In the figure, particle A moves along the line y = 31 m with a constant velocity v with arrow of magnitude 2.8 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration a with arrow of magnitude 0.35 m/s2. What angle between a with arrow and the positive direction of the y axis would result in a collision?

In The Figure, Particle A Moves Along The Line Y = 31 M With A Constant Velocity V With Arrow Of Magnitude

Answers

Answer 1

Answer:

59.26°

Explanation:

Since a is the acceleration of the particle B, the horizontal component of acceleration is a" = asinθ and the vertical component is a' = acosθ where θ angle between a with arrow and the positive direction of the y axis.

Now, for particle B to collide with particle A, it must move vertically the distance between A and B which is y = 31 m in time, t.

Using y = ut + 1/2a't² where u = initial velocity of particle B = 0 m/s, t = time taken for collision, a' = vertical component of particle B's acceleration =  acosθ.

So, y = ut + 1/2a't²

y = 0 × t + 1/2(acosθ)t²

y = 0 + 1/2(acosθ)t²

y = 1/2(acosθ)t²   (1)

Also, both particles must move the same horizontal distance to collide in time, t.

Let x be the horizontal distance,

x = vt (2)where v = velocity of particle A = 2.8 m/s and t = time for collision

Also,  using x = ut + 1/2a"t² where u = initial velocity of particle B = 0 m/s, t = time taken for collision, a" = horizontal component of particle B's acceleration =  asinθ.

So, x = ut + 1/2a"t²

x = 0 × t + 1/2(ainsθ)t²

x = 0 + 1/2(asinθ)t²

x = 1/2(asinθ)t²  (3)

Equating (2) and (3), we have

vt = 1/2(asinθ)t²   (4)

From (1) t = √[2y/(acosθ)]

Substituting t into (4), we have

v√[2y/(acosθ)] = 1/2(asinθ)(√[2y/(acosθ)])²  

v√[2y/(acosθ)] = 1/2(asinθ)(2y/(acosθ)  

v√[2y/(acosθ)] = ytanθ

√[2y/(acosθ)] = ytanθ/v

squaring both sides, we have

(√[2y/(acosθ)])² = (ytanθ/v)²

2y/acosθ = (ytanθ/v)²

2y/acosθ = y²tan²θ/v²

2/acosθ = ytan²θ/v²

1/cosθ = aytan²θ/2v²

Since 1/cosθ = secθ = √(1 + tan²θ) ⇒ sec²θ = 1 + tan²θ ⇒ tan²θ = sec²θ - 1

secθ = ay(sec²θ - 1)/2v²

2v²secθ = aysec²θ - ay

aysec²θ - 2v²secθ - ay = 0

Let secθ = p

ayp² - 2v²p - ay = 0

Substituting the values of a = 0.35 m/s, y = 31 m and v = 2.8 m/s into the equation, we have

ayp² - 2v²p - ay = 0

0.35 × 31p² - 2 × 2.8²p - 0.35 × 31 = 0

10.85p² - 15.68p - 10.85 = 0

dividing through by 10.85, we have

p² - 1.445p - 1 = 0

Using the quadratic formula to find p,

[tex]p = \frac{-(-1.445) +/- \sqrt{(-1.445)^{2} - 4 X 1 X (-1)}}{2 X 1} \\p = \frac{1.445 +/- \sqrt{2.088 + 4}}{2} \\p = \frac{1.445 +/- \sqrt{6.088}}{2} \\p = \frac{1.445 +/- 2.4675}{2} \\p = \frac{1.445 + 2.4675}{2} or p = \frac{1.445 - 2.4675}{2} \\p = \frac{3.9125}{2} or p = \frac{-1.0225}{2} \\p = 1.95625 or -0.51125[/tex]

Since p = secθ

secθ = 1.95625 or secθ = -0.51125

cosθ = 1/1.95625 or cosθ = 1/-0.51125

cosθ = 0.5112 or cosθ = -1.9956

Since -1 ≤ cosθ ≤ 1 we ignore the second value since it is less than -1.

So, cosθ = 0.5112

θ = cos⁻¹(0.5112)

θ = 59.26°

So, the angle between a with arrow and the positive direction of the y axis would result in a collision is 59.26°.


Related Questions

why clinical thermometer cannot be used to measure the boiling point of water​

Answers

Answer:

: No, a clinical thermometer cannot be used to measure the temperature of boiling water because it has a small range and might break due to extreme heat. ... The temperature is around 100 degrees Celsius.

The outer surface of a spacecraft in space has an emissivity of 0.44 and a solar absorptivity of 0.3. If solar radiation is incident on the spacecraft at a rate of 950 W/m2, determine the surface temperature of the spacecraft when the radiation emitted equals the solar energy absorbed.

