Given the following two (2) force vectors F₁-5i-2j+3k [N] and F2= 8i+2j+3k [N], find (a)
The angle between both vectors. Next, find (b) the projection (or shadow length) of force F1 on F2.
Lastly, find (c) the projection of F2 on F₁. Show all work and make sure you use proper vector
otation. (Hint: Use Dot Product)

a rc circuit is constructed with a (initially uncharged) 5 uf capacitor and a 5-ohm resistor which are connected in series to an ideal battery with emf 60 is Q = CV = 9.5 x 10^-6 x 70  = 6.65 x 10^-4 C

What is constructed?

To create something by combining or arranging various pieces or components: the act of building a bridge. also: invent and contrive. put together a plan. to create a drawing of a geometrical figure using the appropriate tools and under the required circumstances

a) time constant  = RC  = 16.5 x 10^3 x 9.5 x 10^-6  = 0.157 s

b) V = V0 ( 1- e ^ -(t/RC))

after very long time,

V = V0 = e = 105 V

c) Q = CV  =  9.5 x 10^-6 x 105 = 9.97 x 10^-4 C

d) I = I0 ( e^(-t/RC))

I0 = e/R  = 105/16.5x10^3  = 6.36 mA

after very long time I = 0

e) I0/3 =  I0 ( e^-t/RC)

e^-t/RC =  (1/3)

-t/RC  = ln(1/3)

t  = 1.10 x RC  = 0.172 sec

f)) V = 105( 1 - e^(-t/RC))

V = 105 ( 1 - e^(-(0.172/0.157)) )

V = 70 V

Q = CV = 9.5 x 10^-6 x 70  = 6.65 x 10^-4 C

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To determine the spring constant of the scale, you can use the formula:

k = (F / x)

where k is the spring constant, F is the force acting on the spring, and x is the displacement of the spring.

In this case, the force acting on the spring is the weight of the water bottle, which can be calculated using the weight = mass * gravitational acceleration formula:

F = m * g

where m is the mass of the water bottle in kilograms and g is the gravitational acceleration of 9.8 m/s^2.

Plugging in the values given, we get:

k = (F / x) = (m * g / x)

= (350 g / (11.5 cm - 10.0 cm))

= 307.8 g/cm

This is the spring constant of the scale. It represents the force required to stretch the spring by 1 centimeter.

Answer: The third law.

Explanation:

Answer:

Explanation:

The correct answer is A. 32.5

Mechanical advantage is the ratio of force that is input into a machine to the force output.

Mechanical advantage of a wheel and axle is calculated by dividing the radius of the wheel by that of the axle.

MA=R/r where R is the radius of the wheel and  r is the radius of the axle.

Substituting for the values in the question gives:

MA=26cm/0.8cm

   =32.5

Required the moment of inertia of the merry go round.

a. I = 12 MR2 is the formula for the merry-go-moment round's of inertia.

I = ½ * 231 * (1.3 * 1.3)

I = 195.195 kgm2

b. The boy's angular speed is specified as = v/R = 2.5/1.3 = 1.92 rad/s.

c. I' = I + mR2 is the formula for the merry-go-moment round's of inertia following the boy's jump on it.

I’ = 195.195 + 48 * (1.3 * 1.3)

I’ = 276.315 kg/m2

The conservation of angular momentum principle determines the merry-go-angular round's speed. As a result, I (0) + m R = 'I' and = (48 * 1.92* 1.3) / 276.315 = 0.433 rad/s

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Answer:The key results explains how you achieve a certain goal. They have to be quantitative, but always measurable in terms of their progress.

Explanation:

Modular floor panels that rest on pedestals or stringers make up most access flooring systems. Typically, panel dimensions start at 24 by 24 inches square with same distance.

Their dimensions are constant; a raised floor panel is typically 600 mm by 600 mm. A standard access flooring panel in the USA is slightly larger, measuring 24" x 24". (around 610mm). A brand-new and cutting-edge patented solution that comprises of a polished concrete floor panel system that is intended to be put on to a new or retrofit building project is available. The imperfections and traits of a normal polished concrete floor are evident in this appealing, authentic concrete surface. The longest dimension of an object in geometric terms is its distance. International System of Quantities.

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Answer:

10 Newtons.

Explanation:

F=MA

F=(5kg)(2 m/s^2)

10 N

The components of velocity v  have magnitudes of v x = v cos and v y = v sin, where v seems to be the magnitude of something like the speed and is its direction with respect to the horizontal.

Velocity, as opposed to speed, refers to the pace and direction of the an object's movement as it moves down a path. In other words, whereas velocity is a vector, speed is a scalar quantity.

