A speaker creates uniformly spherical sounds w/ 500 watts of power

a)What is the intensity, I, of the sound at a distance of 20 meters from the speaker? What is the sound intensity level, β, of the sound at a distance of 20 meters from the speaker?

b) What is the intensity, I, of the sound at a distance of 10 meters from the speaker? What is the sound intensity level, β, of the sound at a distance of 10 meters from the speaker?

c) How many deciBels do you increase walking from 20 meters away from the speaker to 10 meters away from the speaker?

c) What power output would the speaker have to put out in order to create 100 dB at a distance 20 meters from the speaker?

Answers

Answer 1

Answer:

A) I = 0.09947 W , β = 109 db , B) β = 116 db , β = 116 db , c) Δβ = 7 dB,

D)  P = 50.27 W

Explanation:

A) The intensity of a spherical sound wave is

          I = P / A

where A is the area of ​​the sphere where the sound is distributed

          A = 4π R²

       

we substitute

          I = P / 4πR²

let's calculate

          I = 500 / (4π 20²)

          I = 0.09947 W

to express this quantity in decibels we use relate

         β = 10 log (I / I₀)

The detectivity threshold is I₀ = 1 10⁻¹² W / m²

         β = 10 lob (0.09947 / 10⁻¹²)

         β = 10 (10.9976)

         β = 109 db

B) intensity at r = 10m

          I = 500 / (4π 10²)

          I = 0.3979 W / m²

          β = 10 log (0.3979 / 10⁻¹²)

          β = 10 (11.5997)

          β = 116 db

C) the change in intensity in decibles is

          Δβ = β₁ - β₂

          Δβ = 116 - 109

          Δβ = 7 dB

D) let's find the intensity for 100 db

          I = I₀ 10 (β / 10)

          I = 10⁻¹² 10 (100/10)

          I = 10⁻² W / m²

Thus

           P = I A

           P = I 4π R²

           P = 10⁻² 4π 20²

           P = 50.27 W


Related Questions

Does anyone skateboard still?

Answers

Answer:

yes

Explanation:

people still skateboard that is an easy question

a current of 200 mA through a conductor converts 40 joules of electrical energy into heat in 30 second
s determine the p
otential drop across the conductor

Answers

Answer:

V = 6.65 [volt]

Explanation:

First, we must calculate the power by means of the following equation, where the voltage is related to the energy produced or consumed in a given time.

[tex]P=E/t\\P = 40/30\\P = 1.33[s][/tex]

Using the power we can calculate the voltage, by means of the following equation that relates the voltage to the current.

[tex]P=V*I[/tex]

where:

V = voltage [Volts]

I = current = 200 [mA] = 0.2 [A]

[tex]V = 1.33/0.2\\V = 6.65 [volt][/tex]

A projectile is shot straight up from the earth's surface at a speed of 11,000 km/hr. How high does it go? ________km?

Taken from "Physics for Scientists and Engineers by Randall D. Knight 2nd Edition. Chapter 13 #34. There is an answer in the database already, but I do not understand it.

Answers

Answer:

476.35 km

Explanation:

The following data were obtained from the question:

Initial velocity (u) = 11000 km/hr

Final velocity (v) = 0 km/hr (at maximum height)

Acceleration due to gravity (g) = 9.8 m/s²

Maximum height (h) = ?

Next, we shall convert 9.8 m/s² to km/hr². This is illustrated below:

1 m/s² = 12960 km/hr²

Therefore,

9.8 m/s² = 9.8 m/s² × 12960 km/hr² / 1 m/s²

9.8 m/s² = 127008 km/hr²

Thus, 9.8 m/s² is equivalent to 127008 km/h²

Finally, we shall determine the maximum height reached by the projectile.

This is illustrated below:

Initial velocity (u) = 11000 km/hr

Final velocity (v) = 0 km/hr (at maximum height)

Acceleration due to gravity (g) = 127008 km/hr²

Maximum height (h) = ?

v² = u² – 2gh (since the projectile is going against gravity)

0² = 11000² – (2 × 127008 × h)

0 = 121×10⁶ – 254016h

Collect like terms

0 – 121×10⁶ = – 254016h

– 121×10⁶ = – 254016h

Divide both side by – 254016

h = – 121×10⁶ / – 254016

h = 476.35 km

Thus, the maximum height reached by the projectile is 476.35 km

A 50kg boy stands on rough horizontal ground. The coefficient

of static friction, us, is 0.68. The maximum static friction

between the boy and the ground is __N.

