A small object with mass 3.80 kg moves counterclockwise with constant speed 1.65 rad/s in a circle of radius 2.70 m centered at the origin. It starts at the point with position vector 2.70 m. Then it undergoes an angular displacement of 8.70 rad.
(a) What is its new position vector?
in meters
(b) In what quadrant is the particle located and what angle does its position vector make with the positive x-axis?
(c) What is its velocity?
in m/s
(d) In what direction is it moving?
_____° from the +x direction.
(e) What is its acceleration?
in m/s2
(f) What total force is exerted on the object?
in N

Answer:

The horizontal component is  [tex]v_h = 1.7096 \ m/s[/tex]

Explanation:

A diagram illustrating the projection is  shown on the first uploaded image  (from  IB Maths Resources from British international school Phuket )

From the question we are told that  

    The initial velocity is  [tex]v_o = 7.6 \ m/s[/tex]

      The angle of projection is  [tex]\theta = 1.27 \ rad = 72.77^o[/tex]

The  horizontal component of this  projectile  velocity is  mathematically represented as

          [tex]v_h = v_o * cos (\theta )[/tex]

substituting values  

         [tex]v_h = 7.6 * cos (72.77 )[/tex]

        [tex]v_h = 1.7096 \ m/s[/tex]

Answer:

Explanation:

a. Is the sphere charged negatively or positively?

The sphere us negatively charged. In a Millikan type experiment, there will be two forces that will be acting on the sphere which are the electric force which acts upward and also the gravity which acts downward.

Because the upper plate is positively charged, there'll what an attractive curve with an upward direction which will be felt by the negatively charged sphere.

b. What is the magnitude of the electric field intensity between the plates?

The magnitude of the electric field intensity between the plates is 18400v/m.

C. Calculate the magnitude of the charge on the latex sphere.

The magnitude of the charge on the latex sphere hae been solved and attached

d. How many excess or deficit electrons does the sphere have?

There are 5 excess electrons that the sphere has.

Check the attachment for further explanation.

Answer:

The two methods will yield different results as one is subject to experimental errors that us the Archimedes method of measurement, the the density measurement method will be more accurate

Explanation:

This is because the density method using the calculated volume will huve room for less errors that's occur in practical method i.e Archimedes method due to human error

Answer:

The main points of difference between a citizen and alien are: (a) A citizen is a permanent resident of a state, while an alien is a temporary resident, who comes for a specific duration of time as a tourist or on diplomatic assignment. ... Aliens do not possess such rights in the state where they reside temporarily

Explanation:

Answer:

Explanation:

The current through the  resistor is 0.83 A

.

Part b

The current through  resistor is 0.53 A

.

Part c

The current through  resistor is 0.30 A

Answer:

An asteroid that has an orbital period of 3 years will have an orbital with a semi-major axis of about  2 years.

Explanation:

Given;

orbital period of 3 years, P = 3 years

To calculate the years of an orbital with a semi-major axis, we apply Kepler's third law.

Kepler's third law;

P² = a³

where;

P is the orbital period

a is the orbital semi-major axis

(3)² = a³

9 = a³

a = [tex]a = \sqrt[3]{9} \\\\a = 2.08 \ years[/tex]

Therefore, An asteroid that has an orbital period of 3 years will have an orbital with a semi-major axis of about  2 years.

Answer:

The astronaut and the satellite are 53.718 m apart.

Explanation:

Given;

mass of spacewalking astronaut, = 88 kg

mass of satellite, = 645 kg

force exerts by the satellite, F = 110N

time for this action, t = 0.45 s

Determine the acceleration of the satellite after the push

F = ma

a = F / m

a = 110 / 645

a = 0.171 m/s²

Determine the final velocity of the satellite;

v = u + at

where;

u is the initial velocity of the satellite = 0

v = 0 + 0.171 x 0.45

v = 0.077 m/s

Determine the displacement of the satellite after 1.4 m

d₁ = vt

d₁ = 0.077 x (1.4 x 60)

d₁ = 6.468 m

According to Newton's third law of motion, action and reaction are equal and opposite;

Determine the backward acceleration of the astronaut after the push;

F = ma

a = F / m

a = 110 / 88

a = 1.25 m/s²

Determine the final velocity of the astronaut

v = u + at

The initial velocity of the astronaut = 0

v = 1.25 x 0.45

v = 0.5625 m/s

Determine the displacement of the astronaut after 1.4 min

d₂ = vt

d₂ = 0.5625 x (1.4 x 60)

d₂ = 47.25 m

Finally, determine the total separation between the astronaut and the satellite;

total separation = d₁ + d₂

total separation = 6.468 m + 47.25 m

total separation = 53.718 m

Therefore, the astronaut and the satellite are 53.718 m apart.

Answer:

The maximum speed of the mass is 4.437 m/s.

Explanation:

Given;

length of pendulum, L = 1.62 m

attached mass, m = 117 g

angle of inclination, θ = 38°

This mass was raised to a height of

h = 1.62 - cos38° = 1.0043 m

Apply the principle of conservation of mechanical energy

PE = KE

mgh = ¹/₂mv²

v  = √(2gh)

v = √(2 * 9.8 * 1.0043)

v = 4.437 m/s.

