Nuclear decay occurs according to first-order kinetics. What is the half-life of polonium-218 if a sample decays from 55. 4 g to 31. 7 g in 2. 50 minutes?.

Answers

Answer 1

The half-life of polonium-218 if a sample decays from 55. 4 g to 31. 7 g in 2. 50 minutes is 3.5 minutes.

Rate of first order reaction is given by:[tex]kt = 2.303 * log(R'/R)[/tex]

Where , k = rate of reaction

             t= time = 2.5 minutes

             R= final amount = 31.7g

             R'= initial amount = 55.4g

Putting these values in above equation we get k = 0.22

Now half life of a first order reaction is given by: 0.693/k

Putting k= 0.22 , we get half life = 3.5 minutes.

So the half-life of polonium-218 if a sample decays from 55. 4 g to 31. 7 g in 2. 50 minutes is 3.5 minutes.

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Related Questions

An electric iron consumes energy at the rate of 420 W when heating is at the maximum rate and 180 W when heating is at the minimum rate. The applied voltage is 220 V. What is the current in each case?

Answers

when heating is at the minimum rate. The applied voltage is 220 V. The current in each case is 271.60 (approx)

P = VI   V is voltage and I is current

then,

I = P/V

when heating is at maximum

current:

I = 420W/220V

=1.9(approx)

resistance:

R = V/I

= 220V/1.9A

=115.78(approx)

when heating in minimum

current:

I = P/V

= 180W/220V

= 0.81 (approx)

resistance:

R = V/I

=220V/0.81A

=271.60 (approx)

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a car traveling at 15 m/s slams on its brakes and the wheels lock. the car comes to rest after skidding 20 m. determine how far the car would skid if the car had been traveling, instead, at 45 m/s.

Answers

The distance travelled by the car if had been travelling at a speed of 45 m/s is 180 m.

What is the distance travelled by the car?

The distance travelled  by the car is calculated by applying the following kinematic equation as shown below.

v² = u² + 2as

where;

v is the final velocity of the car when it stops = 0u is the initial velocity of the car = 15 m/ss is the distance travelled by the car = 20 ma is the acceleration of the car = ?

0 =  u² + 2as

-2as =  u²

a = -(u²)/2s

a = - (15²) / (2 x 20)

a = -5.625 m/s²

The distance travelled by the car if had been travelling at a speed of 45 m/s is calculated as;

v² = u² + 2as

0 =  u² + 2as

s = -(u²)/2a

s = -(45²) / (2 x - 5.625)

s = (45²) / (2 x 5.625)

s = 180 m

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A lab technician uses laser light with a wavelength of 640 nm to test a diffraction grating. When the grating is 40.8 cm from the screen, the first-order maxima appear 6.00 cm from the center of the pattern.

Answers

A lab technician uses laser light with a wavelength of 640 nm to evaluate a diffraction grating, and this particular grating has 195.31 lines per millimeter.

Its wavelength is 640 nm.

L=40.8 cm The distance between the grating and the screen

The first dazzling fringe is six centimeters away from the centre of the order for laser light. According to the deduced results from Young's experiment, which tie the order of bright fringes to the central order,

With the approach of laser light is small-angle approximation, y = m(wavelength)(L)/d and d = m()(L)/y

Using the value d= 1*640*10^-9*0.48/0.06m = 5.120*10^-9 as a starting point

The line density is 1/d = 1/5.120*10^-9, or 195.31 lines per millimeter.

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A book weighing 10 kg is preparing to fall off the desk from a 1 meter height. The book's
gravitational potential energy is 980 Joules.
O True
O False

Answers

Answer:

False

Explanation:

gravitational potential energy = mgh

10*10*1 = 100 joules

a spring has a natural length of 12.0 cm. if a 26.0-n force is required to keep it stretched to a length of 26.0 cm, how much work w is required to stretch it from 12.0 cm to 19.0 cm? (round your answer to three decimal places.)

Answers

The work required to stretch the spring from 12 cm to 19 cm is 0.91 J

What is work done ?

When an object is moved across a specific distance by an external force, work is the quantity of energy that is transmitted to the object.