Answers

Given :

A 50 kg boy stands on rough horizontal ground. The coefficient  of static friction, us, is 0.68.

To Find :

The maximum static friction  between the boy and the ground is _ N.

Solution :

We know maximum static friction is given by :

[tex]F = \mu mg \\\\F= 0.68\times 50\times 9.8\\\\F = 333.2\ N[/tex]

Therefore, maximum static friction is 333.2 N.

Hence, this is the required solution.

10- The coefficient of volumetric expansion for gold is 4.20 x 10°/C°. The density of gold is
19 300 kg/m at 0.0 °C. What is the density of gold at 1050 °C?
(a) 20 200 kg/m
(b) 19 000 kg/m
(c) 18 500 kg/m
(d) 19 300 kg/m
(e) 18 800 kg/m

Answers

Answer:

 ρ = 19215 kg / m³ , the answer the correct  is D

Explanation:

All materials are sold when heated, in first approximation

              ΔV = β V₀ (T -T₀)

for this case

              ΔV = 4.20 10⁻⁶ Vo (1050 - 0)

              ΔV = 4.41 10⁻³ Vo m³

              V-Vo = 4.41 10⁻³ Vo

              V = 1.00441 Vo

density is defined by

           ρ = m / V

a T = 0ºc

            ρ₀ = m / Vo

aT= 1050ºC

             

           ρ = m / V

           ρ = m / (1,00441 Vo)

           ρ = 1 / 1.00441      m/Vo

          ρ = 0.9956 ρ₀

          ρ = 0.9956 19300

          ρ = 19215 kg / m³

when checking the answers the correct one is D

If you were standing at the center of a circular wave what would you see in all directions?
a.waves moving away from you
b.waves moving towards you
c.waves moving across you
d.no movement at all

Answers

I believe that the answer will be A because if you standing in a the middle you would be moving so the waves go away from you.

What is the answer to this question

Answers

Answer:

0.11 m/s

Explanation:

From the question given above, the following data were obtained:

Initial displacement (d1) = 1.09 m

Final displacement (d2) = 2.55 m

Time (t) = 12.8 s

Average velocity =?

Next, we shall determine the total displacement (i.e change in displacement). This can be obtained as follow:

Initial displacement (d1) = 1.09 m

Final displacement (d2) = 2.55 m

Total displacement = d2 – d1

Total displacement = 2.55 – 1.09

Total displacement = 1.46 m

Finally, we shall determine the average velocity of the beetle. This can be obtained as follow:

Total Displacement = 1.46 m

Total time (t) = 12.8 s

Average velocity =?

Average velocity = Total Displacement / Total time

Average velocity = 1.46/12.8

Average velocity = 0.11 m/s

Thus, the average velocity of the beetle is 0.11 m/s

Lisa throws a stone horizontally from the roof edge of a 50 meter high dormitory. It hits the ground at a point 60 m from the building. Find the time of flight.

Answers

Answer:

Explanation:

Time of flight is the time of takes to hit the ground

Given

Height H = 50m

Acceleration due to gravity g = 9.8m/s³

Using the equation of motion;

S = ut+1/2gt²

u = 0m/s

Substitute and get time t

50 = 0(t)+1/2(9.8)t²

50 = 4.9t²

t² = 50/4.9

t² = 10.204

t = √10.204

t = 3.19secs

Hence the time of flight is 3.19secs

An explanation of the relationships among particular phenomena.

Answers

Answer:

Theory

Explanation:

Theory is a term that is used often in academic work or scientific research to explain certain things or conditions established on universal principles or laws.

It is used to describe the "why and how" or the reason behind the occurrence of a situation.

Hence, it is correct to conclude that THEORY is "an explanation of the relationships among particular phenomena."

Answer:

E) Theory

Explanation:

Edge 2020

Brainliest?

If 10 calories of energy are added to 2 grams of ice at -30° C, calculate the final temperature of the ice. (Notice that the specific heat of ice is different from that of water.)

-30° C
40° C
-20° C
30° C

Answers

Answer:

-20°C

Explanation:

The specific heat capacity of ice using the cgs system is 0.5cal/g°C

The enthalpy change is calculated as follows

ΔH=MC∅ where M represents mass C represents specific heat and ∅ represents the temperature change.

10cal = 2g×0.5cal/g°C×∅

∅=10cal/(2g×0.5cal/g°C)

∅=10°C

Final temperature= -30°C+ 10°C= -20°C

200. Un automóvil se desplaza

hacia la izquierda con

velocidad constante v,

en el momento en que se

deja caer un saco de lastre

desde un globo en reposo.

