A heavy rope, 60 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 130 ft high. (Let x be the distance in feet below the top of the building. Enter xi* as xi.)
a) How much work W is done in pulling the rope to the top of the building?
-Show how to approximate the required work by a Riemann sum.
-Express the work as an integral.
-Evaluate the intergral

Answer:

Approximately \(8.4 \times 10^{2}\; \rm N\), assuming that \(g = 9.8\; \rm m \cdot s^{-2}\).

Explanation:

Let \(m\) and \(a\) denote the mass and acceleration of Spiderman, respectively.

There are two forces on Spiderman:

The directions of these two forces are exactly opposite of one another. Besides, because Spiderman is accelerating upwards, the magnitude of \(F(\text{tension})\) (which points upwards) should be greater than that of \(W\) (which points downwards towards the ground.)

Subtract the smaller force from the larger one to find the net force on Spiderman:

\((\text{Net Force}) = F(\text{tension}) - W\).

On the other hand, apply Newton's Second Law of motion to find the value of the net force on Spiderman:

\((\text{Net Force}) = m \cdot a\).

Combine these two equations to get:

\(m \cdot a = (\text{Net Force}) = F(\text{tension}) - W\).

Therefore:

\(\begin{aligned}& F(\text{tension})\\ &= m \cdot a + W \\ &= m \cdot (a + g)\\ &= 76\; \rm kg \times \left(1.3\; \rm m \cdot s^{-2} + 9.8\; \rm m \cdot s^{-2}\right)\\ &\approx 8.4\times 10^{2}\; \rm N\end{aligned}\).

By Newton's Third Law of motion, Spiderman would exert a force of the same size on the strand of web. Hence, the size of the force in the strand of the web should be approximately \(8.4\times 10^{2}\; \rm N\) (downwards.)

Answer:

orbit the sun have very elliptical orbits

are made of frozen gas and ice

Explanation:

Comets are the made up of dry ice, frozen water, gases and dust particles. it is called dirty snow balls as their nucleus carry frozen water and pieces of rock.

Comets move around the sun in an elliptical orbits and follow Kepler's Laws saying that they move faster when closer to the Sun.

Comets have tails even when they are far from the sun and the tails that point away from the sun.

Hence, the correct options are "orbit the sun have very elliptical orbits and are made of frozen gas and ice".

Answer:

Orbit the sun

have very elliptical orbits

are made of frozen gas and ice

Explanation:

:)

Answer:

1.Magnetic Force - Used in cranes to separate metal junk from junkyards.

2.Frictional Force- Helps us to walk.

Answer: It is the act of measuring internal resistance.

Explanation:

It should be understood that when that action is exhibited, it is towards of measuring the internal resistance.

And it should be noted that, no matter how much or little load we attach to the battery, the voltage at the source's terminals will always stay the same.

Answer:

4 seconds

Explanation:

Answer:

They subtract the atomic number from the atomic mass

Hope this helps

Please mark as the brainliest

The orbital period of the Earth around the Sun is determined by its distance from the Sun and its mass. If the Earth had twice its present mass but orbited at the same distance from the Sun, its gravitational attraction to the Sun would be stronger, resulting in a longer orbital period. Using Kepler's third law of planetary motion, we can calculate the new orbital period as follows:

T^2 = (4π^2/G) x (r^3/m)

where T is the orbital period, G is the gravitational constant, r is the distance from the Earth to the Sun, and m is the mass of the Earth.

Plugging in the values, we get:

T^2 = (4π^2/6.6743 x 10^-11) x [(149.6 x 10^6)^3 / (2 x 5.9722 x 10^24)]
T^2 = 1.085 x 10^20
T = √(1.085 x 10^20)
T = 1.09 x 10^10 seconds

Converting this to years, we get:
T = 346 years

Therefore, if the Earth had twice its present mass but orbited at the same distance from the Sun as it does now, its orbital period would be approximately 346 years.

To know more about Kepler's third law :

https://brainly.com/question/30404084

#SPJ11

The scalar components R and R₂ of the force R along the nonrectangular axes a and b are determined using given information. The orthogonal projection Pa of R onto axis a is also calculated.

Given information:

Magnitude of force R = 810 N

Angle between R and axis a = 117°

Angle between R and axis b = 25°

To find the scalar components R and R₂, we can use trigonometry. Let's denote the angle between R and the x-axis as θ. We can express R in terms of its components as follows:

R = R₁ + R₂

Where R₁ is the component of R along axis a, and R₂ is the component of R along axis b.