Velocity is the rate at which displacement changes  Since it consists both of magnitude and direction, velocity is a vector quantity. Since acceleration is merely the rate at which velocity changes, it too is a vector quantity.

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The average speed of the bowling ball 40 meter/second..

The pace at which an object's position changes in any direction is referred to as speed.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity. Si unit of speed be meter/second.

Given parameters:

Distance travelled by the ball: s = 32 meter.

Time taken by the ball: t = 0.8 second.

So, average speed of the ball = distance travelled/ time taken

= 32 meter/ 0.8 second

= 40 meter/second.

Hence,  the average speed of the bowling ball 40 meter/second.

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The difference between the two plot is shown clearly by the distance between the two waves.

Wave is defined as a disruption in an energy-conducting medium without a net movement of particles. Wind is the most frequent cause of waves. Wind-driven waves, sometimes referred to as surface waves, are created by friction between the wind and the water's surface.

The two difference between the two plot are the first is the difference between the distance of two crust and trough between the wave in the plot. The second difference is that the first plot is between displacement and distance from the source and the second graph is plot between displacement and time.

Thus, the difference between the two plot is shown clearly by the distance between the two waves.

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Answer:

1) B. The use of heat to kill any microorganisms living in a substance

2) B. Burning coal to produce electricity

3) A. Because he misinterpreted the Burgess Shale fossil data

Answer:

Mercury, Venus, Earth, Mars

A heat pump's operating overall efficiency is just 15.88, claims the inquiry.

Heat energy is created by the movement of tiny atoms, ions, or atoms in solid, liquids, and gases. Overheating can be transferred of one thing to another. When two items are already at varying temperatures from one another, a movement or exchange called heat occurs. Atoms and molecules move more quickly and clash when the temperature rises, producing heat generated (also known as heat energy). The power that comes from the heated object's temperature is referred to as thermal energy.

Maximum COP of heat pump:

COP = [tex]T_{H} /T_{H} - T_{C}[/tex]

Here, [tex]T_{H}[/tex] =  271 K and [tex]T_{C}[/tex] = 288 K

Hence, COP = 271/288-271

COP = 15.88

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The values of time (t) = 7.20, 0.62, and the model rocket is launched with an initial upward velocity of 125 ft/s and height of h.

The directional speed of an object in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.

height of the rocket is given as,

h = 125t - 16t²

now, when h = 71 then,

71 = 125 t - 16 t²

16 t² - 125t + 71 = 0

Using the quadratic formula, we have:

          - (-125) + √ (-125)² - 4 × 16 × 71

t =             ____________________

                              2 × 16

           125 + √11081                               125 - √11081

t =         _________                   t =         _________

                  32                                                 32

t = 7.20,   t = 0.62

Hence, the values of time (t) = 7.20, 0.62.

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a 1500 watt hair dryer uses 1500 J every second.

1500 J = 1500 Ws = 1500/3600 Wh = 0.000417 kWh

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Required the moment of inertia of the merry go round.

a. I = 12 MR2 is the formula for the merry-go-moment round's of inertia.

I = ½ * 231 * (1.3 * 1.3)

I = 195.195 kgm2

b. The boy's angular speed is specified as = v/R = 2.5/1.3 = 1.92 rad/s.

c. I' = I + mR2 is the formula for the merry-go-moment round's of inertia following the boy's jump on it.

I’ = 195.195 + 48 * (1.3 * 1.3)

I’ = 276.315 kg/m2

The conservation of angular momentum principle determines the merry-go-angular round's speed. As a result, I (0) + m R = 'I' and = (48 * 1.92* 1.3) / 276.315 = 0.433 rad/s

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The angle from the vertical does the fish see the top of the fishermans head is 42.24 degrees and can be finded out by snells law.

According to Snell’s Law when light is incident on an interface separating two media, the angles of incidence and refraction, θ1 and θ2, are related,

n1 sin(θ1) = n2 sin(θ2)

where θ1 or θ2 is the angle between the normal to the interface and the direction in which incident or refracted wave is propagating. The quantities n1 and n2 are the indices of refraction of the two media.

While the speed of light is constant in a vacuum, the speed of light in air and in transparent solids is somewhat less. The ratio of the speed of light in a vacuum (c) to the speed of light in a solid (v) is called the index of refraction (n) of the solid.

Applying snells law,

nwater *sinα = nair *sinβ

nwater *sinα = sinβ

sinα = sinβ/nwater

sinβ = 1.33 sinα

AB = 3.5m-BC

AB = 3.5m-CDtanβ

AB = 3.5m-1.55*tanβ

Also, AB = 4.5m*tandα

4.5m*tandα = 3.5m-1.55*tanβ

4.5m*tandα = 3.5m-1.55*(sinβ/cosβ)

4.5m*tandα = 3.5m-1.55*1.33sinα/[tex]\sqrt{1-(1.33)^2*(sin\alpha )^2}[/tex]

α=42.24 degrees.