El vector que representa

la velocidad del saco vista

desde el automóvil en ese

instante en que se suelta es

Answers

Skajwopwpoe eueusjjeww

which of the following elements is the most reactive? Chlorine Bromine Fluorine Helium

Answers

Answer:

Fluorine is the most reactive

Explanation:

Among the halogens, fluorine, chlorine, bromine, and iodine, fluorine is the most reactive one. It forms compounds with all other elements except the noble gases helium (He), neon (Ne) and argon (Ar), whereas stable compounds with krypton (Kr) and xenon (Xe) are formed.

A peregrine falcon dives at pigeon . the falcon start downward from rest with free-fall acceleration . if the pigeon is 76.0 m below the initial position of the falcon , how long the falcon take to reach the pigeon? Assume that the pigeon remains at rest .

Answers

Answer:

3.94 s

Explanation:

Take down to be positive.  Given:

Δy = 76.0 m

v₀ = 0 m/s

a = 9.8 m/s²

Find: t

Δy = v₀ t + ½ at²

76.0 m = (0 m/s) t + ½ (9.8 m/s²) t²

t = 3.94 s

According to the Law of Reflection, the angle of incidence the angle of reflection. O A. is greater than B. is less than C. equals D. is opposite from​

Answers

Answer:

C. Equals

Explanation:

Law of reflection Equals the angle of incidence

20- A gram of distilled water at 4° C:
(a) will increase slightly in weight when heated to 6 C
(b) will decrease slightly in weight when heated to 6 C
(C) will increase slightly in volume when heated to 6 C
(d) will decrease slightly in volume when heated to 6 C
(e) will not change in either volume or weight

Answers

Answer:

D. will decrease slightly in volume when heated to 6° C

Explanation:

A gram of distilled water at 4° C  will increase slightly in volume when heated to 6 C. Hence option C is correct.

What is Water ?

Water has the chemical formula H2O, making it an inorganic substance. It is the primary chemical component of the Earth's hydrosphere and the fluids of all known living things (in which it serves as a solvent[1]). It is translucent, flavourless, odourless, and almost colourless. In spite of not supplying food, energy, or organic micronutrients, it is essential for all known forms of life. Its molecules are made up of two hydrogen atoms joined by covalent bonds and have the chemical formula H2O. The angle at which the hydrogen atoms are joined to the oxygen atom is 104.45°.[2] The liquid condition of H2O at normal pressure and temperature is known as "water" as well.

Water occurs because the environment on Earth is pretty near to the triple point of water.

To know more about Water :

https://brainly.com/question/28465561

#SPJ2.

If the net force acting on an object is not zero, then the object is definitely

at rest
moving with a constant velocity
being accelerated
losing mass

Answers

Answer:

C

Explanation:

Since the net force is changing, and not the speed, it is C

Hope this helped!

Calculating the Velocity of a Wave Quick Check What is the speed of a wave that has a frequency of 173 Hz and a wavelength of 2.59 meters? Express your answer to the nearest whole number. m/s I need answers ​

Answers

Answer:

448m/s

Explanation:

The speed of the wave with a given wavelength and frequency can be calculated using the formula:

λ = v/f

Where;

λ = wavelength (m)

v = speed of wave (m/s)

f = frequency of wave (Hz)

In this question, λ = 2.59 metres, f = 173 Hz, v = ?

λ = v/f

v = λ × f

v = 2.59 × 173

v = 448.07m/s

To the nearest whole number, 448.07 can be written as 448

Hence, the speed of the wave (v) is 448m/s.

Answer:

What is the speed of a wave that has a frequency of 173 Hz and a wavelength of 2.59 meters? Express your answer to the nearest whole number.

448

 m/s

Explanation:

9)A skier starts from rest from the top of a 40 m high slope which makes 40 degrees with the ground. Coefficient of friction is 0.1 What is the velocity of the skier at the bottom of the ramp?

Answers

Answer:

The velocity of the skier at the bottom of the ramp is approximately 26.288 meters per second.

Explanation:

We can determine the final velocity of the skier at the bottom of the ramp by Principle of Energy Conservation and Work-Energy Theorem, whose model is:

[tex]U_{g,1}+K_{1} = U_{g,2}+K_{2}+W_{disp}[/tex] (1)

Where:

[tex]U_{g,1}[/tex], [tex]U_{g,2}[/tex] - Initial and final gravitational potential energy, measured in joules.

