an 11.0-w energy-efficient fluorescent lightbulb is designed to produce the same illumination as a conventional 40.0-w incandescent lightbulb. assuming a cost of $0.112/kwh for energy from the electric company, how much money does the user of the energy-efficient bulb save during 115 h of use? (give your answer to the nearest cent.)

Answer:

The half-life of a radioactive substance is the time it takes for half of the original sample to decay. We can use the information given to calculate the half-life of nitrogen-16 as follows:

Let t1/2 be the half-life of nitrogen-16.

At t=0 (initial time), the sample has a mass of 100.0 g.

After one half-life (t=t1/2), the sample will have decayed to 50.0 g.

After two half-lives (t=2t1/2), the sample will have decayed to 25.0 g.

After three half-lives (t=3t1/2), the sample will have decayed to 12.5 g.

We know that the sample decays from 100.0 g to 12.5 g in 21.6 seconds, which is equivalent to 3 half-lives (t=3t1/2). Therefore, we can write the following equation:

12.5 g = 100.0 g * (1/2)^(3)

Simplifying, we get:

(1/2)^3 = 12.5 g / 100.0 g

(1/2)^3 = 0.125

Taking the logarithm of both sides (to base 2, since we are dealing with half-lives), we get:

log2(1/2)^3 = log2(0.125)

-3*log2(1/2) = -3

3 = 3*t1/2/21.6

Simplifying, we get:

t1/2 = (3 * 21.6) / 3 = 21.6 seconds

Therefore, the half-life of nitrogen-16 is 21.6 seconds.

Explanation:

The wave speed of the musical tone sounded on a piano with a frequency of 410 hz and a wavelength in the air of 0.800 is 328 m/s. Option C

To determine the wave speed of a musical tone sounded on a piano with a frequency of 410 hz and a wavelength in the air of 0.800, we need to use the formula v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength.
Plugging in the values given, we get:
v = (410 hz) x (0.800 m)
v = 328 m/s
Therefore, the wave speed of the musical tone sounded on a piano with a frequency of 410 hz and a wavelength in the air of 0.800 is 328 m/s.
This means that the sound waves produced by the piano are traveling through the air at a speed of 328 meters per second. It is important to note that the wave speed is dependent on the medium through which the waves are traveling. For example, sound waves travel faster through denser mediums like water and solids than through air.        

In conclusion, the formula v = fλ can be used to calculate the wave speed of any sound wave, and understanding the relationship between frequency, wavelength, and wave speed is important in the study of acoustics and sound engineering. Option C is correct.

For more such questions on frequency  visit:

https://brainly.com/question/254161

#SPJ11

a) The magnitude of the change in momentum is 4.05 kg m/s.

b) The direction of the change in momentum of the bullet is opposite to its initial direction since the bullet bounces back after hitting the wall.

a) To find the magnitude of the change in momentum of the 15.0 g rubber bullet, we first need to calculate its initial and final momentum.

Initial momentum (p_initial) = mass x initial velocity
p_initial = 0.015 kg x 150 m/s (Note: mass is converted to kg)
p_initial = 2.25 kg m/s

Final momentum (p_final) = mass x final velocity
p_final = 0.015 kg x (-120 m/s) (Note: negative sign because the bullet bounces back)
p_final = -1.80 kg m/s

Now, we can find the magnitude of the change in momentum:

Δp = p_final - p_initial
Δp = -1.80 kg m/s - 2.25 kg m/s
Δp = -4.05 kg m/s

The magnitude of the change in momentum is 4.05 kg m/s.

b) The direction of the change in momentum of the bullet is opposite to its initial direction since the bullet bounces back after hitting the wall. If we consider the initial direction as positive, then the direction of the change in momentum would be negative.

Learn more about "momentum": https://brainly.com/question/1042017

#SPJ11

a. The average speed of the Moon is about 1,013.26 meters per second.

b. The Moon's acceleration is approximately 0.0004 meters per second squared, directed towards the center of the Earth.

To find the average speed of the Moon, we can use the formula:

average speed = distance traveled / time taken

In this case, the distance traveled by the Moon is the circumference of its orbit around the Earth, which is given by:

2πr = 2π(3.8×10⁸ m) = 2.39×10⁹ m

The time taken for one complete orbit is 27.3 days, or 2,358,720 seconds.

