A 500-mm-long, 16-mm-diameter rod made of a homogenous,
isotropic material is observed to increase in length by 300 mm, and
to decrease in diameter by 2.4 mm when subjected to an axial 12-
kN load. Determine the modulus of elasticity and Poisson's ratio of
the material. [20 marks]

Answer:

True:

F1 = G M1 M2 / R^2

F2 = G (2 M1) * (2 M2) / (2 R)^2

F1 = F2

Answer:

6.45

Explanation:

Got it right on Acellus

Answer:

Explanation:

charge on each proton = 1.6 x 10⁻¹⁹ C

mass of proton = 1.67 x 10⁻²⁷ kg

Electrostatic force of repulsion Fe = 9 x 10⁹ x ( 1.6 x 10⁻¹⁹ )² / d²

= 23.04 x 10⁻²⁹ / d²

Gravitational  force of attraction = G Mm / d²

M = m = 1.67 x 10⁻²⁷ kg

Gravitational  force of attraction  Fg = 6.67  x 10⁻¹¹ x ( 1.67 x 10⁻²⁷ )² / d²

= 18.60 x 10⁻⁻⁶⁵ / d²

So Fg is far less than Fe and former is attractive , later is repulsive .

Fe > Fg, opposite direction , is the answer .

Answer:

C

Explanation:

The total height of the building from which the brick is thrown is 33.60 meters.

Speed is the rate of change of position of an object in any direction with respect to time. Speed is measured as the ratio of distance to the time in which the distance was covered. The SI unit of speed is m/s (meter per second).

The time of flight of the object from the building is:

t = 2μ sinθ/ g

t = 2 × 15 × sin10/ 9.8

t = 30 × 0.175/ 9.8

t = 0.535 seconds

Total time to cover the distance = 2.9 seconds

Total time = 2.9 - 0.535

Total time = 2.365

μg = μ sinθ

h = 15 × sin10  × 2.365 + 1/2 × 9.8 × (2.365)²

h = 2.625 × 2.365 + 1/2 × 9.8 × (2.365)²

h = 6.20 + 4.9 × 5.59

h =  6.20 + 27.40

h = 33.60 meters

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Answer:

a) Joules

b) W (symbol for work) (J is symbol for Joules)

c) seconds

d) watts

According to the right-hand rule, the magnetic field of the solenoid will be directed towards the left direction.

Right Hand Thumb Rule is the rule which is used If a current carrying conductor is imagined to be held in the right hand direction such that the thumb always points along the direction of the current flow, then the direction of the wrapped fingers in the hand will give the direction of the magnetic field lines of the bar magnet.

By the application of the right-hand rule, the magnetic field of the solenoid will be directed towards the left hand direction.

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The two charges, each of magnitude 6.0 μC, exert a force of 0.70 N at separation  of 1.47 meters.

Electric force is the attracting or repulsive interaction between any two charged things. Similar to any force, Newton's laws of motion describe how it affects the target body and how it does so. One of the many forces that affect objects is the electric force.

We know that electric force can be defined as:

Force: F = kQq/r²

0.70 = 9.0 × 10⁹ × (6.0×10⁻⁶)²/r²

r = 1.47 meter.

Hence, the separation between them is 1.47 meters.

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Answer:

a) the modulus of elasticity (E) is 68.22 GPa

b) the modulus of elasticity in shear is 25.28 GPa

Explanation:

Given the data in the question;

First we determine the cross-sectional area A of the road;

A = π/4 × d²

given that; diameter d = 20 mm

we substitute

A = π/4 × ( 20 mm )²

A = π/4 × 400 mm

A = 314.159 mm²

Next, we find, the normal stress of the rod σ

σ = P / A

given that load p = 50 kN = 50,000 Newton

we substitute

σ = 50,000 N / 314.159 mm²

σ = 159.155 N/mm²

σ = 159.155 Mpa

Next, is the normal strain ε

ε = δ / L

given that; change in length δ = 1.40 mm and Length of rod L = 600 mm

we substitute

ε = 1.40 mm / 600 mm

ε = 0.002333

Now, we find the modulus of elasticity;

we know that;

σ = Eε

modulus of elasticity E = σ / ε

we substitute

E = 159.155 Mpa / 0.002333

E = 68219.031 MPa

E = ( 68219.031 / 1000 ) GPa

E = 68.22 GPa

Therefore, the modulus of elasticity (E) is 68.22 GPa

b)

we know that the Poisson's ratio v is;

v = -(ε[tex]_{lat[/tex] / ε )

v = - (((d[tex]_f[/tex] - d)/d) / ε )

where d[tex]_f[/tex]  is the final diameter of the rod ( 19.9837  mm ) and ε[tex]_{lat[/tex] is the lateral strain

so we substitute

v = - ((( 19.9837 - 20 ) / 20 ) / 0.002333  )

v = - (( -0.0163 / 20 ) / 0.002333  )

v = - ( - 0.000815 / 0.002333 )

v = - ( - 0.3493 )

v = 0.3493

So, our shear modulus will be;

G = E / 2( 1 + v )

we substitute

G = 68.22 GPa / 2( 1 + 0.3493  )