[tex]K_{1}[/tex], [tex]K_{2}[/tex] - Initial and final translational kinetic energy, measured in joules.

[tex]W_{disp}[/tex] - Work dissipated by friction, measured in joules.

By definitions of gravitational potential and translational kinetic energy and work, we expand and simplify the model:

[tex]m\cdot g \cdot (z_{1}-z_{2})+\frac{1}{2}\cdot m \cdot (v_{1}^{2}-v_{2}^{2}) =\mu_{k}\cdot N\cdot \Delta s[/tex] (2)

Where:

[tex]m[/tex] - Mass, measured in kilograms.

[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.

[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final heights of the skier, measured in meters.

[tex]N[/tex] - Normal force from the incline on the skier, measured in newtons.

[tex]\Delta s[/tex] - Distance covered by the skier, measured in meters.

[tex]\mu_{k}[/tex] - Kinetic coefficient of friction, dimensionless.

The normal force exerted on the skier and the covered distance are, respectively:

[tex]N = m\cdot g\cdot \cos \theta[/tex] (3)

[tex]\Delta s = \frac{z_{1}-z_{2}}{\sin \theta}[/tex] (4)

Where [tex]\theta[/tex] is the angle of the incline above the horizontal, measured in sexagesimal degrees.

By applying (3) and (4) in (2), we get that:

[tex]m\cdot g \cdot (z_{1}-z_{2})+\frac{1}{2}\cdot m\cdot (v_{1}^{2}-v_{2}^{2}) = \mu_{k}\cdot m\cdot g \cdot \cos \theta \cdot \left(\frac{z_{1}-z_{2}}{\sin \theta} \right)[/tex]

[tex]g\cdot (z_{1}-z_{2}) +\frac{1}{2}\cdot (v_{1}^{2}-v_{2}^{2})= \mu_{k}\cdot g \cdot \left(\frac{z_{1}-z_{2}}{\tan \theta} \right)[/tex] (5)

Then, we clear the velocity of the skier at the bottom of the ramp is: ([tex]v_{1} = 0\,\frac{m}{s}[/tex], [tex]\mu_{k} = 0.1[/tex], [tex]\theta = 40^{\circ}[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], [tex]z_{1}-z_{2} = 40\,m[/tex])

[tex]\left[\frac{\mu_{k}}{\tan \theta}-1 \right]\cdot g\cdot (z_{1}-z_{2}) = \frac{1}{2}\cdot (v_{1}^{2}-v_{2}^{2})[/tex]

[tex]2\cdot \left[\frac{\mu_{k}}{\tan \theta}-1 \right]\cdot g\cdot (z_{1}-z_{2}) = v_{1}^{2}-v_{2}^{2}[/tex]

[tex]v_{2} = \sqrt{v_{1}^{2}-2\cdot \left[\frac{\mu_{k}}{\tan \theta}-1 \right]\cdot g\cdot (z_{1}-z_{2})}[/tex] (6)

[tex]v_{2} = \sqrt{\left(0\,\frac{m}{s} \right)^{2}-2\cdot \left(\frac{0.1}{\tan 40^{\circ}} -1\right)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (40\,m)}[/tex]

[tex]v_{2} \approx 26.288\,\frac{m}{s}[/tex]

The velocity of the skier at the bottom of the ramp is approximately 26.288 meters per second.

Two blocks with different masses are dropped, hitting the ground with the same velocity. Which of the following is true?
They have same change in velocity but different changes in kinetic energy
The lighter object started at a smaller height.
The heavier object started at a smaller height
They started at the same height
They have same change in kinetic energy but different changes in velocity

Answers

Answer: • They have same change in velocity but different changes in kinetic energy

•They started at the same height.

Explanation:

First and foremost, we need to note that both balls have thesame acceleration due to gravity and due to this, even though they've different masses, they'll fall at same speed.

Also, since kinetic energy that's, the energy relating to motion of a mass, us dependent on mass and speed, their kinetic energy will be different.

Therefore, based in the explanation, the correct options are:

• They have same change in velocity but different changes in kinetic energy

•They started at the same height.

what are the two outcomes for a proto star?
Brown dwarf or main sequence star
Brown dwarf or red dwarf
Red giant or red dwarf
Black hole or main sequence star​

Answers

Answer:

Brown dwarf or main sequence star

List Five examples from daily life in which you see periodic motion caused by a pendulum
(Marking Brainliest)

Answers

Answer:

by a rocking chair, a bouncing ball, a vibrating tuning fork, a swing in motion, the Earth in its orbit around the Sun, and a water wave.