Therefore, the average speed of the Moon is:

average speed = distance traveled / time taken

= (2.39×10⁹ m) / (2,358,720 s)

= 1,013.26 m/s

To find the acceleration of the Moon, we can use the formula:

acceleration = change in velocity / time taken

The Moon's velocity is constantly changing as it orbits the Earth, but its average velocity over one orbit is equal to its average speed, which we calculated in part (a).

The time taken for one orbit is also known, and is equal to 27.3 days, or 2,358,720 seconds.

Therefore, the change in velocity over one orbit is:

change in velocity

= (average speed at end of orbit) - (average speed at beginning of orbit)

= 0 - 1,013.26 m/s

= -1,013.26 m/s

The negative sign because the Moon's velocity is decreasing as it moves towards the Earth during this time period.

Thus, the acceleration of the Moon is:

acceleration = change in velocity / time taken

= (-1,013.26 m/s) / (2,358,720 s) = -0.00043 m/s²

This acceleration is directed towards the center of the Earth, and is responsible for keeping the Moon in its orbit.

To know more on average speed

https://brainly.com/question/9834403

#SPJ4

A red giant of spectral type K9 and a red main sequence star of the same spectral type have the same "Luminosity". Option A is answer.

A red giant of spectral type K9 and a red main sequence star of the same spectral type have the same luminosity. Spectral type is a classification system that is based on the temperature and surface features of a star, and not directly related to its size or luminosity. Therefore, two stars of the same spectral type, whether they are a red giant or a red main sequence star, will have the same luminosity, meaning they emit the same amount of energy per unit of time.

However, the red giant will have a larger size and lower surface temperature compared to the red main sequence star.

Option A is answer.

You can learn more about spectral type at

https://brainly.com/question/30199520

#SPJ11

At the center of the diffraction pattern of a circular aperture, you will find a bright spot called the central maximum.

This is due to the constructive interference of light waves passing through the aperture. Surrounding the central maximum are alternating dark and bright rings, known as Airy pattern or Airy disk, which are a result of destructive and constructive interference, respectively. This central spot is surrounded by a series of concentric rings of alternating bright and dark fringes called the diffraction rings. The central spot is the result of light passing through the center of the circular aperture, where the diffraction effects are minimal.

The size of the central spot depends on the size of the circular aperture, the wavelength of the light, and the distance between the aperture and the screen where the diffraction pattern is observed. For a small circular aperture, the central spot will be relatively large, while for a larger aperture, the central spot will be smaller and more sharply defined. In general, the central spot is the brightest and most intense part of the diffraction pattern, and it contains the most energy.

To know more about diffraction pattern, please click on:

https://brainly.com/question/12290582

#SPJ11

To solve this problem, we need to use the principle of conservation of energy. The heat lost by the copper piece is equal to the heat gained by the water and the aluminum calorimeter.

First, let's calculate the heat lost by the copper piece:

Q = mCΔT

Q = (80.0 g)(0.0920 cal/g°C)(295°C - T)

Where T is the final temperature of the system.

Next, let's calculate the heat gained by the water and the calorimeter:

Q = (mwater + maluminum + mcopper) cw ΔT

Q = (250 g + 300 g + 80.0 g)(1.00 cal/g°C)(T - 10.0°C)

Where cw is the specific heat of water, and ΔT is the change in temperature.

Since the heat lost by the copper piece is equal to the heat gained by the water and the calorimeter, we can set the two equations equal to each other and solve for T:

(80.0 g)(0.0920 cal/g°C)(295°C - T) = (250 g + 300 g + 80.0 g)(1.00 cal/g°C)(T - 10.0°C)

Simplifying and solving for T, we get:

T = 16.5°C

Therefore, the final temperature of the system is 16.5°C. The answer is option (b).

Learn more about conservation of energy here:

https://brainly.com/question/2137260

#SPJ11

To calculate the height of the atmosphere needed to produce an atmospheric pressure of 1.0 × 10^5 N/m² with a constant air density of 1.29 kg/m³, we can use the following equation:

Pressure = density × gravity × height

Here, we are given the atmospheric pressure (1.0 × 10^5 N/m²) and the air density (1.29 kg/m³). We will also use the standard acceleration due to gravity (approximately 9.81 m/s²).

