does your data show a relationship between the tension in an the linear density of the elastic string? if so, what is that relationship

\(Work=Force \: × \: displacement \\ => W=Fs \\ \\ Given, \\ Force=25 \: N \\ Displacement=2m \\ \\ so \: work = 25 \: N \: \times 2m \\ = > work = 25kgm {s}^{ - 2} \times 2m \\ = > work = 50kg {m}^{2} {s}^{ - 2} \\ = > work = 50J\)

This is the answer.

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A weightlifter must exert 25 Newtons of force to lift a set of barbells 2 meters off the ground, the weightlifter did 50 Nm of work on the barbells when he lifted them. The correct option is A.

To calculate the work done by the weightlifter in lifting the barbells, we can use the formula:

Work = Force × Distance

Here, it is given that:

Force = 25 Newtons

Distance = 2 meters

Substituting the values into the formula:

Work = 25 N × 2 m

Calculating the multiplication:

Work = 50 Nm (Newton-meters)

Thus, the weightlifter did 50 Nm of work on the barbells when he lifted them, the correct answer is A. 50 Nm.

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You have 8.66 kilometres to bike before you turn north and arrive at your friend's house The Pythagorean theorem allows us to calculate the following distance from your starting point to your friend's street:

\(d = √[(10.0 km)^2 - (6.0 km)^2] = 8.66 km\)

This is the length of a right triangle's hypotenuse, with the horizontal leg being 6.0 km (the distance to your friend's street in the north) and the vertical leg being the remaining distance to ride before making a northward turn. To determine the length of the vertical leg, we can apply trigonometry:

\(opposite/hypotenuse = sinsin = 8.66 kilometres of vertical legsin = horizontal leg / d(vertical leg / d) = sin1(6.0 km / 8.66 km) = sin (1θ = 37.13°\)

You must therefore cycle a distance equal to:

\(d sin  = 8.66 km sin 37.13° = 5.35 km vertical leg\)

The distance you must cycle in total Adding the distance to the turn and the distance from the turn to your friend's street will get you to your friend's house.

Distance total: 5.35 km plus 6.05 km equals 11.35 km

However, keep in mind that this distance is greater than the 10.0 km straight distance between your starting place and your friend's house, so if you want to reduce the amount of bicycling you do, you might want to think about finding an alternative route that completely avoids the hill.

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Given data

The vector in the x-direction is Cx = -105 m

The vector in the y-direction is Cy = - 88.2 m

The expression for the direction of the vector is given as:

Substitute the value in the above equation.

Thus, the direction of the vector is 40 degrees.

The number of oscillations of the toy in a second is 1.25.

The given parameter:

The frequency of an object is calculated as follows;

\(f = \frac{n}{t} \\\\\)

where;

The number of oscillations of the toy in a second is calculated as follows;

\(1.25 = \frac{n}{1} \\\\n = 1.25\)

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Answer: oxidizes or reduces

Explanation: When you change the number of protons in an atom, you will change the atom from one element to a different element.

Answer:

Explanation:

A scalar quantity is a physical quantity that has only one characteristic - a numerical value.

The scalar value can be positive or negative.

Examples of scalar quantities: temperature, mass, volume, time, density.

A vector quantity is a physical quantity that has two characteristics:

1) a numerical value that is always positive (vector modulus);

2) direction.

Examples of vector physical quantities: speed, acceleration, force.

You may assume that seawater has a specific gravity of 1.03 and that the subsea wellhead was 5053 feet below the surface of the Gulf.(a)The gauge pressure in the Gulf at a depth of 5053 ft is approximately is 2319 psig.(b) The estimated specific gravity of the drilling mud is approximately 0.976.(c)The calculated mass fraction of barite in the slurry is approximately -0.0071

To solve the given problems, we need to apply principles of fluid pressure and buoyancy. Let's go through each question:

a. Estimate the gauge pressure (psig) in the Gulf at a depth of 5053 ft

To estimate the gauge pressure at a certain depth in a fluid, we can use the formula:

P = ρgh

where:

P is the pressure,

ρ is the density of the fluid,

g is the acceleration due to gravity,

h is the depth.

In this case, the fluid is seawater, and we're given its specific gravity as 1.03. Since specific gravity is the ratio of the density of a substance to the density of a reference substance (in this case, water), we can calculate the density of seawater:

ρ_seawater = ρ_water × SG_seawater

where:

ρ_seawater is the density of seawater,

ρ_water is the density of water (1000 kg/m³),

SG_seawater is the specific gravity of seawater (1.03).