Explanation:

If the velocity of a car changes from 0 meters per second (m/s) to 100 m/s in 10 seconds, what is the acceleration over that 10 second period?

Answers

Answer:

10m/s²

Explanation:

Given parameters:

Initial velocity  = 0m/s

Final velocity  = 100m/s

Time taken  = 10s

Unknown:

Acceleration  = ?

Solution:

Acceleration is the rate of change of velocity with time.

  A = [tex]\frac{v - u}{t}[/tex]

v = final velocity

u = initial velocity

t = time taken

 So, insert the parameters and solve;

  A = [tex]\frac{100 - 0}{10}[/tex]   = 10m/s²

At high noon, the sun is almost directly above (about 2.0 degrees from the vertical) and a tall redwood tree casts a shadow that is 10m long. How tall is the redwood tree?

Answers

290m

The light always travels in a straight line.

At high noon, the ray from the sun is 2° from the vertical axis.

tan θ = (Opposite side)/(Adjacent side)

On applying above trigonometric formula, we get,

tan 2 = 10/h

0.035 = 10/h

∴ h = 10/0.035 = 290 m

A solid sphere rolling without slipping on a horizontal surface. If the translational speed of the sphere is 2.00 m/s, what is its total kinetic energy?

Answers

Answer:

The total kinetic energy is 2.8m J. (NOTE: m is mass of the sphere)

Explanation:

The total kinetic energy of a sphere is given by the sum of the rotational kinetic energy and the translational kinetic energy. That is,

[tex]K_{Total} = K_{R} + K_{T}[/tex]

The rotational kinetic energy [tex]K_{R}[/tex] is given by

[tex]K_{R} = \frac{1}{2}I\omega^{2}[/tex]

Where [tex]I[/tex] is the moment of inertia

and [tex]\omega[/tex] is the angular velocity

The translational kinetic energy [tex]K_{T}[/tex] is given by

[tex]K_{T} = \frac{1}{2}mv^{2}[/tex]

Where [tex]m[/tex] is the mass

and [tex]v[/tex] is the translational speed (velocity)

∴ [tex]K_{Total} = \frac{1}{2}I\omega^{2} + \frac{1}{2}mv^{2}[/tex]

But, the moment of inertia [tex]I[/tex] of a sphere is given by

[tex]I = \frac{2}{5}mr^{2}[/tex]

Where [tex]m[/tex] is mass

and [tex]r[/tex] is radius

∴ [tex]K_{Total} = \frac{1}{2}\times \frac{2}{5}mr^{2} \omega^{2} + \frac{1}{2}mv^{2}[/tex]

[tex]K_{Total} = \frac{1}{5}mr^{2} \omega^{2} + \frac{1}{2}mv^{2}[/tex]

Also, [tex]\omega = \frac{v}{r}[/tex]

∴ [tex]\omega^{2} = \frac{v^{2} }{r^{2} }[/tex]

Then,

[tex]K_{Total} = \frac{1}{5}mr^{2} \times \frac{v^{2} }{r^{2} } + \frac{1}{2}mv^{2}[/tex]

[tex]K_{Total} = \frac{1}{5}mv^{2} + \frac{1}{2}mv^{2}[/tex]

∴ [tex]K_{Total} = \frac{7}{10}mv^{2}[/tex]

From the question, [tex]v = 2.00 m/s[/tex]

Then,

[tex]K_{Total} = \frac{7}{10}m(2.00)^{2}[/tex]

[tex]K_{Total} = \frac{7}{10}m\times 4.00[/tex]

[tex]K_{Total} = 2.8m J[/tex]

Hence, the total kinetic energy is 2.8m J. (NOTE: m is mass of the sphere)

What is the de Broglie wavelength of an electron accelerated from rest through a potential difference of 50.0 V?
(a) 0.100 nm
(b) 0.139 nm
(c) 0.174 nm
(d) 0.834 nm
(e) none of those answers

Answers

Answer:

(c) 0.174 nm

Explanation:

According to de Broglie hypothesis, the wavelength of the wave associated with electron is given by:

[tex] \boxed{ \bf{\lambda = \sqrt{\dfrac{150}{V \ (in \ Volt)}} \: \text{\AA}}}[/tex]

V → Potential Difference (50.0 V)

By substituting value of potential difference in the equation, we get:

[tex] \rm \longrightarrow \lambda = \sqrt{\dfrac{150}{50}} \: \text{\AA} \\ \\ \rm \longrightarrow \lambda = \sqrt{3} \: \text{\AA} \\ \\ \rm \longrightarrow \lambda = 1.74 \: \text{\AA} \\ \\ \rm \longrightarrow \lambda = 0.174 \: nm[/tex]

which statement is not correct for lamps connected in parallel

Answers

Answer:

This question is not complete but the completed question is below

Which statement is not correct for lamps connected in parallel?