According to the given information

Natural length = 12 cm

Stretched length = 26 cm

Change in length ( x ) = 26 - 12 = 14 cm = 0.14 m

Force required = 26 N

It is known to us that spring force F = K x

K = [tex]\frac{F}{x}[/tex]

K = [tex]\frac{26}{0.14}[/tex]

K = 185.7 N/m

This is the stiffness of the spring

Now the Force that is required to stretch the spring F = K[tex]x_{1}[/tex]

[tex]x_{1}[/tex] = change in length of the spring = 19 - 12 = 7 cm = 0.07 m

F = 185.7 × 0.07

F = 13 N

Now the work that is done in stretching the spring W = F × [tex]x_{1}[/tex]

W = 13 × 0.07

W = 0.91 J

The work required to stretch the spring from 12 cm to 19 cm is 0.91 J

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a satellite is orbiting a planet a distance r from its center and another satellite is orbiting at a distance 3r from its center. what is the relation between the accelerations due to gravity for each case?

Answers

Answer:

The relation between acceleration due to gravity for both cases [tex]g_{1} = 9g_{2}[/tex]

Explanation:

What is acceleration due to gravity ?

Any object's acceleration when it is only being affected by gravity.

According to the given information

Acceleration due to gravity could be found by  [tex]\frac{GM}{r^{2} }[/tex]

Distance between satellite orbiting planet from center = r

Acceleration due to gravity for this case [tex]g_{1}[/tex] = [tex]\frac{GM}{r^{2} }[/tex]

Distance between satellite orbiting planet from center = 3r

Acceleration due to gravity for this case [tex]g_{2}[/tex] = [tex]\frac{GM}{(3r)^{2} }[/tex]

relation between the acceleration due gravity in each case

[tex]\frac{g_{1} }{g_{2} } =\frac{(3r)^{2} }{r^{2} } \\[/tex]

[tex]\frac{g_{1} }{g_{2} } =\frac{9r^{2} }{r^{2} } \\[/tex]

[tex]\frac{g_{1} }{g_{2} }[/tex] = 9

[tex]g_{1} = 9g_{2}[/tex]

The relation between acceleration due to gravity for both cases [tex]g_{1} = 9g_{2}[/tex]

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A slinky is stretched by two forces. When the forces are removed, the slinky returns to its original length. The slinky has been __________ deformed.

Answers

A slinky is stretched by two forces. When the forces are removed, the slinky returns to its original length. The slinky has been permanently deformed.

What causes permanent deformed?

When a material is subjected to stresses that are greater than its yield strength and cause it to elongate, compress, buckle, bend, or twist, this permanent distortion is known as plastic deformation.

Plastic deformation occurs when a metal is sufficiently stressed to permanently alter its shape. A few atomic bonds are broken during plastic deformation, as was covered in the section on crystal defects, as a result of the movement of dislocations.

When a structural part of a rail vehicle experiences permanent deformation, its shape changes.

Therefore, A slinky is stretched by two forces. When the forces are removed, the slinky returns to its original length. The slinky has been permanently deformed.

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force on moving charges: an electron moves with a speed of 8.0 × 106 m/???? along the x-axis. it enters a region where there is a magnetic field of 2.5 T, directed at an angle of 60° to the x ????x???????? and lying in the xy p????????????????. calculate the magnitude of:

Answers

The electron is subjected to a magnetic field accelerates at a rate of 3.0 E18 m/s.

What is a good example of the magnetic force?

The magnets are attracted to or repelling one another as a result of this force. A compass, a motor, magnetic magnets that hold items in refrigerators, railroad tracks, and modern roller coasters are examples of objects that use magnetic force. A magnetic field is created by all moving charges, and any charges that move across its regions feel a force.

F=qvBsinθ

F=1.6×10−19 C×8.0×106m/s×2.5T×sin60∘

F=2.8×10−12 N

What is an example of a Class 8 magnetic force?

A magnet exerts a magnetic pull on particular materials like metal, steel, nickel, and cobalt. This force can work from a distance, making it a sort of non-contact force. It does not needed that the objects be in direct contact. We learnt how to utilize a magnet to draw coins in the example above.

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Show that the Poisson bracket of two constants of the motion is itself a constant of the motion, even when the constants depend upon time explicitly.

Answers

Poisson brackets are powerful and sophisticated tool in the Hamilton formalism of classical mechanism.

The nonverbal code that most explicitly deals with movements and motion-based behaviors is known as kinesics.