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(a) The maximum height attained by the car is 21.57 m.

(b) The thermal energy generated by friction is 85,017.6 J.

(c) The average force of friction of the hill is 370.8 N.

The maximum height attained by the car is calculated by applying the principle of conservation of energy as follows;

P.E = K.E

mgh = ¹/₂mv²

h = (v²) / (2g)

where;

h = (20.56²) / (2 x 9.8)

h = 21.57 m

The thermal energy generated by friction is determined from the change in the mechanical energy of the car.

ΔE = K.E - P.E

ΔE = ¹/₂mv² - mgh

where;

ΔE = ¹/₂(750)(20.56)² - (750)(9.8)(10)

ΔE = 85,017.6 J

The average force of friction of the hill is calculated as follows;

Fd = ΔE

where;

d = h/sin(2.5) = 10 m / sin(2.5) = 229.26 m

F(229.26) = 85,017.6

F = (85,017.6) / (229.26)

F = 370.8 N

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a. The chip thickness after the cut is 0.5 mm

b. The shear angle is 21.05

c. The shear strain is 3.086

The formula is

r = t / tc

where we have r = 0.4

t = 0.2

0.4 = 0.2 / tc

cross multiply

tc = 0.5 mm

b. The shear angle is the angle at which a chip will detach from the work piece when cutting metal.

tan ∅ = r cos α / 1 - r sin α

= 0.4 cos (-0.5) / 1 - 0.4 sin(-5)

= 0.385

∅ = tan ⁻¹0.385

∅ = 21.05

c. When a medium is subjected to a lateral force, shear strain results. It is possible to produce a shear force wave that moves perpendicular to the direction of the applied force.

r = cot ∅ + tan(∅ - α)

r = cot (21.05)+ tan(22.05 -(-5)

r = 2.598 + 0.488

= 3.086

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The minimum velocity the roller coaster would need when going over the 12m hill to make it to the top of the 30m hill is 24.25 m/s.

The relationship between the kinetic energy and potential energy of a body is given by the law of conservation of energy which states that the sum of the energy in a system is conserved.

Hence, the sum of the kinetic energy and the potential energy of a body is given as follows:

Kinetic energy = Potential Energy

Kinetic energy = ¹/₂ mv²

Potential energy = mgh

where;

Assuming energy is conserved, the energy when going over the top of the 12 m is equal to the energy required to climb the 30 m hill.

¹/₂ mv² = mgh

v = √ 2gh

v = √ 2 * 9.8 * 30

v = 24.25 m/s

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A meridional pattern favors formation of major anticyclones.

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The statement that best describes the change in energy is the acorns potential energy decreases as it’s kinetic energy increases.

option A is the correct answer.

The law of conservation  of energy states that energy can neither be created nor destroyed but can be converted from one form to another.

Based on the law of conservation of energy, the total mechanical energy of the acorn will be conserved as it rolls off the roof. This implies that the change in the kinetic energy of the acorn is equal to change in potential energy of the acorn.

ΔP.E = ΔK.E

where;

The potential energy of the acorn is greatest at the maximum height, and decreases as the acorn fall to the ground. As the potential energy of the acorn decreases, it is being converted into kinetic energy and consequently results in increases of the kinetic energy.

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Answer:

(Question) A city gets its electricity from a dam, where water is stored in a reservoir. How does the water provide the city with its power?

(Answer) Potential energy in the water becomes kinetic energy as it moves through turbines, which turn kinetic energy into mechanical energy that spins a generator, which changes mechanical energy into electricity.

(Question) An acorn rolls off a roof and falls to the ground. Which statement best describes the change in energy?

(Answer) The acorn’s potential energy decreases as its kinetic energy increases.

(Question) An airplane carries 320 passengers from Phoenix to Los Angeles flying at an average speed of 490 miles per hour. On the return flight, the plane carries 164 passengers and travels at the same average speed. What happens to the plane’s kinetic energy?

(Answer) On the return flight, the plane has less kinetic energy.

(Question) A racehorse is running at 42 miles per hour, equivalent to 18.8 meters per second. The horse and its jockey have a combined mass of 512 kilograms. How much kinetic energy do they have?

(Answer) 90,480.6 J

(Question) Which object has kinetic energy?

(Answer) balloon rising in the sky

(Question) Mr. Starr pushed a cart full of groceries to his car. After emptying the cart, he pushed it back to the store. He pushed the cart at a speed of 2 meters per second each way. Which is the best prediction?

(Answer) When it was empty, the cart had less kinetic energy.