To find the height, we will rearrange the equation:

Height = Pressure / (density × gravity)

Now, plug in the values:

Height = (1.0 × 10^5 N/m²) / (1.29 kg/m³ × 9.81 m/s²)

Height ≈ 7,986.9 m

Therefore, the height of the atmosphere needed to produce this pressure is approximately 7,987 meters.

To know more about air density:

https://brainly.com/question/3551743

#SPJ11

The height of the atmosphere needed to produce this pressure is approximately 7,987 meters.

To calculate the height of the atmosphere needed to produce an atmospheric pressure of 1.0 ×[tex]10^5[/tex]N/m² with a constant air density of 1.29 kg/m³, we can use the following equation:

Pressure = density × gravity × height

Here, we are given the atmospheric pressure (1.0 × [tex]10^5[/tex] N/m²) and the air density (1.29 kg/m³). We will also use the standard acceleration due to gravity (approximately 9.81 m/s²).

To find the height, we will rearrange the equation:

Height = Pressure / (density × gravity)

Now, plug in the values:

Height = (1.0 × [tex]10^5[/tex] N/m²) / (1.29 kg/m³ × 9.81 m/s²)Height ≈ 7,986.9 m

Therefore, the height of the atmosphere needed to produce this pressure is approximately 7,987 meters.

To know more about air density:

brainly.com/question/3551743

#SPJ4

The center of mass of the system is located 4.0 m from the 4.0 kg mass, towards the 6.0 kg mass.

The center of mass of this system will be between the 4.0 kg mass and the center, but closer to the 6.0 kg mass due to its larger mass.
To find the center of mass, we can use the formula:
x_cm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
where m1, m2, and m3 are the masses of the rod, 4.0 kg mass, and 6.0 kg mass respectively, and x1, x2, and x3 are their respective positions.

The position of the center of the rod can be found by taking half of its length, which is 2.5 m.

Therefore, we can plug in the values and solve for x_cm:
x_cm = (3.0 kg * 2.5 m + 4.0 kg * 0 m + 6.0 kg * 5.0 m) / (3.0 kg + 4.0 kg + 6.0 kg)
x_cm = 4.0 m

Thus, the center of mass of the system is located 4.0 m from the 4.0 kg mass, towards the 6.0 kg mass.

Learn more about "center of mass": https://brainly.com/question/28021242

#SPJ11

In a fusion reaction, the binding energy per nucleon of the fusion product generally compares to that of the pieces that combined to form it in the following way:

1. The product has a greater binding energy per nucleon than the pieces.

This is because, during fusion, lighter nuclei combine to form a heavier nucleus, which results in a more stable configuration and higher binding energy per nucleon. This process releases energy as a consequence of the increased stability. However, it's essential to note that the specific reaction or pieces involved may have an impact on the exact outcome.

So, to summarize, the binding energy per nucleon of a fusion product is typically greater than that of the pieces that combined to form it.

To know more about fusion reaction:

https://brainly.com/question/20169581

#SPJ11

The correct answer is b. Lateral resolution typically has a higher numerical value than axial resolution with standard diagnostic imaging instrumentation.

Axial resolution refers to the ability to distinguish objects along the axis of the imaging plane, while lateral resolution refers to the ability to distinguish objects perpendicular to the imaging plane. With standard diagnostic imaging instrumentation, axial resolution typically has a higher numerical value than lateral resolution. This is because axial resolution measures the ability to distinguish two objects along the direction of the ultrasound beam, while lateral resolution measures the ability to distinguish objects perpendicular to the beam. Axial resolution is generally better due to the use of short pulses in diagnostic imaging.

Learn more about ultrasound  here: https://brainly.com/question/30363405

#SPJ11

The smaller wheel turns 19.2π radians when the larger wheel turns 4.0 revolutions.

To find how many radians the smaller wheel turns when the larger wheel turns 4.0 revolutions,

1. First, find the gear ratio by dividing the radius of the larger wheel by the radius of the smaller wheel:
Gear ratio = (60 cm) / (25 cm) = 2.4

2. Next, convert the 4.0 revolutions of the larger wheel to radians:
1 revolution = 2π radians, so 4.0 revolutions = 4.0 × 2π = 8π radians

3. Now, use the gear ratio to determine how many radians the smaller wheel turns:
Radians turned by smaller wheel = Radians turned by larger wheel × Gear ratio
Radians turned by smaller wheel = 8π × 2.4 = 19.2π radians

So, the smaller wheel turns 19.2π radians when the larger wheel turns 4.0 revolutions.