Plugging in the values, we have:

ρ_seawater = 1000 kg/m³ × 1.03 = 1030 kg/m³

Next, we need to convert the depth from feet to meters:

h = 5053 ft × 0.3048 m/ft = 1540.27 m

Now we can calculate the gauge pressure:

P = ρgh = 1030 kg/m³ × 9.8 m/s² × 1540.27 m = 1.6 x 10^7 Pa

To convert the pressure from Pascals (Pa) to pounds per square inch gauge (psig), we can use the conversion factor:

1 psig = 6894.76 Pa

Therefore, the gauge pressure in the Gulf at a depth of 5053 ft is approximately:

P = 1.6 x 10^7 Pa / 6894.76 Pa/psig ≈ 2319 psig

b. Estimate the specific gravity of the drilling mud.

To estimate the specific gravity of the drilling mud, we can use the principle of balancing pressures between the Gulf surface and the wellhead. Since the pressure inside the wellhead is given as 4400 psig, the pressure at the Gulf surface must also be 4400 psig to achieve equilibrium.

Using the same formula as before:

P = ρgh

Let's assume the specific gravity of the drilling mud as SG_mud.

The pressure at the Gulf surface can be calculated as:

P_surface = ρ_seawater × g × h

The pressure difference between the Gulf surface and the wellhead is:

ΔP = P_surface - P_wellhead

Since ΔP = 4400 psig, we have:

4400 psig = ρ_seawater × g × h - ρ_mud × g × h

We can rearrange the equation to solve for SG_mud:

SG_mud = (ρ_seawater × g × h - 4400 psig) / (ρ_seawater × g × h)

Plugging in the known values:

SG_mud = (1030 kg/m³ × 9.8 m/s² × 1540.27 m - 4400 psig) / (1030 kg/m³ × 9.8 m/s² × 1540.27 m)

Calculating the specific gravity of the drilling mud:

SG_mud ≈ 0.976

Therefore, the estimated specific gravity of the drilling mud is approximately 0.976.

c. Calculate the mass fraction of barite in the slurry.

To calculate the mass fraction of barite in the slurry, we need to consider the specific gravity of barite and the specific gravity of the mud (which we estimated to be 0.976).

The formula for calculating the mass fraction is:

mass fraction = (SG_mud - SG_water) / (SG_barite - SG_water)

Given that SG_water is 1 and SG_barite is 4.37, we can substitute these values into the formula:

mass fraction = (0.976 - 1) / (4.37 - 1)

Calculating the mass fraction:

mass fraction ≈ -0.024 / 3.37 ≈ -0.0071

The calculated mass fraction of barite in the slurry is approximately -0.0071.

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The situation in which there will be an increase in kinetic energy is C. A fan is switched from "low speed" to "high speed."

Kinetic energy is the energy of motion. When an object's speed increases, its kinetic energy also increases. In the case of the fan, switching from "low speed" to "high speed" will increase the speed of the fan blades, and therefore increase the kinetic energy of the fan.

In the other options, there is no increase in kinetic energy. A kicked football approaching its maximum height is actually losing kinetic energy as it slows down due to gravity. A filing cabinet pushed across a rough floor at constant speed has a constant amount of kinetic energy, as does a train pulled up a mountain at a constant speed. And the planet Venus moving in its nearly circular orbit around the Sun also has a constant amount of kinetic energy, as its speed does not change.

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Answer:

The atomic number tells us the number of protons.

Explanation:

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Answer:

x=50

Explanation:

Answer:

vertically opposite angles are equal

Explanation:

so

2x+30=3x-20

2x-3x= -20-30

-1x= -50

so x is 50

as minus gets cancelled both sides.

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The acceleration of this car include the following: A. 2 m/s².

In Science, the acceleration of a car can be calculated by using this mathematical expression:

a = (V - U)/t

Where:  

By substituting the given parameters into the acceleration formula, we have;

Acceleration, a = (40 - 10)/15

Acceleration, a = 30/15

Acceleration, a = 2 m/s².

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Answer:

power= work done /time.

Answer:

W = Force  * distance

Power = W/ time

Explanation:

Balloon A is positively charged, and balloon C is negatively charged. If balloon A approaches balloon C, there will be an electrostatic force of attraction between them.

