum, leading to slower rotation.

Hence, the formation of a protostar without an accretion disk would have a significant impact on the subsequent evolution of the system, limiting the growth of the protostar and preventing the formation of planets.

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The wheel passes through approximately 6.28 revolutions as it slows down.

We can use the equation for angular acceleration to solve this problem:

α = (ωf - ωi) / t

where:

α = angular acceleration

ωi = initial angular velocity = 45.0 rad/s

ωf = final angular velocity = 10.0 rad/s

t = time interval = 1.75 s

Substituting the values given:

α = (10.0 rad/s - 45.0 rad/s) / 1.75 s = -20.0 rad/s^2 (negative sign indicates deceleration)

Now we can use the equation for angular displacement to find the number of revolutions:

θ = ωi t + (1/2) α t^2

where:

θ = angular displacement

ωi = initial angular velocity = 45.0 rad/s

t = time interval = 1.75 s

α = angular acceleration = -20.0 rad/s^2

Substituting the values given:

θ = (45.0 rad/s)(1.75 s) + (1/2)(-20.0 rad/s^2)(1.75 s)^2

θ = 39.53 rad

To find the number of revolutions, we need to convert radians to revolutions:

1 revolution = 2π radians

So, the number of revolutions is:

θ / (2π) = 39.53 rad / (2π) = 6.28 revolutions

Therefore, the wheel passes through approximately 6.28 revolutions as it slows down.

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Not enough information is provided to compare the average force exerted by the table on the clay ball to that exerted on the superball, as the masses of the two balls and the velocities before and after the collision are not given.

When an object collides with a surface, the surface exerts an average force on the object during the time of contact.

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If the sun's core temperature suddenly increased, leading to an increase in nuclear fusion, the sun would expand, become more luminous, and potentially cause various effects on Earth due to the increased energy output.

If the core of the sun suddenly became hotter and the rate of nuclear fusion increased, the following would happen:

1. Increased nuclear fusion: As the core temperature rises, the rate of nuclear fusion reactions would increase, causing hydrogen atoms to combine into helium at a faster pace. This would release more energy in the form of light and heat.

2. Expansion of the sun: The increased energy output would cause the sun to expand as the additional pressure from the fusion reactions pushes against the sun's gravitational pull.

3. Increased luminosity: With more nuclear fusion occurring, the sun would become more luminous, emitting more light and heat into space.

4. Effects on Earth: The increase in solar energy output could lead to various effects on Earth, such as warmer temperatures, climate changes, and potential harm to ecosystems.

In summary, if the sun's core temperature suddenly increased, leading to an increase in nuclear fusion, the sun would expand, become more luminous, and potentially cause various effects on Earth due to the increased energy output.

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As you compress the air in a syringe by pushing the piston in slowly, the pressure will increase. The mathematical relationship between pressure (P) and volume (V) is given by Boyle's Law, which states that for a given amount of gas at a constant temperature, the product of pressure and volume remains constant.

Mathematically, this is represented as:

P1 * V1 = P2 * V2

where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. In this case, as the volume (V) decreases, the pressure (P) will increase proportionally, maintaining the constant product of pressure and volume.Therefore,As you compress the air in a syringe by pushing the piston in slowly, the pressure will increase.

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Before being caught by the policeman, the thief covers a distance of approximately 302.2 meters.

To solve this problem, we need to use the formula:

distance = speed x time

Let's first convert the speeds from km/hr to m/s:

Thief's speed = 6 km/hr = 6 x 1000 / 3600 m/s = 1.67 m/s
Policeman's speed = 8 km/hr = 8 x 1000 / 3600 m/s = 2.22 m/s

Now, let's assume that the thief is caught after time t seconds. During this time, the policeman runs a distance of 100 m + d, where d is the distance covered by the thief.

We can set up two equations using the formula above:

distance covered by thief = 1.67t
distance covered by policeman = 2.22t + 100

We want to find d, which is the distance covered by the thief before being caught. This means that the time it takes for the thief to be caught is the same as the time it takes for the policeman to catch him. Therefore, we can set the two equations equal to each other and solve for t:

1.67t = 2.22t + 100
0.55t = 100
t = 181.8 seconds

Now that we know the time it takes for the thief to be caught, we can plug it back into either equation to find d:

distance covered by thief = 1.67t
distance covered by thief = 1.67 x 181.8
distance covered by thief = 302.2 meters

Therefore, the thief covers a distance of 302.2 meters before being caught.

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Here is your Answer:

0.25 s

At 3R/2 location will have the greatest electric field strength. The correct option is (B).

The electric field is a physical quantity used to describe the influence that an electric charge exerts on other charges in its vicinity. An electric charge creates an electric field in the space around it, which can be represented as a vector field. The electric field at a point in space is defined as the force per unit charge that would be experienced by a hypothetical small positive test charge placed at that point, assuming that the other charges in the system are held constant.

Inside the metal sphere, the electric field is zero because the charges in the metal sphere will distribute themselves evenly on its surface, canceling out any electric field inside the sphere. So, option (A) 0 is not correct.