Learn more about "gear ratio": https://brainly.com/question/14455728

#SPJ11

The car moves through an angular distance of 60 radians in 4.00 minutes.

To calculate the angular distance the car moves in 4.00 minutes,

a) Angular distance calculation:
1. First, find the radius (r) of the circle. The diameter is given as 120 meters, so the radius is half of that:
r = 120 m / 2 = 60 m

2. Next, we'll find the total distance (s) traveled by the car in 4.00 minutes. The car's speed is given as 15.0 m/s, and we'll convert the time to seconds:
4.00 minutes * 60 s/minute = 240 s

Total distance (s) = speed × time
s = 15.0 m/s × 240 s = 3600 m

3. Now we'll calculate the angular distance (θ) in radians. Since the car is traveling in a circle, we can use the formula:
θ = s / r

θ = 3600 m / 60 m = 60 radians

As a result, the car travels 60 radians of angle in 4 minutes.

Learn more about "angular distance": https://brainly.com/question/30332159

#SPJ11

The net torque about the axle on the pulley is 20 Ncm.

The net torque about the axle on the pulley can be calculated by first determining the direction of rotation. Since there are two forces acting in opposite directions, the pulley will not rotate in either direction unless there is a net torque acting on it. Therefore, we need to find the difference between the clockwise torque and the counterclockwise torque.

To calculate the torque, we need to use the formula: torque = force x distance. The distance is the radius of the pulley, which is half of the diameter, or 2 cm.

On the left side, the force of 20 N is pulling down and to the left, creating a clockwise torque. The distance from the axle to the force is 2 cm, so the torque is 20 N x 2 cm = 40 Ncm.

On the right side, the force of 30 N is pulling down and to the right, creating a counterclockwise torque. The distance from the axle to the force is also 2 cm, so the torque is 30 N x 2 cm = 60 Ncm.

Therefore, the net torque is the difference between these two torques: 60 Ncm - 40 Ncm = 20 Ncm.

For more such questions on Net torque.

https://brainly.com/question/3388202#

#SPJ11

The recommended following time for safe driving is four to six seconds for speeds under 30 MPH, and 6-8 seconds for speeds over 30 MPH. This means that you should maintain a distance from the vehicle in front of you that allows you to react and come to a complete stop if necessary within the designated time frame. Keeping a safe following distance can help prevent accidents and allow for smoother traffic flow.
To reiterate, the suggested following time is:
- Four to six seconds for speeds under 30 MPH
- Six to eight seconds for speeds over 30 MPH

These following times help ensure that you maintain a safe distance from the vehicle in front of you, giving you enough time to react to any sudden changes in traffic conditions or potential hazards. Always remember to adjust your following distance based on factors such as road conditions, weather, and visibility to ensure safe driving.

To know more about potential hazards:

https://brainly.com/question/21819671

#SPJ11

The final angular speed of the chimney when it falls over is approximately 0.311 rad/s when it makes an angle of 35 degrees with the vertical.

We can use conservation of energy to find the final angular speed of the chimney when it falls. At the instant when the chimney makes an angle of 35 degrees with the vertical, it has potential energy with respect to its final position when it falls over:

U = mgh = (M/L)gL^2(1-cosθ)

where M is the mass of the chimney and θ is the angle it makes with the vertical.

At the same instant, the chimney also has rotational kinetic energy:

K = (1/2)Iω^2

where I is the moment of inertia of the chimney about its center of mass and ω is its angular speed.