When two objects carry opposite charges, they exert an attractive force on each other. This force is known as the electrostatic force and follows Coulomb's law. According to Coulomb's law, the magnitude of the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this scenario, since balloon A is positively charged and balloon C is negatively charged, they have opposite charges. Therefore, the electrostatic force between them will be attractive. The magnitude of the force depends on the charges of the balloons and the distance between them. It is important to note that without specific information about the charges of the balloons and their distance, it is not possible to determine the exact magnitude of the force. To calculate the force, you would need the values of the charges and the distance between the balloons.

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Given data

*The given mass of the car is m = 1610 kg

*The given effective force constant is k = 5.75 × 10^4 N/m

(a)

The formula for the period of oscillation of a 1610 kg car is given as

Substitute the known values in the above expression as

Hence, the time period of oscillation of a 1610 kg car is T = 1.05 s

(b)

As from the given data, the amplitude of the oscillation of the car decreases by a factor of 5.00. Then, the expression for the amplitude of the oscillation, and the damping constant (b) is calculated as

Substitute the known values in the above expression as

Hence, the damping constant is b = 9871.2 kg/s

At the point X after 2 seconds, the stone has a magnitude of velocity equal to 10 m/s, and its direction is purely horizontal.

When a stone is projected horizontally in a vacuum, it only experiences horizontal motion due to the absence of air resistance. The vertical motion is governed by the force of gravity alone. In this scenario, the stone will undergo uniform horizontal motion with a constant horizontal velocity.

Given that the stone is projected horizontally with a velocity of 10 m/s, its horizontal velocity remains constant throughout the motion. After 2 seconds, the stone will have traveled a horizontal distance equal to the product of its horizontal velocity and the time, which is 10 m/s * 2 s = 20 m. Therefore, the stone will be located 20 meters horizontally from the point of projection. Since the stone is moving horizontally, its vertical velocity remains zero throughout the motion. The magnitude of the velocity at this point is equal to the horizontal velocity, which is 10 m/s. However, since the stone is moving horizontally, there is no vertical component of velocity.

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For a human jumper to reach a height of 110 cm, the person will need to leave the ground at a speed of 4.65 m/s.  

We can calculate the initial speed to reach 110 cm of height with the following equation:

\( v_{f}^{2} = v_{i}^{2} - 2gh \)

Where:

\( v_{f}\): is the final speed = 0 (at the maximum height of 110 cm)

\( v_{i}\): is the initial speed =?

g: is the acceleration due to gravity = 9.81 m/s²

h: is the height = 110 cm = 1.10 m

Hence, the initial velocity is:

\( v_{i} = \sqrt{v_{f}^{2} + 2gh} = \sqrt{2*9.81 m/s^{2}*1.10 m} = 4.65 m/s \)

Therefore, the initial speed that the person must have to reach 110 cm is 4.65 m/s.

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Answer:

see below

Explanation:

1000 m / 60 s = 16 2/3  m/s

Answer:

5

Explanation:

Because it right

Answer:

A) 250 J

B) 150 J

C) The efficiency = 0.6 and the percentage efficiency = 60%

Explanation:

The question relates to definition of terms in energy transfer and the calculation of efficiency

The parameters of the given are;

The energy the object transfers = 150 J

The amount of electrical energy supplied to the motor = 250 J

Therefore, we have;

A) The total energy supplied to the motor = The amount of electrical energy supplied to the motor = 250 J

B) The useful energy transferred = The energy used to do work = 150 J

C) The efficiency = (Useful energy transferred (out))/(Total energy supplied (in)

\(The \ efficiency = \dfrac{Useful \ energy \ transferred \ (out)}{Total \ energy supplied \ (in)} = \dfrac{150 \, J}{250 \, J} = 0.6\)

The percentage efficiency is given as follows;

\(The \ percentage \ efficiency = \dfrac{Useful \ energy \ transferred \ (out)}{Total \ energy supplied \ (in)} \times 100\)

\(\therefore The \ percentage \ efficiency = \dfrac{150 \, J}{250 \, J} \times 100 = 0.6 \times 100 = 60\%\)

Answer:

A) 250 J

B) 150 J

C) efficiency = 0.6, percentage efficiency = 60%

Explanation:

Answer:

30q1

Explanation:

Uniformly charged spheres are “touching”. 4. What must be the distance between point charge q1 = 26.0µC and point charge q2 = −47.0µC

Assuming the car stops instantaneously and that the spring is the only force acting against the car's kinetic energy:

When the car hits the wall, the spring-loaded bumper compresses 0.30 m. This means that the spring must have exerted a force on the car in the opposite direction of its motion.