Answers

Answer:

[tex]T=326.928K[/tex]

Explanation:

From the question we are told that:

Emissivity [tex]e=0.44[/tex]

Absorptivity [tex]\alpha =0.3[/tex]

Rate of solar Radiation [tex]R=0.3[/tex]

Generally the equation for Surface absorbed energy is mathematically given by

 [tex]E=\alpha R[/tex]

 [tex]E=0.3*950[/tex]

 [tex]E=285W/m^2[/tex]

Generally the equation for Emitted Radiation is mathematically given by

 [tex]\mu=e(\sigmaT^4)[/tex]

Where

T=Temperature

 [tex]\sigma=5.67*10^8Wm^{-2}K_{-4}[/tex]

Therefore

 [tex]\alpha*E=e \sigma T^4[/tex]

 [tex]0.3*(950)=0.44(5.67*10^-8)T^4[/tex]

 [tex]T=326.928K[/tex]

) Efficiency of a lever is always less than hundred percent.​

Answers

Yes. Because it opposes the law of friction

I hope this helps.

Explanation:

Please mark me brainliest

How do the magnitudes of the currents through the full circuits compare for Parts I-III of this exercise, in which resistors are combined in series, in parallel, and in combination

Answers

Answer: hello tables and data related to your question is missing attached below are the missing data

answer:

a) I = I₁ = I₂ = I₃ = 0.484 mA

b) I₁ =  0.016 amps

   I₂ =  0.0016 amps

   I₃ = 7.27 * 10^-4 amps

c)  I₁ = 1.43 * 10^-3 amp

    I₂ =  0.65 * 10^-3 amps

Explanation:

A) magnitude of current for Part 1

Resistors are connected in series

Req = r1 + r2 + r3

       = 3300 Ω  ( value gotten from table 1 ) ,

          V = 1.6 V ( value gotten from table )

hence I ( current ) = V / Req = 1.6 / 3300 = 0.484 mA

The magnitude of current is the same in the circuit

Vi = I * Ri

B) magnitude of current for part 2

Resistors are connected in parallel

V = 1.6 volts

Req = [ ( R1 * R2 / R1 + R2 ) * R3 / ( R1 * R2 / R1 + R2 ) +  R3 ]

      = [ ( 100 * 1000 / 100 + 1000) * 2200 / ( 100 * 1000 / 100 + 1000 ) + 2200]

      = 87.30 Ω

For a parallel circuit the current flow through each resistor is different

hence the magnitude of the currents are

I₁ = V / R1 = 1.6 / 100 = 0.016 amps

I₂ = V / R2 = 1.6 / 1000 = 0.0016 amps

I₃ = V / R3 = 1.6 / 2200 = 7.27 * 10^-4 amps

C) magnitude of current for part 3

Resistors are connected in combination

V = 1.6 volts

Req = R1 + ( R2 * R3 / R2 + R3 )

       = 766.66 Ω

Total current ( I ) = V / Req = 1.6 / 766.66 = 2.08 * 10^-3 amps

magnitude of currents

I₁ = ( I * R3 ) / ( R2 + R3 ) = 1.43 * 10^-3 amps

I₂ = ( I * R2 ) / ( R2 + R3 ) = 0.65 * 10^-3 amps

A flat, 75-turn, coil is oriented with its plane perpendicular to a uniform magnetic field that varies steadily from 0.00 To 1.20 T in 20.0 ms. The diameter of each coil is 10 cm. Calculate the emf induced in the coil during this time, in volts.

Answers

40 m long what is 6 m on

A small ball of uniform density equal to 1/2 the density of water is dropped into a pool from a height of 5m above the surface. Calculate the maximum depth the ball reaches before it is returned due to its bouyancy. (Omit the air and water drag forces).

Answers

Answer:

1.67 m

Explanation:

The potential energy change of the small ball ΔU equals the work done by the buoyant force, W

ΔU = -W

Now ΔU = mgΔh where m = mass of small ball = ρV where ρ = density of small ball and V = volume of small ball. Δh = h - h' where h = final depth of small ball and h' = initial height of small ball = 5 m. Δh = h - 5

ΔU = mgΔh

ΔU = ρVgΔh

Now, W = ρ'VgΔh'   where ρ = density of water and V = volume of water displaced = volume of small ball. Δh' = h - h' where h = final depth of small ball and h' = initial depth of small ball at water surface = 0 m. Δh' = h - h' = h - 0 = h

So, ΔU = -W

ρVgΔh = -ρ'VgΔh'

ρVg(h - 5) = -ρ'Vgh

ρ(h - 5) = -ρ'h

Since the density of the small ball equals 1/2 the density of water,

ρ = ρ'/2

ρ(h - 5) = -ρ'h

(ρ'/2)(h - 5) = -ρ'h

ρ'(h - 5)/2 = -ρ'h

(h - 5)/2 = -h

h - 5 = -2h

h + 2h = 5

3h = 5

h = 5/3

h = 1.67 m

So, the maximum depth the ball reaches is 1.67 m.