Kinesics in Poisson bracket describes the way our hands, arms, faces, and bodies move to express meaning. It's our body language throughout a discussion or how we appear when we're speaking. This might show that we are interested in the interaction and are confident in it.

Poisson bracket refers to a broad range of visual codes involving the movement of the human body. Among these codes are gestures, posture, eye gaze, and facial expressions. Artifacts represent the various ways that we adorn or manipulate the body to communicate cultural or personal meanings.

Therefore, these Poisson bracket also shows a link between quantum and classical mechanism.

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Nasa’s orion spacecraft, which left earth last week, flew within 81 miles of the surface of which celestial body on monday?.

Answers

Nasa’s Orion spacecraft, which left earth last week, flew within 81 miles of the surface of the moon on Monday .

What is the Orion spacecraft?The NASA Artemis program uses the crewed Orion spacecraft, which is largely reusable. The spacecraft is made up of an Airbus Defence and Space European Service Module and a Lockheed Martin Crew Module space capsule.This picture, obtained by a camera on the tip of one of Orion's solar arrays on the sixth day of the Artemis I mission, shows a significant chunk of the far side of the moon just beyond the Orion spacecraft.On Nov. 20, 2022, the spacecraft entered the lunar sphere of influence, making the moon the major gravitational force pulling on it rather than Earth. Its closest approach, which occurred on November 21, was at a distance of 80 miles from the lunar surface.Orion takes pictures of Earth and the moon at various phases and distances using its optical navigation camera.

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which term best describes the shape of jupiter's orbit around the sun?

Answers

Answer:

Explanation:

Kepler's First Law Describes the Shape of an Orbit

The orbit of a planet around the Sun (or of a satellite around a planet) is not a perfect circle. It is an ellipse—a “flattened” circle. The Sun (or the center of the planet) occupies one focus of the ellipse.

a resistor and inductor are connected to a 9.0 v battery by a switch as shown. the moment the switch is closed, current flows through the circuit. the resistor has a resistance of r

Answers

The resistance of the resistor r so maximum current is 40.9 mA.

A Resistor and inductor are connected to a 9.0 v battery by a switch as shown. the moment the switch is closed, current flows through the circuit. the resistor has a resistance of r.

Calculation:-

Maximum current imax = V/R

= 9/220

= 40.9 mA.

Resistors are used for many purposes. a few examples consist of restricting electric powered cutting-edge, voltage division, warmth generation, matching and loading circuits, benefit manage, and setting time constants. they may be commercially available with resistance values over various extra than nine orders of magnitude.

A circuit is a entire circular direction that energy flows via. A easy circuit includes a modern supply, conductors and a load. The time period circuit may be utilized in a preferred sense to consult any fixed route that energy, records or a sign can travel via.

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from peak to trough a wave on the ocean measures 15\;\mathrm{m}15m in height and has a wavelength of 12\;\mathrm{m}12m. what is the amplitude of the wave?

Answers

The size of a wave is equivalent to half its top to valley distance, which is the solution to the question.

How can one measure wavelength? What is a wave length?

A wave sensor's length, which corresponds to the distance between two identical locations (next crests) in successive cycles, determines whether it is sent through space or via a wire. In wireless systems, this length is often specified in meters (m), centimeters (cm), or millimeter (mm) (mm). The duration can be calculated as the distance between two contiguous wave front peaks or waves propagating compressions. It is often represented in meters. Such waves have a relationship between their energy and wavelength. Waves with a shorter wavelength have had more energy than waves with a longer wavelength of the same intensity.

Briefing:

A = 1/2* distance

A = 1/2* 5.8

A = 2.9m

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The complete question is-

From Peak To Trough A Wave On The Ocean Measures 5.8 M And Has A Wavelength Of 22.5 M. What Is The Amplitude Of The Wave?

in situ quantification of the active sites turnover frequency and stability of ni-fe oxy hydrooxide for the oxygen evolution reaction

Answers

The intrinsic catalytic characteristics of nanoscale electro catalysts requires quantification of the active site count and site-specific turnover frequency (TOF).

How does turnover frequency and stability of ni-fe oxy hydroxide for the oxygen evolution reaction?

Understanding the intrinsic catalytic characteristics of nanoscale electro catalysts requires quantification of the active site count and site-specific turnover frequency (TOF).