Using trigonometry, we can determine the values of R₁ and R₂ as follows:

R₁ = R cos(θ)

R₂ = R sin(θ)

To find the angle θ, we subtract the given angles between R and axes a and b from 90° (since axis a and b are nonrectangular):

θ = 90° - 117° = -27°

Now we can calculate R₁ and R₂ using the given magnitude of R and the calculated angle θ:

R₁ = 810 N cos(-27°)

R₂ = 810 N sin(-27°)

Finally, to determine the orthogonal projection Pa of R onto axis a, we use the formula:

Pa = R₁ = 810 N cos(-27°)

Substituting the values into the equations, we can calculate the numerical values of R₁, R₂, and Pa.

To learn more about force refer:

https://brainly.com/question/12970081

#SPJ11

Answer:

8000cm³/hr

Explanation:

Given parameters:

Volume of the liquid draining off per hour   = 8000cm³

Time taken to drain off  = 1hr

Unknown:

Flow rate  = ?

Solution:

Flow rate is the volume of fluid that passes per unit of time.

 Flow rate  = \(\frac{volume of fluid}{time taken}\)  

 Flow rate  = \(\frac{8000cm^{3} }{1hr}\)  

Flow rate  = 8000cm³/hr

Wavelength and Frequency:

The relationship between wavelength and frequency of light is inversely proportional.

Mathematically,

Where λ is the wavelength, f is the frequency, and c is the speed of light.

The speed of light is 3×10⁸ m/s

For the given case, the frequency is 4.40×10¹⁴ Hz

Therefore, the wavelength of the red stop light is 6.81×10⁻⁷ m

When Albert has an impulse of 29-newton seconds and an impact time of 12 seconds. then the force experienced is 2.4166 N

The product of the average applied force and the time for which it is exerted is known as an impulse.

the mathematical relation for impulse is

Impulse  = F * Δt

where F represents the force applied and Δt represents the time for which the force is applied

As given in the problem Albert has an impulse of 29-newton seconds and an impact time of 12 seconds

By using the formula for impulse

Impulse  = F * Δt

By substituting the respective values in the formula

29 = F×12

F = 2.4166 N

Thus, when Albert has a 29-newton-second impulse and a 12-second impact time. then 2.4166 N of force was applied.

Learn more about impulse, here

brainly.com/question/16980676

#SPJ1

Answer:

D

Explanation:

their octet is complete they don't react with any thing

Argon and krypton have similar properties, and they have a complete octet, which means that they do not react with anyone. Hence, option D is correct.

The phrase "inert gas" is a bit misleading because, in some circumstances, these gases can really be reactive. As a result, these gases are typically referred to as noble gases in the context of chemistry and materials science.

The term "noble" has historically been used in chemistry (and earlier in alchemy) to characterize the resistance of some metals to chemical reaction, and the term "noble gas" denotes the same resistance.

These are the inert gases which are mentioned in the periodic table.

To get more information about inert gases :

https://brainly.com/question/14234951

#SPJ5

Answer:

The single touch method of making a magnet is a simple way to magnetize a ferromagnetic material, such as a piece of iron. The process involves taking a magnet and bringing it into contact with the material to be magnetized, while moving it along the length of the material in a single direction. This process aligns the magnetic domains within the material, causing it to become magnetized. The strength of the resulting magnet depends on the strength of the magnet used and the length of time it is in contact with the material.

The process of making an electromagnet involves using an electric current to create a magnetic field. To make an electromagnet, a wire is wound into a coil around a magnetic core, such as an iron rod. When an electric current flows through the wire, it creates a magnetic field around the coil, which in turn magnetizes the magnetic core. The strength of the resulting magnet depends on the strength of the current flowing through the wire, the number of coils in the wire, and the type of magnetic core used. Electromagnets are commonly used in a variety of applications, including electric motors, speakers, and MRI machines.

Explanation:

Answer:

Air temperature and air pressure both decreases

Answer: A

Explanation:

Answer: D

Explanation:

Answer:

6097 = x

Explanation:

x = VT + at²/2

x= 2.7 * 35 + 9.8 * (35)²/2

x=6097

Answer: Heat and Light

Explanation:

The force that the other person must  apply is 75 N in opposite direction (right).

Applied force is defined as the force exerted on an object by another body or object.

The force applied by the other person is determined by applying Newton's second law of motion as follows;

F1  - F2= ma

where;

When an object moves at constant, acceleration = 0

F1 - F2 = 0

F1 = F2

F1 = 75 N, then F2 = 75 N in opposite direction.

Thus, the force that the other person must  apply is 75 N in opposite direction (right).

Learn more about applied force here: https://brainly.com/question/14428983

#SPJ1

Answer:(D.)

Explanation:

Answer:

C. Bacteria

Explanation:

Bacteria and archaea are the two domains which consist of organisms with prokaryotic cells. Prokaryotic cells are cells without nuclei or membrane-bound organelles.