A point charge is positioned in the center of a hollow metallic shell of radius R. During four experiments the value of the point charge and the total charge on shell were, respectively:

Answers

Complete question is;

A point charge is positioned in the center of a hollow metallic shell of radius R. During four experiments the value of point charge and charge of the shell were respectively:

+5q; 0

-6q; +2q

+2q; -3q

-4q; +12q

Rank the results of experiments according to the charge on the inner surface of the shell, most positive first:

a. 2, 3, 1, 4

b. 1, 2, 3, 4

c. 2, 4, 3, 1

d. 1, 3, 4, 2

Answer:

c. 2, 4, 3, 1

Explanation:

In this question, we can say that;

q_in = q_b

Where;

q_in is the charge on the inner surface of the shell

q_b is the point charge on the shell.

Thus q_in = -q_b was written because, as the shell is conducting, it means that the electric field would have a value of zero and thus the radius inside will be zero.

Thus;

- For +5q; 0:

q_in = -(+5q)

q_in = -5q

- For -6q; +2q :

q_in = - (-6q)

q_in = +6q

- For +2q; -3q :

q_in = -(+2q)

q_in = -2q

- For -4q; +12q:

q_in = -(-4q)

q_in = +4q

Ranking the most positive to the least positive ones, we have;

+6q, +4q, -2q, -5q

This corresponds to options;

2, 4, 3, 1

Un objeto de 0.5kg de masa se desplaza a lo largo de una trayectoria rectilínea con aceleración constante de 0.3m/s2. Si partió del reposo y la magnitud de su cantidad de movimiento en kg*m/s después de 8s es:

Answers

Answer:

p = 1.2 kg-m/s

Explanation:

The question is, "An object of mass 0.5kg is moving along a rectilinear path with constant acceleration of 0.3m / s2. If it started from rest and the magnitude of its momentum in kg * m / s after 8s is".

Mass of the object, m = 0.5 kg

Acceleration of the object, a = 0.3 m/s²

We need to find the momentum after 8 seconds.

We know that,

[tex]p=F\times t[/tex]

i.e.

p = mat

So,

[tex]p=0.5\times 0.3\times 8\\\\p=1.2\ kg-m/s[/tex]

So, the momentum of the object is 1.2 kg-m/s.

Question 3 of 10
Which statement describes the law of conservation of energy?
A. Air resistance has no effect on the energy of a system.
B. Energy cannot be created or destroyed.
C. The total energy in a system can only increase.
D. Energy cannot change forms.
هما
SUBMIT

Answers

Answer:

B . energy cannot be created or destroyed

PLEASE HELP ME WITH THIS ONE QUESTION
What is the rest energy of a proton? (c = 2.9979 x 10^9 m/s, mp = 1.6726 x 10^-27)

Answers

Answer:

multiply mp and c^2

Explanation:

e=mc^2

Warm air rises because faster moving molecules tend to move to regions of less

A) density.
B) pressure.
C) both of these
D) none of the above

Answers

Answer:

76rsfy7zfyuutfzufyztudzutdT7dFy9y8fr6s

Explanation:

rshyyjfshfsgfshfsyhrsyhuydtufhr6ra6yris7toe7r9w7rr6w996ryrowosotusuogsuoufsutot

which has higher eneergy electron r proton

Answers

Answer:

proton have higher energy than electron

Explanation:

tag me brainliest

Answer:

proton

Explanation:

proton is higher energy than the electron

If one lawn mower causes an 80-dB sound level at a point nearby, four lawnmowers together would cause a sound level of ____________ at that point. a.92 dB b.84 dB c.86 dB d.none of the above

Answers

Answer:

The intensity of 4 lawn movers is 86 dB.

Explanation:

Intensity of one lawnmower = 80 dB

Let the intensity is I.

Use the formula of intensity

[tex]dB = 10 log\left ( \frac{I}{Io} \right )\\\\80=10log\left ( \frac{I}{Io} \right )\\\\10^8 = \frac{I}{10^{-12}}\\\\I = 10^{-4} W/m^2[/tex]

Now the intensity of 4 lawn movers is

[tex]dB = 10 log\left ( \frac{4I}{Io} \right )\\\\dB=10log\left ( \frac{4\times10^{-4}}{10^{-12}} \right )\\\\dB = 86 dB\\[/tex]

The voltage across a membrane forming a cell wall is 74.0 mV and the membrane is 9.20 nm thick. What is the electric field strength in volts per meter

Answers

Answer:

7.60× 10^6 V/m

Explanation:

electric field strength can be determined as ratio of potential drop and distance, I.e

E=V/d

Where E= electric field

V= potential drop= 74.0 mV= 0.07 V

d= distance= 9.20 nm = 9.2×10^-9 m

Substitute the values

E= 0.07/ 9.2×10^-9

= 7.60× 10^6 V/m

An ice skater with a mass of 50 kg is gliding acrossthe ice at a speed of 8 m/s when herfriend comes up from behind and gives her a push,causing her speed to increase to 12m/s. How much work did the friend do on the skater

Answers

Answer:

[tex]W=2KJ[/tex]

Explanation:

From the question we are told that:

Mass [tex]M=50kg[/tex]

Initial Velocity [tex]v_1=8m/s[/tex]

Final Velocity [tex]v_2=12m/s[/tex]

Generally the equation for Work-done is mathematically given by

W=\triangle K.E

Therefore

 [tex]W=0.5M(v_2^2-v_1^2)[/tex]

 [tex]W=0.5*50(12^2-8^2)[/tex]

 [tex]W=2KJ[/tex]

Q 26.12: Assume current flows in a cylindrical conductor in such a way that the current density increases linearly with radius, from zero at the center to 1.0 A/m2 at the surface of the conductor. If the conductor has a cross sectional area of 1.0 m2, what can you say about the current in this conductor

Answers

Answer:

The current is 0.67 A.