The understanding of Ni-Fe (oxy)hydroxides' electro catalytic activity and stability is hampered by the lack of efficient methods for measuring the Fe active site number and the intrinsic turnover frequency per active Fe site (TOFFe), despite the fact that Fe has been proposed as one of the most active noble-metal-free electro catalysts for the alkaline oxygen evolution reaction (OER).

The direct in situ quantification of the electrochemically active Fe site number and associated TOFFe values of Ni-Fe (oxy)hydroxides using previously unstudied Fe2+/3+ redox electrochemistry in alkaline solutions is described in this article.

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what is the capacitive reactance ????c of a 60.0 μf capacitor placed in an ac circuit driven at a frequency of ????

Answers

Capacitive reactance is measured in Ohms, just like resistance. 1,000,000 divided by 6.28 times 60 hertz times 106.1 microfarads, or 25 ohms, is the capacitive reactance.

The amount of charging a capacitor can accomplish depends on its capacitance. Capacitive reactance is a measurement of the capacitor's resistance to alternating current. The following formula can be used to determine a capacitor's capacitive reactance or impedance: The constant one million (or 106) divided by the product of 2p (or 6.28) times frequency times capacitance is known as capacitive reactance, abbreviated as x sub c (XC). where XC is the capacitance, expressed in ohms.

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A 100-g firecracker is launched vertically into the air and explodes into two pieces at the peak of its trajectory. If a 72-g piece is projected horizontally to the left at 20 m/s, what is the speed and direction of the other piece?.

Answers

The second particle would therefore move at a speed of (-51.5) m/s.

What is Velocity ?

Velocity is the directionally speed of an object in motion, as measured by a certain unit of time and seen from a particular point of reference.

According to the given information

Mass (m) = 100 gm

20 m/s is the speed.

Vertical velocity is zero at its maximum.

The system's horizontal momentum is conserved because there is no horizontal force acting on it.

[tex]m_{2}[/tex] = 100-72= 28g

[tex]m_{1}v_{1} + m_{2}v_{2}[/tex] = 0

[tex]v_{2} = -\frac{m_{1}v_{1} }{m_{2} }[/tex]

[tex]v_{2}[/tex] = (72×20)/(28)

[tex]v_{2}[/tex] = -51.5 m/s

The second particle would therefore move at a speed of (-51.5) m/s.

Negative signs point in the direction of rightward motion.

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sunlight just outside earth's atmosphere has an intensity of 1.40 kw/m2. (a) calculate em for sunlight, assuming it to be a plane wave.

Answers

Electromagnetic waves for sunlight is  966.48  V/m

a) We know that the intensity of light

                 I = (1/2)ε0cEm2

From the above equation we can write

                Em = √(2I / ε0c)

                      = √2 * 1.24 x 103 / 8.85 x 10-12 * 3 x108

                      = 966.48  V/m

When an electric field and a magnetic field vibrate together, electromagnetic waves, or EM waves, are produced. Thus, magnetic and electric fields oscillate to form electromagnetic waves (EM waves). When an electric field and a magnetic field interact, electromagnetic waves are produced. It follows that they are referred to as "electromagnetic" waves. An electromagnetic wave's electric and magnetic fields are parallel to one another and form a right angle. In addition, they are parallel to the EM wave's direction.

In vacuum, the speed of electromagnetic waves is constant at 3.00 x 108 ms-1. Neither the electric nor magnetic fields can deflect them. On the other hand, they can exhibit diffraction or interference.

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a ball is thrown upward with an initial velocity of 64 feet per second at an initial height of 80 feet. find the positio

Answers

The position of the object thrown upward with an initial velocity of 64 feet per second at an initial height of 80 feet from the ground after 10 seconds from the ground is 709.38 m

According to equation of motion,

s = u t + 1 / 2 a t²

s = Displacement

u = Initial velocity

t = Time

a = Acceleration

u = 64 ft / s

u = 19.5 m / s

t = 10 s

s = ( 19.5 * 10 ) + ( 1 / 2 * 9.8 * 10² )

s = 195 + 490

s = 685 m

Total distance from the ground,

d = h + s

h = 80 ft = 24.38 m

d = 24.38 + 685

d = 709.38 m

The final position of the object from the ground is 709.38 m

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the flux through a loop of wire changes at a uniform rate from 4.0x10-5 wb to 5x10-5 wb in 0.10 s. determine the emf induced in the coil

Answers

The emf induced in the coil is 4.0x10-4 V.