Work is performed while initially lifting books off the floor. The work is due to gravity.

To determine the velocity of the system after the catch, we need to consider the concept of momentum conservation. The momentum of an object is the product of its mass and velocity.

Given that the mass of the NFL football is 430 g, we need to convert it to kilograms:

Mass = 430 g = 0.43 kg

Let's assume the football is caught by a receiver who is also moving to the right. Since both the football and the receiver are moving in the same direction, their velocities will have the same sign.

The momentum before the catch is zero since the football is in motion and the receiver is stationary. After the catch, the momentum of the system should still be zero to conserve momentum.

Using the equation for momentum:

Momentum = Mass × Velocity

Since the momentum before the catch is zero, the momentum after the catch should also be zero. Therefore, the product of the mass and velocity of the football and the receiver should sum up to zero.

0 = (Mass of football × Velocity of football) + (Mass of receiver × Velocity of receiver)

Given the mass of the football and assuming the mass of the receiver is unknown, we cannot determine the exact velocity of the system after the catch without additional information.

Therefore, without the mass or velocity of the receiver provided, we cannot calculate the velocity of the system after the catch.

Learn more about momentum conservation here:

brainly.com/question/29220242

#SPJ11.

Answer:

If you have a parental figure or guardian ask them for assistance. Contact a lawyer if you are willing to take action against your attacker.

Heat received by cold water equals heat lost by hot water. 60°C is the ultimate temperature.

An evaluation of an object or substance's warmth or coolness in relation to a reference value.

a measurement of how much heat is required to raise the temperature of a material by one degree Celsius for every gramme.

The unit of measurement for specific heat is Joules per gramme per degree Celsius (J/g °C).

Let c represent the water's specific heat.

based on the calorimetry concept.

Heat received by cold water equals heat lost by hot water.

200 * c * (80 - T) = 100 * c * (T - 20) (T - 20)

∴ 200c (80-T) = 100c(T-20) (T-20)

∴2 (80-T) = T - 20

∴160-2T=T-20

∴ 160+20 = T +2T

∴180 = 3T

∴T = 60 C.

To learn more about temperature refer to:

https://brainly.com/question/12180540

#SPJ1

To achieve a net eastward speed despite the wind, the plane should aim to move in a direction south of east. This means the plane needs to offset the wind's westward component by adjusting its course to the east.

By flying south of east, the plane's velocity vector will have both an eastward and southward component. To determine the specific angle south of east, we can use trigonometry. Let's assume the angle south of east is θ. The wind's velocity vector can be represented as Vw, and the plane's velocity relative to the ground can be represented as Vp.

We can break down the wind's velocity into its eastward (Vwe) and northward (Vwn) components using the angle θ. The eastward component is given by Vwe = Vw * cos(θ), and the northward component is Vwn = Vw * sin(θ).

To achieve a net eastward speed, the plane's velocity relative to the ground in the eastward direction (Vpe) should be equal to the wind's eastward component: Vpe = Vwe.

Finally, the plane's velocity relative to the ground can be calculated as Vp = √(Vpe² + Vwn²).

For the speed of the plane relative to the ground, we only need to consider the magnitude of Vp.

Therefore, to find the direction south of east and the speed of the plane relative to the ground in this case, we would need the specific values for the wind's velocity and the desired speed of the plane.

to know more about wind's velocity  click this link-

brainly.com/question/8486728

#SPJ11

The density for a. Mass= 14 g Volume= 28 ml is 0.5 g/ml.

The density for b. Mass= 48 g Volume= 6 cm³ is  8 g/cm³.

The density for c. Mass= 125 g Volume= 12.5 ml is 10 g/ml.

The density for d. Mass=18.7 g Volume =18.7 cm^3 is 1 g/cm³.

The density for e. Mass=15 g Volume=60 ml is 0.25 g/ml.

The density of an object is the ratio of mass to volume of the object. The unit of density is kg/m³, g/cm³ or g/ml, etc.

The density of each object is calculated as follows;

density = mass /volume

density = 14 g / 28 ml

density = 0.5 g/ml

density = mass /volume

density = 48g / 6 cm³

density = 8 g/cm³

density = mass /volume

density = 125 g / 12.5 ml

density = 10 g/ml

density = mass /volume

density = 18.7g / 18.7 cm³

density = 1 g/cm³

density = mass /volume

density = 15 g / 60 ml

density = 0.25 g/ml

Learn more about density here: https://brainly.com/question/6838128

#SPJ1

Answer:

it's answer is Compound chemical energy

hope it helps you

Answer:

T is less than or equal to 19 N

Explanation:

Answer:

Below

Explanation:

384 400 km / 300 000 km/s = 1.28 seconds