A They can be switched on and off separately.

B They will remain bright if another lamp is connected in parallel.

C They share the supply voltage equally between them.

D They still operate if one lamp is removed.

The correct option is A

Explanation:

Lamps connected in series have the same voltage running across each lamp in the connection and will thus have the same brightness if any lamp is added or removed. This property also means they can only be switched on and off by a single switch, hence option A is not correct about lamps connected in parallel.

Lamps connected in a parallel circuit will have the same voltage and different current.

A parallel circuit contains resistors arranged parallel to each other. some basic characteristics of parallel circuit include the following;

the voltage in all the resistors is the samethe current flowing in each resistor is different

V = I₁R₁ + I₂R₂ + I₃R₃ + ---

where;

V is the voltage in the circuitI is the different currentsR is the different resistors

Thus, we can that lamps connected in a parallel circuit will have the same voltage and different current.

Learn more about parallel circuit here: https://brainly.com/question/12739827

There is gravitational force on the Earth from the Sun, and a gravitational force on the Sun from the Earth. Which pulls harder?

Answers

Answer:

They both pull the same amount. For every force there is an equal and opposite force.

Explanation:

A tennis ball moves 18 meters northward, then 22 meters

southward, then 14 meters northward, and finally 28 meters

southward.

Answers

Answer:

The distance moved is 82 m.

The displacement is 18 m to the south.

Explanation:

The distance is a measure of the total length traveled along the path, while the displacement only takes into account the length between the starting position (departure) and final position (arrival). That is, distance refers to how much space an object travels during its movement, being the amount moved, while displacement refers to the distance and direction of the final position with respect to the initial position of an object.

So, the distance being the sum of the distances traveled, you get:

18 m + 22 m + 14 m + 28 m= 82 m

The distance moved is 82 m.

You know that the tennis ball moves 18 meters to the north, then 22 meters to the south, then 14 meters to the north, and finally 28 meters to the south. Then the tennis ball moves:

northward:  18 m + 14 m= 32 mto the south: 22 m + 28 m=  50 m

Calculating the displacement as the difference between the final position and the initial position, you get:

displacement= 50 m - 32 m= 18 m

The displacement is 18 m to the south.

What is the difference between renewable energy non-renewable energy? Use in your own words.

Answers

Non renewable energy are limited energy which would go away soon. Ex. Coal, oil, fossil fuels

Renewable energy comes from natural resources which would be there for a much longer time. Ex. Wind, sun, and water

Given F1: a force of magnitude 6 N at an angle of 30°
F2: a force of magnitude 8 N at an angle of 50°C

a. Find F1+ F2 analytically (using equations instead of graphing) and write it in the form Fr1i + Fr2 j
b. Find the magnitude FR and θ_resultant

Answers

Answer:

13.8 N

[tex]41.44^{\circ}[/tex]

Explanation:

[tex]F_1=6\ \text{N}[/tex]

[tex]F_2=8\ \text{N}[/tex]

[tex]F_1\cos\theta_1\hat{i}+F_1\sin\theta_1\hat{j}\\ =6\cos30^{\circ}+6\sin30^{\circ}\hat{j}\\ =5.2\hat{i}+3\hat{j}[/tex]

[tex]F_2\cos\theta_2\hat{i}+F_2\sin\theta_2\hat{j}\\ =8\cos50^{\circ}+8\sin50^{\circ}\hat{j}\\ =5.14\hat{i}+6.13\hat{j}[/tex]

[tex]F_R=F_1+F_2=10.34\hat{i}+9.13\hat{j}[/tex]

[tex]|F_R|=\sqrt{10.34^2+9.13^2}=13.8\ \text{N}[/tex]

The magnitude of the resultant is 13.8 N

Direction is given by

[tex]\tan^{-1}=\dfrac{y}{x}=\tan^{-1}\dfrac{9.13}{10.34}=41.44^{\circ}[/tex]

The angle of the resultant is [tex]41.44^{\circ}[/tex]

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