Since there is no external torque acting on the chimney, the conservation of energy equation is:

U = K

Substituting the expressions for U and K:

(M/L)gL^2(1-cosθ) = (1/2)Iω^2

For a thin rod rotating about its center of mass, the moment of inertia is:

I = (1/12)ML^2

Substituting the given values:

I = (1/12)(M/L)L^2 = (1/12)ML^2

(M/L)gL^2(1-cosθ) = (1/2)(1/12)ML^2ω^2

Simplifying and solving for ω:

ω^2 = (2/3)g(1-cosθ)

ω = sqrt[(2/3)g(1-cosθ)]

Substituting the given values:

ω = sqrt[(2/3)(9.81 m/s^2)(1-cos35°)]

ω ≈ 0.311 rad/s

Therefore, the final angular speed of the chimney when it falls over is approximately 0.311 rad/s when it makes an angle of 35 degrees with the vertical.

To learn more about solving visit:

https://brainly.com/question/24083632

#SPJ11

When the ball is tossed straight up from the surface of the small asteroid, gravitational force and inertial force are the two forces acting on it while it is on the way up.

Forces acting on a ball tossed straight up from the surface of a small asteroid.

When the ball is on its way up from the surface of the asteroid, two main forces act on it:

1. Gravitational force: This force is exerted by the asteroid on the ball, pulling it towards the center of the asteroid. It acts throughout the entire motion of the ball, both on its way up and down.

2. Inertial force: This is the force associated with the ball's initial velocity when it is tossed upwards. It is responsible for the ball's motion away from the asteroid's surface.

So, when the ball is tossed straight up from the surface of the small asteroid, gravitational force and inertial force are the two forces acting on it while it is on the way up.

To know more - https://brainly.com/question/18893265

#SPJ11

The electron moved into a region of higher potential.

When an electric field is applied to an electron, the electric force exerted on the electron causes it to accelerate. If the electric field is in the direction opposite to the initial velocity of the electron, the electron will eventually come to a stop and then start moving in the opposite direction.

In this scenario, the initial speed of the electron is 380,000 m/s, which means that it has kinetic energy. When the electron is brought to rest by the electric field, its kinetic energy is converted into potential energy. This suggests that the electron has moved into a region of higher potential, where the electric potential energy is greater than the initial kinetic energy of the electron.

Therefore, the electron moved into a region of higher potential.

To learn more about kinetic energy visit: https://brainly.com/question/26472013

#SPJ11

The electric field in the middle of the capacitor can be calculated using the equation E = V/d, where E is the electric field, V is the potential difference, and d is the distance between the plates.

Substituting the given values, we get:

E = 40 V / 0.02 m = 2000 V/m

Therefore, the electric field in the middle of the capacitor is 2000 V/m.

to know more about A capacitor consisting of two parallel plates click this link -

brainly.com/question/13897985

#SPJ11

Yes, the statement that the rate at which information can be transmitted on an electromagnetic wave is proportional to the frequency of the wave is consistent with the fact that laser telephone transmission at visible frequencies carries far more conversations per optical fiber than conventional electronic transmission in a wire.

This is because visible frequencies have a much higher frequency than the frequencies used in electronic transmission, which allows for a much greater amount of information to be transmitted in a given amount of time. As for the implication for ELF (extremely low frequency) radio communication with submarines, it is important to note that ELF waves have a much lower frequency than visible light waves. This means that the rate at which information can be transmitted on an ELF wave is much slower than that of visible light waves. Therefore, it may be more challenging to transmit large amounts of information over ELF waves, and this could potentially limit the effectiveness of ELF radio communication with submarines.

learn more about electromagnetic wave

https://brainly.com/question/18165320

#SPJ11

Beyond a certain stimulus frequency, there is no further increase in peak force generated by a muscle. This occurs when the muscle reaches a state called tetanus.

Tetanus is the point at which individual muscle contractions blend into a single, sustained contraction due to the rapid frequency of stimuli. This results in the maximal possible tension produced by the muscle fibers.

At lower frequencies, individual twitches can be observed, and these are called twitch contractions. As the frequency increases, the twitches begin to overlap, and the force generated by the muscle increases. This phenomenon is called summation. When the frequency reaches a level where the muscle can no longer fully relax between stimuli, it enters incomplete tetanus.

Further increases in frequency lead to complete tetanus, where individual contractions are indistinguishable, and the muscle generates its maximum force.

The specific frequency at which tetanus occurs can vary depending on the type of muscle and other factors. Generally, the threshold is around 40-60 Hz for most human skeletal muscles. At or beyond this stimulus frequency, no further increase in peak force can be observed as the muscle has reached its maximum tension-generating capacity.