G = 68.22 GPa / 2( 1.3493  )

G = 68.22 GPa / 2.6986

G = 25.28 GPa

Therefore, the modulus of elasticity in shear is 25.28 GPa

Answer:

d = 11.1 m

Explanation:

Since the inclined plane is frictionless, this is just a simple application of the conservation law of energy:

[tex] \frac{1}{2} m {v}^{2} = mgh[/tex]

Let d be the displacement along the inclined plane. Note that the height h in terms of d and the angle is as follows:

[tex] \sin(15) = \frac{h}{d} \\ or \: h = d \sin(15) [/tex]

Plugging this into the energy conservation equation and cancelling m, we get

[tex] {v}^{2} = 2gd \sin(15)[/tex]

Solving for d,

[tex]d = \frac{ {v}^{2} }{2g \sin(15) } = \frac{ {(7.5 \: \frac{m}{s}) }^{2} }{2(9.8 \: \frac{m}{ {s}^{2} })(0.259)} \\ = 11.1 \: m[/tex]

Answer:

Explanation:

Add a horizontal line.  An object that is not moving has no change in distance with respect to time.

If an object is working against gravity, that means gravity must have the opposite sign of the object (this is why we see objects slow down at their peak height and return to us if we throw them in the air!). If the object is working with gravity, though, they must both be moving in the same direction, therefore gravitational acceleration would be the same sign as the velocity (positive or negative depending on how you define your axes).

Therefore, your answer should be C. Different sign + or - on the acceleration.

I hope this helps!

Answer:

Explanation:

Time elapsed to reach the height of 230 m be t

s = ut + 1/2 at²

230 = .5 x 3.45 t²

t = 11.55 s

velocity at height of 230 m

v = u + at

= 0 + 3.45 x 11.55 = 39.84 m/s

This velocity will be attained by canister .

time to reach zero velocity at the top position t

v = u - gt

0 = 39.84 - 9.8 t

t = 4.06 s

height travelled by canister during this 4.06 s

v² = u² - 2gH

0 = 39.84² - 2 X 9.8 H

H = 80.98 M

Total height attained by canister = 80.98 + 230 = 310.98 m

Time of fall by canister t

s = 1/2 gt²

310.98 = .5 x 9.8 t²

t = 7.97 s

Total time taken by canister to reach the ground after its release from rocket

= 4.06 + 7.97 = 12.03 s

Distance travelled by rocket in 12.03 s

s = ut + 1/2 a t²

= 39.84 x 12.03 + .5 x 3.45 x 12.03²

= 479.27 + 249.64

= 728.91 m

height of rocket required = 230 + 728.91

= 958.91 m

2 )

Distance travelled by canister between its release and fall on the ground

= 80.98 + 80.98 + 230

= 391.96 m.

Answer: Pedaling your bike : acceleration :: applying the brakes : inertia.

The reason I think this to be the answer to the analogy is because there is energy and work used in both processes (and the unit focuses on forces); gravity is constant and does not change whether one pedals or applies brakes. And I do not think it's deceleration, as deceleration tends to equate to acceleration within the physics perspective.

Edit: I should also add that since you clarified that your unit is motion and forces, Newtons 1st law is the law of inertia. The way to change an objects motion for it to slow down is by applying an additional force. That resistance the bike experiences to slow is the process of inertia. Inertia happens in order to accelerate an object (either by slowing it down, or speeding it up): i.e., the resistance to change.

The force needed to accelerate the mass of 100 kg is 500 N.

Force is the product of mass and acceleration. The S.I unit of force is Newton (N).

To calculate the amount of force needed to accelerate the mass of 100 kg, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the force is 500 N.

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Answer:

a. 25000J or 25KJ

b.2500w

Explanation:

a. since we say work is force applied in the same line or straight line

W=F(newtons )*D(metres)

b. power is work over time

Answer:

25000 J work with 2500 W power

Explanation:

work done = force . displacement = 500 N . 50 m= 25000 J

Power= work done / time taken = 25000 J / 10 s = 2500 W

Answer:

Describe how one-dimensional vector quantities are added or subtracted.

Answer: A. Earth to circle the sun one time.

Proxima Centauri otherwise known as Alpha Centauri C, is the closest star to our solar system, located about 4.24 light-years away. It was discovered in 1915 by Robert Innes, the director of the Union Observatory in South Africa. Innes identified Proxima Centauri as a possible member of the Alpha Centauri system after noticing that the star had a similar proper motion to Alpha Centauri A and B.

Proxima Centauri was first observed through telescopes, which allowed scientists to study the star's spectra and estimate its distance from Earth. In the following decades, scientists continued to study Proxima Centauri through telescopes, including the Hubble Space Telescope, which provided high-resolution images of the star.

In 2016, the European Southern Observatory announced the discovery of an exoplanet orbiting Proxima Centauri, called Proxima Centauri b. This discovery was made using the radial velocity method, which measures the star's small wobbles caused by the gravitational pull of an orbiting planet.

Despite the advances in our understanding of Proxima Centauri, no spacecraft have ever reached this star. The distance between Proxima Centauri and Earth is so vast that it would take tens of thousands of years to reach the star using current propulsion technology.