(Question) A student fires a toy rocket into the sky. When does the rocket have the most potential energy?

(Answer) when the rocket reaches its highest point

(Question) What is the best description of one billiard ball hitting a second billiard ball?

(Answer) Most of the kinetic energy in the first ball is transferred to the second ball.

(Question) A roller-coaster car is at the top of a hill. The car and its passengers have a combined mass of 1,088 kilograms. If the hill is 62 meters tall, how much potential energy does the car have?

(Answer) 661,068.8 J

(Question) A roller-coaster is at the top of a 62-meter hill. The car and its passengers have a total mass of 1,088 kilograms. By the time the car reaches the bottom of the hill, its speed is 74 miles per hour (33 meters per second). How much kinetic energy does the car have at the bottom of the hill?

(Answer) 592,416 J

(Question) A diagram is drawn showing a swing set with a swing pulled backward prior to release. The diagram shows how the swing will move forward and then backward after it is initially released. At which point in the diagram is all of the energy gravitational potential energy?

(Answer) when the swing is pulled back prior to release

(Question) essay

(Answer) good luck

(Question) essay

(Answer) good luck

Explanation:

I just completed the assignment.

The best choice is A. The formula that can be used to calculate the acceleration is a= dv/t

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Important Formulas:

[tex]F=ma[/tex]

Force = mass(measured in kg) * acceleration(measured in m/s^2)

__________________________________________________________

Given:

[tex]m=120kg[/tex]

[tex]F=14,000N[/tex]

[tex]a=?[/tex]

__________________________________________________________

Rearrange formula:

[tex]F=ma[/tex]

[tex]\dfrac{F}{m} =\dfrac{ma}{m}[/tex]

[tex]a=\dfrac{F}{m}[/tex]

__________________________________________________________

[tex]a=\dfrac{14,000}{120}[/tex]

[tex]\fbox{a = 116.67 m/s squared}[/tex]

A 120 kg elevator is supported by a cable in which the maximum safe tension is, 14000 N. The upward acceleration of the elevator is 116. 67 m/s².

Acceleration is the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates.

Even if the speed is constant, motion on a circle accelerates because the direction is always shifting.

This is the formula to calculate the force.

F = ma

we can modify this, a = F/m

Force = mass(measured in kg) x acceleration(measured in m/s²)

Given, mass = 120 kg

Force = 14000 N

Acceleration

Putting the values in the equation

a = F/m

a =  14000 / 120 = 116. 67 m/s²

Therefore, the upward acceleration of the elevator is 116. 67 m/s².

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Answer:

4/3 ft/s

Explanation:

(3.01+2.99)/2 = 3.00

(4 ft)/(3.00 s) = 4/3 ft/s

Heat transferred in the three steps is Conduction in Step 1 and radiation in Steps 2 and 3.

Conduction. The substance itself does not flow when heat is transported through conduction; instead, heat is internally transferred by the vibrations of atoms and molecules. Metals are typically excellent heat conductors because they can also carry electrons, which can carry heat.

In contrast to atoms, unbound electrons exist in metals. These electrons are free to roam the metal, interacting with the metal atoms and effectively transferring heat to them through collisions. Due of this, metals are generally superior heat conductors than other types of materials.

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On the celestial sphere, a large circle contains all of the Milky Way's stars. This enormous circle is known as the milky circle. The Milky Way Galaxy is a massive spiral structure with several hundred billion stars, including the sun.

The Milky Way galaxy, which contains our solar system, gets its name from how it appears in the night sky from Earth: a hazy strip of light made up of stars that are too close together to be seen separately.

An astronomical object known as a star is made up of a bright plasma spheroid that is held together by gravity. The Sun is the star that is closest to Earth. Other stars are also visible at night with the unaided eye, but because of their great distances from Earth, they appear as stationary points of light.

Hence, On the celestial sphere, a large circle contains all of the Milky Way's stars. This enormous circle is known as the milky circle. The Milky Way Galaxy is a massive spiral structure with several hundred billion stars, including the sun.

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It takes 10 minutes to stop.

What happens when brake is applied in car?

To stop the car, force must act in the opposite direction (Newton's First Law). When a car's brakes are applied, the magnitude of the velocity begins to decrease. As a result, the change in velocity is negative, and the acceleration is also negative.

According to the equation,

[tex]v = u + at[/tex]

after applying brake [tex]v = 0[/tex]

[tex]-u = at\\\\a = \frac{-u}{t} \\\\\a = \frac{-70}{5}\\\\a = - 0.234 m/s^2[/tex]

As it is moving at 140m/s

so,

[tex]-u = at\\\\-140 = -0.234 * t\\\\600s = t\\\\t = 10mins[/tex]

It takes 10 minutes to stop.

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