The spring must have stored a minimum of 286,000 J (40,000 J of kinetic energy + 0.3 m of potential energy) of energy to bring the car to a stop.

Assumptions:

- The car stops instantaneously

- The spring is the only force acting against the car's kinetic energy

- The spring is linear (i.e. Hooke's Law applies)

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1. To find the time when the body reaches the ground, we can use the vertical motion equation:

h = v₀y * t + (1/2) * g * t²

where:

h = height of the tower = 15m

v₀y = initial vertical velocity = v₀ * sin(θ) = 30m/s * sin(30°)

g = acceleration due to gravity = 9.8m/s²

t = time

Plugging in the values:

15 = (30 * sin(30°) * t) + (0.5 * 9.8 * t²)

Simplifying the equation:

15 = 15t * 0.5t² + 4.9t²

Combining like terms:

15 = 7.5t² + 4.9t²

Simplifying further:

15 = 12.4t²

Dividing both sides by 12.4:

t² = 15 / 12.4

Taking the square root of both sides:

t = √(15 / 12.4)

Calculating the value:

t ≈ 1.01 seconds

Therefore, the time it takes for the body to reach the ground is approximately 1.01 seconds.

2. To find the displacement vector, we need to calculate the horizontal and vertical components separately.

Horizontal component:

The horizontal displacement can be calculated using the formula:

x = v₀x * t

where:

v₀x = initial horizontal velocity = v₀ * cos(θ) = 30m/s * cos(30°)

t = time is taken to reach the ground (previously calculated as approximately 1.01 seconds)

Plugging in the values:

v₀x = 30m/s * cos(30°)

t = 1.01 seconds

Calculating the value:

v₀x ≈ 26.02 m/s

Vertical component:

The vertical displacement can be calculated using the formula:

y = v₀y * t + (1/2) * g * t²

where:

v₀y = initial vertical velocity = v₀ * sin(θ) = 30m/s * sin(30°)

g = acceleration due to gravity = 9.8m/s²

t = time is taken to reach the ground (previously calculated as approximately 1.01 seconds)

Plugging in the values:

v₀y = 30m/s * sin(30°)

t = 1.01 seconds

Calculating the value:

v₀y ≈ 15 m/s

Now we have the horizontal and vertical components of the displacement vector:

Horizontal component: x ≈ 26.02 m/s

Vertical component: y ≈ 15 m/s

Therefore, the displacement vector of the body is approximately (26.02 m/s, 15 m/s).

3. To find the angle when the body hits the ground, we can use the vertical and horizontal components of the velocity.

The horizontal component of the velocity, v₀x, can be calculated using the formula:

v₀x = v₀ * cos(θ)

where:

v₀ = initial velocity = 30m/s

θ = angle of projection = 30 degrees

Plugging in the values:

v₀x = 30m/s * cos(30°)

Calculating the value:

v₀x ≈ 26.02 m/s

The vertical component of the velocity, v₀y, can be calculated using the formula:

v₀y = v₀ * sin(θ)

where:

v₀ = initial velocity = 30m/s

θ = angle of projection = 30 degrees

Plugging in the values:

v₀y = 30m/s * sin(30°)

Calculating the value:

v₀y ≈ 15 m/s

Now, to find the angle when the body hits the ground, we can use the inverse tangent function:

θ = arctan(v₀y / v₀x)

Plugging in the values:

θ = arctan(15 m/s / 26.02 m/s)

Calculating the value:

θ ≈ 30.96 degrees

Therefore, the angle when the body hits the ground is approximately 30.96 degrees.

4. To find the maximum height, we can use the vertical motion equation:

h = v₀y² / (2 * g)

where:

h = maximum height

v₀y = initial vertical velocity = v₀ * sin(θ) = 30m/s * sin(30°)

g = acceleration due to gravity = 9.8m/s²

Plugging in the values:

h = (30 * sin(30°))² / (2 * 9.8)

Calculating the value:

h ≈ 27.55 meters

Therefore, the maximum height reached by the body is approximately 27.55 meters.