Explanation:

Density, J = 1 A/m^2

Area, A = 1 m^2

Let the radius is r. And outer is R.

Use the formula of current density

[tex]I = \int J dA = \int J 2\pi r dr\\\\I = \int_{0}^{R}\frac{2\pi r^2}{R} dr\\\\I = \frac{2 \pi R^2}{3}.... (1)Now A = \pi R^2\\\\1 =\pi R^2\\\\R^2 = \frac{1}{\pi}\\\\So, \\\\I = \frac{2\pi}{3}\times \frac{1}{\pi}\\\\I = 0.67 A[/tex]

helppp!!! what's the answer to this??

when an ideal capacitor is connected across an ac voltage supply of variable frequency, the current flowing

a) is in phase with voltage at all frequencies
b) leads the voltage with a phase independent of frequency
c) leads the voltage with a phase which depends on frequency
d) lags the voltage with a phase independent of frequency

what would be the correct option? ​

Answers

Answer:

(b)

Explanation:

The voltage always lags the current by 90°, regardless of the frequency.

A wire 2.80 m in length carries a current of 5.60 A in a region where a uniform magnetic field has a magnitude of 0.300 T. Calculate the magnitude of the magnetic force on the wire assuming the following angles between the magnetic field and the current.

Answers

Complete question:

A wire 2.80 m in length carries a current of 5.60 A in a region where a uniform magnetic field has a magnitude of 0.300 T. Calculate the magnitude of the magnetic force on the wire assuming the following angles between the magnetic field and the current.

a) 60 ⁰

b) 90 ⁰

c) 120 ⁰

Answer:

(a) When the angle, θ = 60 ⁰,  force = 4.07 N

(b) When the angle, θ = 90 ⁰,  force = 4.7 N

(c) When the angle, θ = 120 ⁰,  force = 4.07 N

Explanation:

Given;

length of the wire, L = 2.8 m

current carried by the wire, I = 5.6 A

magnitude of the magnetic force, F = 0.3 T

The magnitude of the magnetic force is calculated as follows;

[tex]F = BIl \ sin(\theta)[/tex]

(a) When the angle, θ = 60 ⁰

[tex]F = BIl \ sin(\theta)\\\\F = 0.3 \times 5.6 \times 2.8 \times sin(60)\\\\F = 4.07 \ N[/tex]

(b) When the angle, θ = 90 ⁰

[tex]F = BIl \ sin(\theta)\\\\F = 0.3 \times 5.6 \times 2.8 \times sin(90)\\\\F = 4.7 \ N[/tex]

(c) When the angle, θ = 120 ⁰

[tex]F = BIl \ sin(\theta)\\\\F = 0.3 \times 5.6 \times 2.8 \times sin(120)\\\\F = 4.07 \ N[/tex]

A uniform horizontal bar of mass m1 and length L is supported by two identical massless strings. String A Both strings are vertical. String A is attached at a distance d

Answers

Answer:

a)  T_A = [tex]\frac{g}{d}\ ( m_2 x + m_1 \ \frac{L}{2} )[/tex] ,  b) T_B = g [m₂ ( [tex]\frac{x}{d} -1[/tex]) + m₁ ( [tex]\frac{L}{ 2d} -1[/tex]) ]

c)  x = [tex]d - \frac{m_1}{m_2} \ \frac{L}{2d}[/tex],  d)  m₂ = m₁  ( [tex]\frac{ L}{2d} -1[/tex])

Explanation:

After carefully reading your long sentence, I understand your exercise. In the attachment is a diagram of the assembly described. This is a balancing act

a) The tension of string A is requested

The expression for the rotational equilibrium taking the ends of the bar as the turning point, the counterclockwise rotations are positive

      ∑ τ = 0

      T_A d - W₂ x -W₁ L/2 = 0

      T_A = [tex]\frac{g}{d}\ ( m_2 x + m_1 \ \frac{L}{2} )[/tex]

b) the tension in string B

we write the expression of the translational equilibrium

       ∑ F = 0

       T_A - W₂ - W₁ - T_B = 0

       T_B = T_A -W₂ - W₁

       T_ B =   [tex]\frac{g}{d}\ ( m_2 x + m_1 \ \frac{L}{2} )[/tex]  - g m₂ - g m₁

       T_B = g [m₂ ( [tex]\frac{x}{d} -1[/tex]) + m₁ ( [tex]\frac{L}{ 2d} -1[/tex]) ]

c) The minimum value of x for the system to remain stable, we use the expression for the endowment equilibrium, for this case the axis of rotation is the support point of the chord A, for which we will write the equation for this system