Outside the metal sphere, the electric field decreases as the distance from the center of the sphere increases. According to Coulomb's law, the electric field at a distance r from a point charge Q is proportional to Q/r^2. The positively charged metal sphere can be modeled as a point charge at its center, with a total charge of Q. So, the electric field strength at a distance r from the center of the sphere is proportional to Q/r^2.

For any distance r greater than the radius R of the sphere, the electric field strength can be calculated using Coulomb's law. The electric field strength will be greatest at the point closest to the surface of the sphere, which corresponds to option (B) 3R/2. At this distance, the electric field strength will be proportional to Q/(3R/2)^2 = 4Q/9R^2.

Option (C) 5R/4 and option (D) 2R are both farther away from the surface of the sphere than option (B), so the electric field strength will be lower at those distances. Option (E) is not correct because the electric field strength decreases as the distance from the center of the sphere increases, and is not constant.

Therefore, The correct option is (B) 3R/2.

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The full moon phase is when the Moon is completely illuminated by sunlight, meaning 100% of its surface is lit up.

Sunlight is the direct light from the sun that is visible to the human eye. It is made up of ultraviolet, visible, and infrared light and is essential for the survival of living things. Sunlight helps organisms to produce food through photosynthesis and also helps to regulate the sleep/wake cycle in humans. Sunlight is an important source of vitamin D, which is essential for healthy bones and tissues. Sunlight also helps to regulate the Earth's temperature and weather patterns. Sunlight is an important part of the Earth's energy balance and is necessary for the health of all living things. Without sunlight, life on Earth would not be possible. Sunlight has been used by humans for centuries for warmth and to help with the growth of crops. Sunlight is a renewable energy source that can be used to generate electricity through solar panels and can also be used to heat water.

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The magnitude of the momentum of the dog in terms of the momentum of the cat is given by [tex]\sqrt(2)p_c.[/tex]

If two objects have the same kinetic energy, their momenta will be different if their masses are different. The momentum p of an object is given by:

p = mv

where m is the mass of the object and v is its velocity.

If the kinetic energy of the dog is the same as the kinetic energy of the cat, we can write:

[tex](1/2)mv_d^2 = (1/2)mv_c^2[/tex]

where m is the mass of the object (either the dog or the cat), and v_d and v_c are their respective velocities.

We are given that the mass of the dog is twice the mass of the cat:

[tex]m_d = 2m_c[/tex]

Substituting this into the equation for the kinetic energy and solving for the velocity of the dog in terms of the velocity of the cat, we get:

[tex](1/2)(2m_c)v_d^2 = (1/2)m_cv_c^2[/tex]

[tex]v_d^2 = v_c^2/2[/tex]

[tex]v_d = \sqrt(v_c^2/2) = v_c/\sqrt(2[/tex])

Now we can calculate the momentum of the dog in terms of the momentum of the cat:

[tex]p_d = m_dv_d = 2m_cv_c/\sqrt(2) = \sqrt(2)pm_c[/tex]

Therefore, the magnitude of the momentum of the dog in terms of the momentum of the cat is given by[tex]\sqrt(2)p_c.[/tex]

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To find the linear acceleration of a point on the edge of a 0.010 m radius drill bit rotating with a constant angular velocity of 5.0 rev/s, we will follow these steps:

1. Convert the angular velocity from rev/s to rad/s.
2. Use the centripetal acceleration formula: a = rω².

Step 1: Convert the angular velocity from rev/s to rad/s.
Angular velocity (ω) = 5.0 rev/s
1 revolution = 2π radians
ω = 5.0 × 2π rad/s ≈ 31.42 rad/s

Step 2: Use the centripetal acceleration formula.
a = rω²
a = (0.010 m) × (31.42 rad/s)²
a ≈ 9.82 m/s²

The linear acceleration of a point on the edge of the 0.010 m radius drill bit rotating with a constant angular velocity of 5.0 rev/s is approximately 9.82 m/s².

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The induced emf in the coil would be twice as much if the change in magnetic field were to happen in half the time.

According to Faraday's law of electromagnetic induction, the magnitude of the induced electromotive force (emf) in a coil is directly proportional to the rate of change of magnetic flux through the coil. Mathematically, this can be expressed as:

emf = -N dΦ/dt

where emf is the induced electromotive force, N is the number of turns in the coil, and dΦ/dt is the rate of change of magnetic flux through the coil.

Assuming that the coil is stationary, the change in magnetic field would induce an emf in the coil according to the above equation. If the magnetic field doubles in a time t, then the rate of change of magnetic flux would be:

dΦ/dt = Bf - Bi / t

where Bf is the final magnetic field, Bi is the initial magnetic field, and t is the time taken for the magnetic field to double.

If the same change in magnetic field were to happen in half the time (t/2), then the rate of change of magnetic flux would be:

dΦ/dt = Bf - Bi / (t/2)

= 2(Bf - Bi) / t

= 2dΦ/dt

Therefore, the induced emf in the coil would be twice as much if the change in magnetic field were to happen in half the time.

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