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Answer:

C. affects

Explanation:

affect means to impact or change. When the system fails it's it impacts or affects the others systems so they become sick.

=====================================================

Explanation:

At 4 seconds, the distance is 8 meters. Note the point (4,8)

At 8 seconds, the distance is 10 meters. The point here is (8,10)

Find the slope of the line through (4,8) and (8,10)

m = (y2-y1)/(x2-x1)

m = (10-8)/(8-4)

m = 2/4

m = 1/2

m = 0.5

The average speed on this interval is 0.5 m/s

-----------------

Another way to look at it:

We've gone from 8 meters to 10 meters, so that's a change of y = 2 meters.

During this, the time has changed from 4 seconds to 8 seconds, which is a difference of x = 4 seconds.

The velocity is the rate of change of distance over time

velocity = (change in distance)/(change in time) = y/x = 2/4 = 0.5 m/s

Answer:

The Gravitational Attraction of Tom and Sally is 28.4631292 N.

Explanation:

The gravitational force formula is

gravitational force =  (gravitationalconstant)(massofobject1)(massofobject2)/(distancebetweenobjects)^2

So if you plug in the values given, you get 28.4631292.

Answer:

ACCELERATING OR DECELERATING

Explanation:

I'M NOT SURE

The fossil record shows that prokaryotes were the first living things. Therefore, choice D is right.

Prokaryotes, which predated plants and animals by billions of years, are now known to have been the first cellular life forms on Earth. The age of the Earth and its moon is estimated to be 4.54 billion years.

Pro means "before" in Latin. They are typically single-celled creatures but can occasionally be multicellular. Prokaryotes are said to have been the first living things discovered on Earth. They are separated into two groups: bacteria and archae. They lack organelles that are membrane-bound, yet all of the water-soluble parts are still present in the cytoplasm without membrane. Because of their basic characteristics, a fossil suggests that they are prokaryotes.

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The complete question is

The first organisms evolved on Earth around 4 billion years ago. The fossil record indicates that the first organisms were which of the following?. A) eukaryotes. B) plastids. C) mitochondria. D) prokaryotes

The length of the rubber band that the boy must use is 0.024 m or 24 mm.

To determine the length of the rubber band, we can use the formula for the potential energy stored in a stretched spring, which is also applicable to a stretched rubber band:

where U is the potential energy stored in the rubber band, k is the spring constant (or in this case, the rubber band constant), and x is the displacement of the rubber band from its natural length.

Since the rubber band is stretched by 0.25 of its natural length, the displacement x is 0.25 times the natural length of the rubber band.

We can solve for the rubber band constant k by using the formula for the velocity of a projectile launched by a spring (or in this case, a rubber band):

where v is the velocity of the projectile, m is the mass of the rubber band, M is the mass of the projectile, and k is the spring constant. We can rearrange this equation to solve for k:

k = (v² M) / (2 m)

We can now combine the two equations to solve for the length of the rubber band, L:

U = 1/2 k x²

U = 1/2 ((v² M) / (2 m)) (0.25 L)²

U = (v² M L²) / (32 m)

The potential energy stored in the rubber band must be equal to the kinetic energy of the projectile when it is launched:

U = 1/2 M v²

(v² M L²) / (32 m) = 1/2 M v²

L = ((16 m v²) / (k M))

L = ((16 m v²) / ((v² M) / (2 m) M))

L = √(32 m^2 / M)

L = (0.032 M)

Substituting the given values, we get:

L = √(0.032 * 0.006)

L = 0.024 m

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The speed of the given point on earth's surface is 428 m/s

A point located 1/4 of the length of the arc between the equator and the pole has an angle:

(1/4) × 90° = 22.5°

Since the arc angle of the line joining the equator and the pole is 90°

So the angle between the line joining the center and the given point, and the line joining center and the pole is  Φ = 90° - 22.5° = 67.5°

Now,

Sin Φ = (radius of the point)/(radius of the earth)

Sin 67.5 = radius of the point/(6.37 × 10⁶)

Radius of the point:

r = 6.37 × 10⁶ × 0.9239 = 5.885 × 10⁶ m

Speed of the point on the globe is v = 2πr/(24 hours)

2πr = 2π × 5.885 × 10⁶ = 3.6977 × 10⁷ m

So the speed of the point is :

v = 3.6977 × 10⁷/24

v = 1.541 × 10⁶ m/h

v = 428 m/s

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