         T_A 0 + W₂ (d-x) - W₁ (L / 2-d) - T_B d = 0

at the point that begins to rotate T_B = 0

          g m₂ (d -x) -  g m₁  (0.5 L -d) + 0 = 0

          m₂ (d-x) = m₁ (0.5 L- d)

          m₂ x = m₂ d - m₁ (0.5 L- d)

          x = [tex]d - \frac{m_1}{m_2} \ \frac{L}{2d}[/tex]

 

d) The mass of the block for which it is always in equilibrium

this is the mass for which x = 0

           0 = d - \frac{m_1}{m_2} \  \frac{L}{2d}

         [tex]\frac{m_1}{m_2} \ (0.5L -d) = d[/tex]

          [tex]\frac{m_1}{m_2} = \frac{ d}{0.5L-d}[/tex]

          m₂ = m₁  [tex]\frac{0.5 L -d}{d}[/tex]

          m₂ = m₁  ( [tex]\frac{ L}{2d} -1[/tex])

If the cornea is reshaped (this can be surgically done or with contact lenses) to correct myopia, should its curvature be made greater or smaller? Explain. Also, explain how hyperopia can be corrected?

Answers

Answer:

Myopia curvature of the cornea if it is negative the curvatures are positive,

hypermetry,

Explanation:

Myopia is the visual defect that does not allow to see distant objects, which is why it is corrected with a divergent lens so that the image is formed on the retina, therefore, by reforming the curvature of the cornea if it is negative

therefore the curvature must decrease

To correct hypermetry, the curvatures are positive, consequently the curvature of the lens must increase

No esporte coletivo, um dos principais fatores desenvolvidos é o desenvolvimento social. Qual desses não faz parte das virtudes ensinadas no esporte?

Companheirismo
Humildade
Ser justo (Fair Play)
Vencer independente do que precise ser feito

Answers

Answer:

fair palybtgshsisuehdh

As a roller coaster car crosses the top of a 48.01-m-diameter loop-the-loop, its apparent weight is the same as its true weight. What is the car's speed at the top?

Answers

Answer:

The speed of the car, v = 21.69 m/s

Explanation:

The diameter is  = 48.01 m

Therefore, the radius of the loop R = 24.005 m

Weight at the top is n = mv^2/R - mg

Since the apparent weight is equal to the real weight.

So, mv^2/R - mg = mg

v = √(2Rg)

v = √[2(24.005 m)(9.8 m/s^2)]

The speed of the car, v = 21.69 m/s

Answer:

The speed is 15.34 m/s.

Explanation:

Diameter, d = 48.01 m

Radius, R = 24.005 m

Let the speed is v and the mass is m.

Here, the weight of the car is balanced by the centripetal force.

According to the question

[tex]m g = \frac{mv^2}{R}\\\\v =\sqrt{24.005\times9.8}\\\\v = 15.34 m/s[/tex]

can some one help me :< its music​

Answers

What do you want to know about the answer

The energy truck travelling at 10 km/h has kinetic energy. How much kinetic energy does it have when it is loaded so its mass is twice and its speed is increased to twice?​

Answers

Explanation:

The initial kinetic energy [tex]KE_0[/tex] is

[tex]KE_0 = \frac{1}{2}m_0v_0^2[/tex]

When its mass and velocity are doubled, its new kinetic energy KE is

[tex]KE = \frac{1}{2}(2m_0)(2v_0)^2 = \frac{1}{2}(2m_0)(4v_0^2)[/tex]

[tex]\:\:\:\:\:\:\:= 8 \left(\frac{1}{2}m_0v_0^2 \right)= 8KE_0[/tex]

Therefore the kinetic energy will increase by a factor of 8.

A frictionless piston-cylinder device contains 10 kg of superheated vapor at 550 kPa and 340oC. Steam is then cooled at constant pressure until 60 percent of it, by mass, condenses. Determine (a) the work (W) done during the process. (b) What-if Scenario: What would the work done be if steam were cooled at constant pressure until 80 percent of it, by mass, condenses

Answers

Answer:

a) the work (W) done during the process is -2043.25 kJ

b) the work (W) done during the process is -2418.96 kJ

Explanation:

Given the data in the question;

mass of water vapor m = 10 kg

initial pressure P₁ = 550 kPa

Initial temperature T₁ = 340 °C

steam cooled at constant pressure until 60 percent of it, by mass, condenses; x = 100% - 60% = 40% = 0.4

from superheated steam table

specific volume v₁ = 0.5092 m³/kg

so the properties of steam at p₂ = 550 kPa, and dryness fraction

x = 0.4

specific volume v₂ = v[tex]_f[/tex] + xv[tex]_{fg[/tex]

v₂ = 0.001097 + 0.4( 0.34261 - 0.001097 )

v₂ = 0.1377 m³/kg

Now, work done during the process;

W = mP₁( v₂ - v₁ )

W = 10 × 550( 0.1377 - 0.5092 )

W = 5500 × -0.3715

W = -2043.25 kJ

Therefore, the work (W) done during the process is -2043.25 kJ

( The negative, indicates work is done on the system )

b)