What is the emf induced in the coil?The induced emf in a coil is determined by multiplying the coil's number of turns by the opposite of the magnetic flux's rate of change. It involves the interaction of a magnetic field and a charge.The induced emf is equal to (BA cos) = − d/dt. The magnetic field's strength might fluctuate over time. The region that the loop encloses is subject to vary throughout time.A motional emf is an emf that is caused by movement in relation to a magnetic field. The length of the object moving at speed v in relation to the magnetic field's strength B is represented by the equation emf = LvB.

Given data :

The induced emf is ε = - d/dt (BA cos θ).

d = 4.0x10-5Δd = 5x10-5t = 0.10 s

Apply the formula ,

induced emf is ε = - d/dt (BA cos θ).

= - 4.0x10-5 /  5x10-5 x 0.10 = 4.0x10-4 V.

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two balls having different speeds roll off the edge of a horizontal table at the same time. which hits the floor sooner, the faster ball or the slower one?

Answers

Two balls having different speeds roll off the edge of a horizontal table at the same time, both will hit the floor at the same time.

What is velocity?

Velocity is defined in physics as a vector measurement of direction and velocity of motion. More specifically, the velocity of an object can also be defined as the rate of change of the object's position with respect to the reference frame and time. Simply put, the term velocity describes how fast an object moves in a particular direction. Indicates whether something is moving slowly or quickly. Let's look at an example where two objects are moving. If two objects are moving in the same direction, it's easy to tell which is moving faster. However, it is very difficult to determine which object is faster when both are moving in opposite directions. Considering such difficulties and ways to overcome them, our scientists developed the concept of velocity to make it easier for observers to identify faster or slower objects.

Both balls will hit the ground simultaneously. This is because both balls were moving parallel to the ground when they left the table (remember the table is horizontal). Both balls have 0 velocity in the direction of interest, both accelerate at the same velocity and land at the same time.

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A 60⁢kg board that is 6 m m long is placed at the edge of a platform, with 4m of its length extending over the edge. The board is held in place by blocks of masses M1M1 and M2M2 placed with their centers of mass on either end. If M2=30kg M2=30kg , what is the minimum value of M1 needed to keep the board from falling off the platform?
30kg
50kg
60kg
70kg
90kg

Answers

The minimum value of M1 to keep a board from falling off the platform is 90 kg.

The mass (M1) placed on the left side edge of the board

the mass of the board = 60 kg

the length of the board = 6 m

If the mass on the right side = 30 kg, and the length of the board L1 = 2m

Then, the length L2 which extend over the edge = 4m

Consider the center of gravity in the board that lies at the length of the board midpoint.

Then, the distance (D) of the gravity center from the platform end = 3 - 2

= 1

The moment when the platform end, the mass (M1) placed on the left side edge of the board can be computed as:

M1= 60kg+120kg/2

M1=180kg/2

M1=90kg

Therefore, The minimum value M1 needed to keep the board from falling off the platform is 90 kg.

Mass is a quantitative measure of inertia, a fundamental property of matter.

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a rope of mass m and length ` hangs from the ceiling. (i) what is the wave speed on the rope a distance y above the lower end?

Answers

A rope with the mass m and length L hangs from a ceiling. Show that the rope's wave speed at a distance of y above the lower end is v = gy.

What is the name for a wave's speed?

Wave speed is a feature of waves that can be used to describe the absolute value of phase velocity or the speed at which a wave phase moves at a specific frequency. group velocity, which differs from the phase velocity for dispersive waves, is the rate of propagation for the envelope of wave groups and frequently of wave energy.

What is a straightforward definition of wave velocity?

The distance a wave travels in a unit of time is measured by its wave velocity. It is the rate at which a particle is disturbed by something like a peak

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A 5. 00-m-long ladder, weighing 200 n, rests against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1. 20 m away from the wall. The center of mass of the ladder is 2. 50 m from its base, and the coefficient of static friction between the ladder and the floor is 0. 200. How far up the ladder, measured along the ladder, can a 600-n person climb before the ladder begins to slip?.