One potential solution to this problem is the use of interstellar travel, which would allow humans to travel to Proxima Centauri within a human lifetime. There are several proposed methods for interstellar travel, including using a starship propelled by fusion engines or a massive light sail pushed by a beam of lasers. However, these technologies are still in the theoretical stage and have not yet been developed.

There are also many other challenges that must be overcome in order for humans to travel to Proxima Centauri. For example, humans would need to find a way to protect themselves from the high levels of radiation that they would be exposed to during the journey. They would also need to find a way to provide enough food, water, and other resources to sustain themselves for the duration of the trip.

Overall, while it is theoretically possible for humans to travel to Proxima Centauri, it would be a massive undertaking that would require significant technological advancements and the development of new solutions to many challenges.

Sources of Works Cited include:

"Proxima Centauri." Wikipedia, Wikimedia Foundation, 5 Jan. 2021,

"Proxima Centauri b." Wikipedia, Wikimedia Foundation, 20 Nov. 2020,

"Interstellar Travel." Wikipedia, Wikimedia Foundation, 4 Jan. 2021,

Therefore, the correct answer is as given above

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Answer:

i think..its fraction that its have multiple fractions on it..if you minus the 397 000-355 it should be 381+ so i say if you get the 5 multiply it by 9!! so you will get it!

Explanation:

HOPE IT HELPS!!

Answer:

Yup

Explanation:

The single cable will pull upward on the sign with a force of 38.3 N.

Single cable is a type of cable that is composed of a single electrical conductor. It is most commonly used in low voltage applications such as wiring for computers and domestic appliances. Single cable is typically insulated with rubber, PVC or other insulating materials. The insulator protects the conductor from short circuits and other electrical hazards.

This is because the sign is supported symmetrically by two cables, which means that the total downward force on the sign is equal to the total upward force. Since the two cables make an angle of 1.0 degrees with the horizontal, the total downward force on the sign is equal to the combined weight of the sign (38.3 N) and the two cables pulling down on it. Therefore, the single cable must pull up with a force of 38.3 N in order to keep the sign in equilibrium.

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Answer:

2 stays the same 1 it will go bad or go good depends on which material you use

Answer:

[tex]\% Error = 2.6\%[/tex]

Explanation:

Given

[tex]x: 1.54, 1.53, 1.44, 1.54, 1.56, 1.45[/tex]

Required

Determine the percentage error

First, we calculate the mean

[tex]\bar x = \frac{\sum x}{n}[/tex]

This gives:

[tex]\bar x = \frac{1.54+ 1.53+ 1.44+ 1.54+ 1.56+ 1.45}{6}[/tex]

[tex]\bar x = \frac{9.06}{6}[/tex]

[tex]\bar x = 1.51[/tex]

Next, calculate the mean absolute error (E)

[tex]|E| = \sqrt{\frac{1}{6}\sum(x - \bar x)^2}[/tex]

This gives:

[tex]|E| = \sqrt{\frac{1}{6}*[(1.54 - 1.51)^2 +(1.53- 1.51)^2 +.... +(1.45- 1.51)^2]}[/tex]

[tex]|E| = \sqrt{\frac{1}{6}*0.0132}[/tex]

[tex]|E| = \sqrt{0.0022}[/tex]

[tex]|E| = 0.04[/tex]

Next, calculate the relative error (R)

[tex]R = \frac{|E|}{\bar x}[/tex]

[tex]R = \frac{0.04}{1.51}[/tex]

[tex]R = 0.026[/tex]

Lastly, the percentage error is calculated as:

[tex]\% Error = R * 100\%[/tex]

[tex]\% Error = 0.026 * 100\%[/tex]

[tex]\% Error = 2.6\%[/tex]

Answer:

a

Explanation:

Answer: b. more precipitation

Explanation:

Resistors limits the current/amps but keep the voltage the same.

You don't want to attach them together with a wire since there would be too much current loose through, such that the battery heats up till it blows or something.

Current is directly corresponding to voltage; a doubling of the voltage will double the current. But the current is also inversely comparable to the resistance; a doubling of the resistance will halve the current.

So we can conclude that Resistance residue is the same, but power becomes four times i.e. multiplication. If the current is I and the voltage is V,

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Option C is correct.

The magnitude of the charge on an electron compared to the magnitude of the charge on a proton is same.

We have a electron and a proton.

We have to estimate the fact whether the magnitude of the charge on an electron compared to the magnitude of the charge on a proton is -

a) is greater

or

b) is smaller

or

c) is the same

The sufficiency or deficiency of electrons is called electric charge.

According to the question -

The charge on a electron is -   q(e) = - 1.6 x [tex]10^{-19}[/tex] Coulombs

The charge on a proton is -   q(p) = + 1.6 x  [tex]10^{-19}[/tex] Coulombs

But, according to the property of magnitude :

| + x| = + x

| - x| = - (- x) = + x

In the similar manner -

|q(e)| = |q(p)| = 1.6 x [tex]10^{-19}[/tex] coulombs

Hence, the magnitude of the charge on an electron compared to the magnitude of the charge on a proton is same.

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