What would the work done be if steam were cooled at constant pressure until 80 percent of it, by mass, condenses

x₂ = 100% - 80% = 20% = 0.2

specific volume v₂ = v[tex]_f[/tex] + x₂v[tex]_{fg[/tex]

v₂ = 0.001097 + 0.2( 0.34261 - 0.001097 )

v₂ = 0.06939 m³/kg

Now, work done during the process will be;

W = mP₁( v₂ - v₁ )

W = 10 × 550( 0.06939 - 0.5092 )

W = 5500 × -0.43981

W = -2418.96 kJ

Therefore, the work (W) done during the process is -2418.96 kJ

four equal magnitude point charges 3 microcoulomb is placed at the corners of a square that is 40cm inside find the force on any one of the charges ​

Answers

Answer:

Approximately [tex]0.97\; \rm N[/tex]. This force would point away from the center of the square (to the left at [tex]45^\circ[/tex] above the horizontal direction.)

Explanation:

Coulomb's constant: [tex]k \approx 8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2}[/tex].

By Coulomb's Law, the electrostatic force between two point charges [tex]q_1[/tex] and [tex]q_2[/tex] that are separated by [tex]r[/tex] (vacuum) would be:

[tex]\displaystyle F = \frac{k \cdot q_1 \cdot q_2}{r^2}[/tex].

Consider the charge on the top-left corner of this square.

Apply Coulomb's Law to find the electrostatic force between this charge and the charge on the lower-left corner.

Convert quantities to standard units:

[tex]q_1 = q_2 = 3 \times 10^{-6}\; \rm C[/tex].

[tex]r = 0.40\; \rm m[/tex].

[tex]\begin{aligned}F &= \frac{k \cdot q_1 \cdot q_2}{r^2} \\ &\approx \frac{8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2} \times (3 \times 10^{-6}\; \rm C)^{2}}{(0.40\; \rm m)^{2}} \\ &\approx 0.506\; \rm N\end{aligned}[/tex].

As the two charges are of the same sign, the electrostatic force on each charge would point away from the other charge. Hence, for the charge on the top-left corner of the square, the electrostatic force from the charge below it would point upwards.

Similarly, the charge to the right of this charge would exert an electrostatic force with the same magnitude (approximately [tex]0.506\; \rm N[/tex]) that points leftwards.

For the charge to the lower-right of the top-left charge, [tex]r = \sqrt{2} \times 0.40\; \rm m[/tex]. Therefore:

[tex]\begin{aligned}F &= \frac{k \cdot q_1 \cdot q_2}{r^2} \\ &\approx \frac{8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2} \times (3 \times 10^{-6}\; \rm C)^{2}}{(\sqrt{2} \times 0.40\; \rm m)^{2}} \\ &\approx 0.253 \; \rm N\end{aligned}[/tex].

This force would point to the top-left of the top-left charge, which is [tex]45^\circ[/tex] above the horizontal direction. Decompose this force into two components that are normal to one another:

Horizontal component: approximately [tex]\sin(45^\circ) \times 0.253\; \rm N \approx 0.179\; \rm N[/tex].Vertical component: approximately [tex]\cos(45^\circ) \times 0.253\; \rm N \approx 0.179\; \rm N[/tex]

Consider the net force on the top-left charge in two components:

Horizontal component: approximately [tex]0.506\; \rm N[/tex] from the charge on the top-right corner and approximately [tex]0.179\; \rm N[/tex] from the charge on the lower-right corner. Both components point to the left-hand side. [tex]F_x \approx 0.506\; \rm N + 0.179\; \rm N = 0.685\;\rm N[/tex] (to the left).Vertical component: approximately [tex]0.506\; \rm N[/tex] from the charge on the lower-left corner and approximately [tex]0.179\; \rm N[/tex] from the charge on the lower-right corner. Both components point upwards. [tex]F_y \approx 0.506\; \rm N + 0.179\; \rm N = 0.685\;\rm N[/tex] (upward).

Combine these two components to find the magnitude of the net force on this charge:

[tex]\begin{aligned}F &= \sqrt{{F_x}^{2} + {F_y}^{2}} \\ &\approx \sqrt{0.685^2 + 0.685^2 }\; \rm N \\ &\approx 0.97\; \rm N\end{aligned}[/tex].

This force would point to the top-left of this charge (also at [tex]45^\circ[/tex] above the horizontal direction, away from the center of the square) because its horizontal and vertical components have the same magnitude.

A massless, hollow sphere of radius R is entirely filled with a fluid such that its density is p. This same hollow sphere is now compressed so that its radius is R/2, and then it is entirely filled with the same fluid as before. As such, what is the density of the compressed sphere?
a. 8p
b. p/8
c. p/4
d. 4p

Answers

Answer:

a. 8p

Explanation:

We are given that

Radius of hollow sphere , R1=R

Density of hollow sphere=[tex]\rho[/tex]

After compress

Radius of hollow sphere, R2=R/2

We have to find density of the compressed sphere.