For more such questions on Stimulus frequency.

https://brainly.com/question/29559948#

#SPJ11

Grating lobes are most common with d. linear arrays

Grating lobes occur when there is a deviation from the linear pattern of elements in an array, resulting in the formation of additional lobes. This can happen with linear arrays when the element spacing is too large, causing the array to behave like an annular array or when the array has a non-uniform element spacing. Continuous wave trdx and mechanical scanners are not typically associated with grating lobes. Grating lobes are the maxima of the main beam, as predicted by the pattern multiplication theorem. When the array spacing is less than or equal to λ / 2, only the main lobe exists in the visible space, with no other grating lobes. Grating lobes appear when the array spacing is greater than λ / 2.

Learn more about array here: https://brainly.com/question/27041014

#SPJ11

The x-component of F3 is 56.67 N and the y-component of F3 is 44.44 N for the three horizontal forces that are pulling on a ring, at rest. F1 is 100 N at a 45.0-degree angle, and F2 is 135 N at a 160-degree angle.

Since the ring is at rest, the vector sum of the three forces must be zero.

First, find the x- and y-components of F1 and F2:

Fx1 = 100 N cos(45) = 70.71 N

Fy1 = 100 N sin(45) = 70.71 N

Fx2 = 135 N cos(160) = -127.38 N

Fy2 = 135 N sin(160) = -115.15 N

Since the sum of the x-components and y-components of the three forces must be zero:

Fx3 = -Fx1 - Fx2 = -70.71 N - (-127.38 N) = 56.67 N

Fy3 = -Fy1 - Fy2 = -70.71 N - (-115.15 N) = 44.44 N

Learn more about horizontal forces at

https://brainly.com/question/3370950

#SPJ4

The point's angular momentum is calculated by adding its mass, the square of the distance from the path's centre, and its angular velocity

To find the angular momentum of a point mass M rotating at a distance R from the center of its path with an angular velocity W, you can use the following formula:

Angular momentum (L) = mass (M) × radius (R) × tangential velocity (V)

First, we need to find the tangential velocity (V) using the angular velocity (W) and the radius (R):

Tangential velocity (V) = radius (R) × angular velocity (W)

Now, we can plug this into the angular momentum formula:

Angular momentum (L) = mass (M) × radius (R) × (radius (R) × angular velocity (W))

This simplifies to:

Angular momentum (L) = mass (M) × radius² (R²) × angular velocity (W)

So the angular momentum of the point is the product of its mass, the square of the radius from the center of its path, and its angular velocity.

Learn more about angular momentum.

brainly.com/question/29897173

#SPJ11

The direction of the acceleration as you come to a stop is directed downwards. This is because acceleration is defined as the rate of change of velocity, which means that if the velocity of the car is decreasing, then the acceleration must be directed in the opposite direction to the velocity.

In this case, since you are driving north and suddenly hit your brakes, your velocity is directed northwards.

for such more questions on acceleration

https://brainly.com/question/460763

#SPJ11

There are approximately 625 turns on the toroid.

The length of the wire in one turn can be calculated using the formula for the circumference of a circle:

C = 2πr

Given that the diameter of the wire is 0.221 mm, the radius of the wire (assuming it is a circular cross-section) would be half of that:

r(wire) = 0.221 mm / 2

= 0.1105 mm

= 0.01105 cm

The length of wire in one turn is then:

L(turn) = 2πr(wire)

The total length of wire required for one turn of the toroid is equal to the circumference of the toroid's path, which can be calculated as the difference between the outer and inner circumferences:

L(total) = 2πR(outer) - 2πR(inner)

Substituting the given values:

L(total) = 2π(28.0 cm - 21.1 cm)

Now, we can find the number of turns by dividing the total length of the wire by the length of the wire in one turn:

Number of turns = L(total) / L(turn)

Calculating the values:

L(total) = 2π(28.0 cm - 21.1 cm)

= 2π(6.9 cm)

= 43.33 cm

L(turn) = 2π(0.01105 cm)

= 0.06937 cm

Number of turns = 43.33 cm / 0.06937 cm

= 624.62

Therefore, there are approximately 625 turns on the toroid.