Answers

the ladder, measured along the ladder, can a 600-n person climb before the ladder begins to slip is 0.488  m  

What is a ladder used for?A ladder is a piece of equipment consisting of repeated bars or steps (rungs) between two upright lengths of metal, wood, or rope, used for climbing up or down something.Choosing the Right Ladder. Ladders are built from one of three basic materials; wood, fiberglass and metal (aluminum).Ladder diagrams are specialized schematics commonly used to document industrial control logic systems. They are called “ladder” diagrams because they resemble a ladder, with two vertical rails (supply power) and as many “rungs” (horizontal lines) as there are control circuits to represent.Maintain a 3-point contact (two hands and a foot, or two feet and a hand) when climbing/ descending a ladder. Stay near the middle of the ladder and face the ladder while climbing up/down. Use a barricade to keep traffic away from the ladder. Keep ladders free of any slippery materials.

0.488  m  

If θ be the angle ladder makes with the plane

cos θ = 1.2 / 5

Tan θ = 4.04

Let the height a person of weight 600 N  can climb be h from the ground .Distance from the base point  where ladder touches the floor  = h / tanθ

= h / 4.04

Total reaction force = total downward force

R = 200 + 600

800 N

Frictional force = μ R

= .2 x 800

= 160 N

Taking moment of force about the point on the ladder  where it  touches the floor  and balancing them

200 x 1.2 x .5 + 600 x   h / tanθ  = μ R x  1.2 / tanθ ( reaction  at the top point of ladder where it touches the wall is  R₁ and

R₁ =μ R   )

= 200 x 1.2 x .5 + 600 x   h / tanθ  = 160 x 1.2 / tanθ

120  - 600 h / 4.04 = 47.52

120 - 47.52 = 600 h / 4.04

72.48= 148.51 h

h = 0.488  m  

=

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. a 750 kg automobile is moving at 20.0 m/s at a height of 5.0 m above the bottom of a hill when it runs out of gasoline. the car coasts down the hill and then continues coasting up the other side until it comes to rest. ignoring frictional forces and air resistance, what is the value of h, the highest position the car reaches above the bottom of the hill?

Answers

The highest position the car reaches above the bottom of the hill is 20.9m.

Solution:

U = mgh

K= 1/2 mv2

Ki+Ui = Uf

750(0.5)(400)+750(9.8)(5)=(750)(9.8)h

200+4.9=9.8h

h = 20.9 m

Frictional force refers to the force created by two surfaces contacting and sliding against each other. Several factors affect frictional forces: These forces are primarily affected by surface textures and the forces that drive them together.

Scientists don't know exactly what causes friction. However, it is thought to be caused by interactions when small bumps on the surface rub against each other. The ridges on each surface flex and exert forces on each other making the surfaces less slippery against each other.

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escribe the following metrology tools: scales, calipers, coordinate measuring machine, and 3-d laser scanner. which is least expensive? which is most accurate?

Answers

3D lasers scanner: uses laser projector and cameras to determine part dimensional coordinates to high degree of accuracy, high cost.

Scales: similar to a ruler used for linear measures with "eyeball" accuracy, traditional, affordable, and occasionally insufficiently exact.

Measurements are fairly accurate thanks to the caliper's ability to expand to fit the part being measured.

Coordinate measuring machine: uses probe to touch part and senses x, y, and z coordinate locations that record information into memory (also known as digitizing model), accuracy in the 0.001 mm range, larger volumes greatly increase system cost

No of the size or surface details of the object being scanned, 3D laser scanner uses either phase-based or LIDAR technology to reliably and effectively gather 3-dimensional data. 3D laser scanning generates clear and accurate digital records of present conditions without actually touching what is being measured. The scan generates countless numbers of measurement points known as "coordinates." "Point clouds" are collections of points that together represent raw data. An x, y, and z value is contained in each coordinate in a point cloud. These values are often referred to as northing (y), easting (x), and elevation (z). These points have such fine precision that it is possible to measure exactly from one point to any other point in the point cloud.

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what is the greatest distance, measured from the pivot, that the center of gravity of an 600 kg piece of heavy machinery can be placed without snapping the rope?

Answers

The greatest distance that is measured from the  the pivot, that the center of gravity of an 600 kg piece of heavy machinery can be placed without snapping the rope is 1.37 m

How to solve for the greatest distance

We would have to solve for the tensile strength first.