We know that

[tex]Density=\frac{mass}{volume}[/tex]

[tex]Mass=Density\times volume=Constant[/tex]

Therefore,[tex]\rho_1 V_1=\rho_2V_2[/tex]

Volume of sphere=[tex]\frac{4}{3}\pi r^3[/tex]

Using the formula

[tex]\rho\times \frac{4}{3}\pi R^3=\rho_2\times \frac{4}{3}\pi (R/2)^3[/tex]

[tex]\rho R^3=\rho_2\times \frac{R^3}{8}[/tex]

[tex]\rho_2=8\rho[/tex]

Hence, the density of  the compressed sphere=[tex]8\rho[/tex]

Option a is correct.

4. Consider a 1 kg block is on a 45° slope of ice. It is connected to a 0.4 kg block by a cable
and pulley. Does the 1 kg block move or down the slope? What is the net force on it and
its acceleration? (8 pts)

Answers

If an icy surface means no friction, then Newton's second law tells us the net forces on either block are

• m = 1 kg:

F (parallel) = mg sin(45°) - T = ma … … … [1]

F (perpendicular) = n - mg cos(45°) = 0

Notice that we're taking down-the-slope to be positive direction parallel to the surface.

• m = 0.4 kg:

F (vertical) = T - mg = ma … … … [2]

Adding equations [1] and [2] eliminates T, so that

((1 kg) g sin(45°) - T ) + (T - (0.4 kg) g) = (1 kg + 0.4 kg) a

(1 kg) g sin(45°) - (0.4 kg) g = (1.4 kg) a

==>   a ≈ 2.15 m/s²

The fact that a is positive indicates that the 1-kg block is moving down the slope. We already found the acceleration is a ≈ 2.15 m/s², which means the net force on the block would be ∑ F = ma ≈ (1 kg) (2.15 m/s²) = 2.15 N directed down the slope.

A 70.0-kg person throws a 0.0430-kg snowball forward with a ground speed of 32.0 m/s. A second person, with a mass of 58.5 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 3.30 m/s, and the second person is initially at rest. What are the velocities of the two people after the snowball is exchanged

Answers

Answer:

The velocities of the skaters are [tex]v_{1} = 3.280\,\frac{m}{s}[/tex] and [tex]v_{2} = 0.024\,\frac{m}{s}[/tex], respectively.

Explanation:

Each skater is not under the influence of external forces during process, so that Principle of Momentum Conservation can be used on each skater:

First skater

[tex]m_{1} \cdot v_{1, o} = m_{1} \cdot v_{1} + m_{b}\cdot v_{b}[/tex] (1)

Second skater

[tex]m_{b}\cdot v_{b} = (m_{2}+m_{b})\cdot v_{2}[/tex] (2)

Where:

[tex]m_{1}[/tex] - Mass of the first skater, in kilograms.

[tex]m_{2}[/tex] - Mass of the second skater, in kilograms.

[tex]v_{1,o}[/tex] - Initial velocity of the first skater, in meters per second.

[tex]v_{1}[/tex] - Final velocity of the first skater, in meters per second.

[tex]v_{b}[/tex] - Launch velocity of the meter, in meters per second.

[tex]v_{2}[/tex] - Final velocity of the second skater, in meters per second.

If we know that [tex]m_{1} = 70\,kg[/tex], [tex]m_{b} = 0.043\,kg[/tex], [tex]v_{b} = 32\,\frac{m}{s}[/tex], [tex]m_{2} = 58.5\,kg[/tex] and [tex]v_{1,o} = 3.30\,\frac{m}{s}[/tex], then the velocities of the two people after the snowball is exchanged is:

By (1):

[tex]m_{1} \cdot v_{1, o} = m_{1} \cdot v_{1} + m_{b}\cdot v_{b}[/tex]

[tex]m_{1}\cdot v_{1,o} - m_{b}\cdot v_{b} = m_{1}\cdot v_{1}[/tex]

[tex]v_{1} = v_{1,o} - \left(\frac{m_{b}}{m_{1}} \right)\cdot v_{b}[/tex]

[tex]v_{1} = 3.30\,\frac{m}{s} - \left(\frac{0.043\,kg}{70\,kg}\right)\cdot \left(32\,\frac{m}{s} \right)[/tex]

[tex]v_{1} = 3.280\,\frac{m}{s}[/tex]

By (2):

[tex]m_{b}\cdot v_{b} = (m_{2}+m_{b})\cdot v_{2}[/tex]

[tex]v_{2} = \frac{m_{b}\cdot v_{b}}{m_{2}+m_{b}}[/tex]

[tex]v_{2} = \frac{(0.043\,kg)\cdot \left(32\,\frac{m}{s} \right)}{58.5\,kg + 0.043\,kg}[/tex]

[tex]v_{2} = 0.024\,\frac{m}{s}[/tex]

A 1,760 W toaster, a 1,420 W electric frying pan, and an 85 W lamp are plugged into the same outlet in a 15 A, 120 V circuit. (The three devices are in parallel when plugged into the same socket.) (a) What current (in A) is drawn by each device