Learn more about the toroid here:

https://brainly.com/question/15174316

#SPJ6

The cable will stretch by 4 mm when a 10 kg mass is hung from a 2 m length of the same cable. The answer is E) 4 mm.

Assuming that the cable obeys Hooke's law (i.e., the force required to stretch or compress the cable is proportional to the amount of stretch or compression), we can use the following equation to find the amount by which the cable will stretch when a 10 kg mass is hung from a 2 m length of the same cable:

ΔL = (F * L) / (A * E)

where:

ΔL is the amount of stretch, measured in meters (m)

F is the force applied to the cable, measured in newtons (N)

L is the original length of the cable, measured in meters (m)

A is the cross-sectional area of the cable, measured in square meters (m^2)

E is the Young's modulus of the cable material, measured in pascals (Pa)

We can assume that the cross-sectional area and Young's modulus of the cable are the same in both cases.

In the first case, a 10 kg mass is hung from a 1 m length of the cable, causing it to stretch by 2 mm (0.002 m). The force applied to the cable is:

F = m * g = 10 kg * 9.81 m/[tex]s^2[/tex] = 98.1 N

Substituting the values into the equation, we get:

0.002 m = (98.1 N * 1 m) / (A * E)

In the second case, a 10 kg mass is hung from a 2 m length of the same cable. The force applied to the cable is still:

F = m * g = 10 kg * 9.81 m[tex]/s^2[/tex] = 98.1 N

Substituting the values into the equation, we get:

ΔL = (98.1 N * 2 m) / (A * E)

Dividing the second equation by the first equation, we can eliminate the unknowns A and E:

ΔL / 0.002 m = [(98.1 N * 2 m) / (A * E)] / [(98.1 N * 1 m) / (A * E)]

Simplifying, we get:

ΔL / 0.002 m = 2

Multiplying both sides by 0.002 m, we get:

ΔL = 0.004 m = 4 mm

Therefore, the cable will stretch by 4 mm when a 10 kg mass is hung from a 2 m length of the same cable. The answer is E) 4 mm.

To learn more about Young's modulus  visit: https://brainly.com/question/30756002

#SPJ11

The correct option is "torque, lever arm". Torque is the force applied at some distance from the fulcrum, and the lever arm is the distance between the applied force and the fulcrum.

A fulcrum is a fixed point around which a lever rotates, and it serves to balance the applied force with the resistance force. Application of force at some distance from the fulcrum creates torque or a turning effect. The distance between the applied force and the fulcrum is called the lever arm or moment arm.
The equation that relates all these terms is the torque equation:
Torque = Force × Distance
This equation states that the torque generated is equal to the applied force multiplied by the distance between the force and the fulcrum.

learn more about Force Refer: https://brainly.com/question/31248352

#SPJ11

In direct proportion to its moment of inertia and angular velocity, the

angular momentum will grow.

Angular momentum is a fundamental quantity in physics that describes

the rotational motion of an object.

For a point particle rotating around an axis, the angular momentum can be expressed as:

L = Iω

where L is the angular momentum,

I is the moment of inertia of the particle about the axis of rotation, and

ω is the angular velocity of the particle.

If the particle is initially not moving, then its angular velocity is zero.

In this case, the angular momentum reduces to:

L = I × 0 = 0

This means that the angular momentum of the particle is zero at the start

of its rotation. As the particle starts to rotate, the angular momentum will

increase in proportion to its moment of inertia and angular velocity.

for such more question on angular momentum

https://brainly.com/question/29512279

#SPJ11

In both cases, the work done by friction has a different sign and direction, and this results in a different change in kinetic energy for the system.

What is Kinetic Energy?

Kinetic energy is important in many areas of science and engineering, such as mechanics, thermodynamics, and electromagnetism. It plays a key role in understanding the behavior of objects in motion, such as projectiles, vehicles, and particles in accelerators. It is also used in various applications, such as energy storage and conversion, transportation, and materials processing.

The kinetic energies are not equal in the two scenarios because the work done by friction is different in each case.

In the first scenario, where the parachutist's horizontal component of velocity is changed, friction does positive work. This means that the force of friction is acting in the direction of motion, and is therefore adding kinetic energy to the system. The kinetic energy of the system increases as a result.

Learn more about Kinetic Energy

https://brainly.com/question/8101588

#SPJ1