The tensile strength is given as: T /A

The radius = diameter / 2

= 7 / 2

= 3.5

area = πr²

=We would have to solve for the maximum force from here

6 x 10⁷ x π *(3.5*10⁻³)² = 2309.1

Next we would have to solve for the greatest distance

The net torque is given as 0

Fmax x L = m*g*x

2309.1*3.5 = 600*9.8*x

8081.85 = 5880x

divide through to get the value of x

x = 8081.85 /  5880

= 1.37m

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46. the sled is pulled up a higher hill that is less steep than the original hill described before question 44. how does the speed of the sled at the bottom of the hill (after it has slid down) compare to that of the sled at the bottom of the original hill?

Answers

Both hills' lowest speeds for the sled are the same.

Why would someone use a sled?

Sleds—also known as sleighs—are wintertime vehicles that are often pulled across ice or snow by either horses or dogs. The travois and the sidecar, which were its predecessors, are said to have been the earliest human-powered vehicles.

What is the difference between a sled and a sleigh?

An open-topped, often medium- to large-sized sleigh is used to transport people or cargo. Reindeer, dogs, or horses are frequently used as the drivers. While the name "sled" is still used generally in American parlance, it frequently refers to a smaller, frequently recreational, equipment.

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A satellite used in a cellular telephone network has a mass of 2050 kg and is in a circular orbit at a height of 880 km above the surface of the earth.
Part A
What is the gravitational force Fgrav on the satellite?
Take the gravitational constant to be G = 6.67×10−11 N⋅m2/kg2 , the mass of the earth to be me = 5.97×1024 kg , and the radius of the Earth to be re = 6.38×106 m .
Express your answer in newtons.

Answers

The Gravitational Force, Fgrav on the satellite is 1.548 x 10⁴  N.

Newton's Gravitational Law - The force between two objects is directly proportional to the product of their masses and the force between two objects is inversely proportional to the square of the distance between them.

We use the Newton's Gravitational Law formula to find the Gravitational Force on the satellite :

F = G (m₁ m₂)/r²

where,

F = Gravitational Force

G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

m₁ = mass of earth = 5.97 x 10²⁴ kg

m₂ = mass of satellite = 2050 kg

radius of earth = 6.38 x 106 m

r = distance between the centre of earth and the centre of satellite

r = distance of satellite from the surface of earth + radius of earth

r = 880000 m + 6380000 m = 7260000 m

Therefore,

             (6.67 x 10-11  N.m²/kg²).(5.97 x 10²⁴ kg).(2050 kg)

    F  =  --------------------------------------------------------------------------

           (7260000 m)²

    F = 1.548 x 10⁴  N

The Gravitational Force, Fgrav on the satellite is 1.548 x 10⁴  N.

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what is the potential energy u of the toy when the spring is compressed 3.2 cm from its equilibrium position?

Answers

Total energy in compressing a spring is [tex]kx^{2}/2[/tex].

When we compress or extend a stretched spring, we experience a force equal to that applied by us in the opposite direction.When a spring deviates from its mean position, it tends to restore its equilibrium by exerting a force equal and opposite to the external force. We have seen the application of spring force in bicycle carriers and launching devices where the energy gained by disturbing the equilibrium of the spring is utilized as its potential energy and converted to other forms.

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suppose that a planet was reported to be orbiting the sun-like star iota horologii with a period of 300 days. find the radius of the planet's orbit, assuming that iota horologii has four times the mass as the sun.

Answers

Radius of the planet's orbit is 2.15 * [tex]10^{-6}[/tex] m

Radius of the orbit can be calculated by applying Kepler's third law, which  compares the motion characteristics of different planets, i.e. it compares the orbital period and the radius of the orbit.

Mathematically, [tex]T^{2} = 4\pi ^{2} * r^{3} / GM[/tex]

Where

T = Time period = 300Days ( Period)

r = radius

G =   Gravitational constant = 6.67 * [tex]10^{-11}[/tex] m³/Kgs

M =  Mass of the object, sun in this case = 1.99 * [tex]10^{30}[/tex] kg

Then, rearranging the Kepler's equation,

[tex]R^{3} = GMT^{2} /4\pi ^{2}[/tex]

R³ = 100 * [tex]10^{-19}[/tex]

R = 2.15 * [tex]10^{-6}[/tex] m

The radius of the planet which is reported to orbiting for 300 days is 2.15 * [tex]10^{-6}[/tex] m

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