Answers

Answer:

Toaster = I = 14.67 A

Frying Pan = 11.83 A

Lamp = 0.71 A

Explanation:

The electric power is given as:

[tex]P = VI\\\\I = \frac{P}{V}[/tex]

where,

I = current

P = Power

V = Voltage = 120 V

FOR TOASTER:

P = 1760 W

Therefore,

[tex]I = \frac{1760\ W}{120\ V}[/tex]

I = 14.67 A

FOR FRYING PAN:

P = 1420 W

Therefore,

[tex]I = \frac{1420\ W}{120\ V}[/tex]

I = 11.83 A

FOR LAMP:

P = 85 W

Therefore,

[tex]I = \frac{85\ W}{120\ V}[/tex]

I = 0.71 A

Other Questions
i've been stuck on this question for 3 days ;< halp meh plesCalculate the average time for each vehicle.What was the average time for the Big Car? Show your work.What was the average time for the Small Car? Show your work.Calculate the average speed for each vehicle. Use the average time for this calculation.What was the average speed for the Big Car? Show your work.What was the average speed for the Small Car? Show your work. i need help.A. 145B. 35C. 55D. 75 Consider the sentence below. Create a sentence using a comparison that indicates the relationship of the items to each other. El semforo es pequeo. El carro es mediano. El puente es grande. How did contact between the Western Hemisphere and Europe change through the exchange of plants, animals, and pathogens? Sticky buns sell for $1.25 each,or $10.89 per dozen. how much does each bun cost if purchased by the dozen? How much do you save on 12 sticky buns? What is the basic concepts of movement and exercises? QUESTION 3 Change the following sentences in reported speech? --1 (a) He said " I like this song" He he liked that (b) Saima says "We spend our money on fat cakes yesterday." sana say that they had spend that (c) Mandy is at home." Stated John Money (d) Max says "Frank often reads a book." Which describes the role ofoxygen in photosynthesis? It is a reactant, so it is released by the plant.O It is aproduct, so it is released by the plant. It is a reactant, so it enters the plant. It is a product, so it enters the plant. Learning from books or learning from the Internet? which is more vulnerable to disturbances, a simple food web with only a few species or a more complex one Anong partidong kinabibilangan n Cory Aquino noong siya ay kumandidato bilang pangulo ng bansa..a.UNIDO b.Nacionalista c.Lakas d. Liberal Rudy rode a bike at the speed of 32 2/3 miles per 3 1/2 minutes. What is his speed in terms of miles per hours? HELPPP The model of competitive markets relies on these three core assumptions: 1. There must be many buyers and sellers-a few players can't dominate the market. 2. Firms must produce an identical product-buyers must regard all sellers' products as equivalent. 3. Firms and resources must be fully mobile, allowing for free entry into and exit from the industry. The first two conditions imply that all consumers and firms are price takers. While the third is not necessary for price-taking behavior, assume for this problem that a market cannot maintain competition in the long run without free entry.Identify whether or not each of the following scenarios describes a competitive market, along with the correct explanation of why or why not. Scenario Competitive1. Several stores in the mall sell hooded sweatshirts. Each store's sweatshirts reflect the style of that particular store. Additionally, some stores use higher-quality cotton than others, which is reflected in the apparel's prices. 2. In a small town, there are two providers of broadband Internet access: a cable company and the phone company. The Internet access offered by both providers is of the same speed. 3. There are hundreds of high school students in need of algebra tutoring services in Dallas. 4. Dozens of companies offer tutoring services, and the parents who seek out tutors view the quality of the tutoring at the different companies to be largely the same. 5. The government has granted a patent to a pharmaceutical company for an experimental AIDS drug. That company is the only firm permitted to sell the drug. Which is an example of temporal isolation?flowers that bloom in different monthsbirds that have different mating callsfruit flies that mate in different locationssquirrels that have different fur colors Howard Inc. had prepaid rent of $79,000 and $88,000 at the end of Year 1 and Year 2, respectively. During Year 2, Howard recorded $244,000 in rent expense in its income statement. Cash outflows for rent in Year 2 were: help and I'll follow you When applying an arm sling, the injured arm's hand should be placed in a ________ position in the sling, and above the level of the elbow. A highway used to not connect to other highways until years later when construction began to connect it to other highways. What power did government express? g For a closed economy, when net capital outflow is measured along the horizontal axis and the real interest rate is measured along the vertical axis, net capital outflow is drawn as a: Group of answer choices line that slopes up and to the right. horizontal line at the world real interest rate. line that slopes down and to the right. vertical line at 0. Which topic sentence would best start the following division paragraph?The key signature tells a musician where to play on aninstrument for the duration of the piece. The temponotations tell a musician how quickly or slowly to play themusic. Finally, there are the musical notes themselves,combined in various ways in various rhythms. Without allthree of these things, musical scores would not exist as weknow them.I A. Every musical score has three crucial elements.B. Musical scores can be grouped into three main categories.di C. Pieces of music are complicated, but they can be grouped intothree classesD. Musicians have to pay attention to three things when they play.