Therefore, the maximum speed of the mass is 4.437 m/s.

Complete Question

The uniform purely axial magnetic induction required by the experiment in a volume large enough to accommodate the Lorentz Tube is produced by the Helmholtz Coils. What is the magnetic induction due to a coil current 1.5 Ampere? Convert the result in the still popular non-SI unit Gauss (1 Tesla = 10^4 Gauss).

B = N*mue*I/(2*r)

# of loops = 140

radius of the coil = 0.14m

Answer:

 The magnetic induction is [tex]B = 2.639 \ Gauss[/tex]

Explanation:

From the question we are told that

     The coil current is  [tex]I = 1.5 \ A[/tex]

     The number of loops is  [tex]N = 140[/tex]

The magnetic field due to the current is mathematically represented as

           [tex]B = \mu_o * N * I[/tex]

[tex]\mu_o[/tex] is the permeability of free space with value  [tex]\mu_o = 4\pi * 10^{-7} N/A^2[/tex]

substituting value

           [tex]B = 4\pi * 10^{-7} * 140 * 1.5[/tex]

           [tex]B = 2.639*19^{-4} \ T[/tex]

From question

        (1 Tesla = [tex]10^4 \ Gauss[/tex]).

=>      [tex]B = 2.693 *10^{-4} *10^4 = 2.63 \ Gauss[/tex]

=>      [tex]B = 2.639 \ Gauss[/tex]

Answer:

C. The atom loses 1 electron to have a total of 36.

Explanation:

Cations have a positive charge. Cations lose electrons.

The number of electrons in a Rubidium atom is 37. If the atom loses 1 electron, then it has 36 left.

Answer:

The  tension on the clotheslines is  [tex]T = 8.83 \ N[/tex]

Explanation:

The  diagram illustrating this  question is  shown on the first uploaded image

From the question we are told that  

    The distance between the two poles is  [tex]d = 12 \ m[/tex]

     The mass tie to the middle of the clotheslines [tex]m = 1 \ kg[/tex]

     The length at which the clotheslines sags is  [tex]l = 4 \ m[/tex]

Generally the weight due to gravity at the middle of the  clotheslines is mathematically represented as

          [tex]W = mg[/tex]

let the angle which the tension on the  clotheslines makes with the horizontal be  [tex]\theta[/tex] which mathematically evaluated using the SOHCAHTOA as follows

        [tex]Tan \theta = \frac{ 4}{6}[/tex]

=>     [tex]\theta = tan^{-1}[\frac{4}{6} ][/tex]

=>     [tex]\theta = 33.70^o[/tex]

   So the vertical component of this  tension is  mathematically represented a  

      [tex]T_y = 2* Tsin \theta[/tex]

Now at equilibrium the  net horizontal force is  zero which implies that

          [tex]T_y - mg = 0[/tex]

=>       [tex]T sin \theta - mg = 0[/tex]

substituting values

          [tex]T = \frac{m*g}{sin (\theta )}[/tex]

substituting values

           [tex]T = \frac{1 *9.8}{2 * sin (33.70 )}[/tex]

           [tex]T = 8.83 \ N[/tex]

Answer:

B = 4.1*10^-3 T = 4.1mT

Explanation:

In order to calculate the strength of the magnetic field, you use the following formula for the magnetic flux trough a surface:

[tex]\Phi_B=S\cdot B=SBcos\alpha[/tex]        (1)

ФB: magnetic flux trough the circular surface = 6.80*10^-5 T.m^2

S: surface area of the circular plate = π.r^2

r: radius of the circular plate = 8.50cm = 0.085m

B: magnitude of the magnetic field = ?

α: angle between the direction of the magnetic field and the normal to the surface area of the circular plate = 43.0°

You solve the equation (1) for B, and replace the values of the other parameters:

[tex]B=\frac{\Phi_B}{Scos\alpha}=\frac{6.80*10^{-5}T.m^2}{(\pi (0.085m)^2)cos(43.0\°)}\\\\B=4.1*10^{-3}T=4.1mT[/tex]

The strength of the magntetic field is 4.1mT

Answer:

(a) Distance between deer and car = 5 m

(b) Vmax = 21.92 m/s

Explanation:

a.

First we calculate distance covered during response time:

s₁ = vt   --------- equation 1

where,

s₁ = distance covered during response time = ?

v = speed of car = 20 m/s

t = response time = 0.5 s

Therefore,

s₁ = (20 m/s)(0.5 s)

s₁ = 10 m

Now, we calculate the distance covered by the car during deceleration. Using 3rd equation of motion:

2as₂ = Vf² - Vi²

s₂ = (Vf² - Vi²)/2a ------ eqation 2

where,

a = deceleration = - 10 m/s²

s₂ = Distance covered during deceleration = ?

Vf = Final Velocity = 0 m/s (since car finally stops)

Vi = Initial Velocity = 20 m/s

Therefore,

s₂ = [(0 m/s)² - (20 m/s)²]/2(-10 m/s²)

s₂ = (400 m²/s²)/(20 m/s²)

s₂ = 20 m

thus, the total distance covered by the car before coming to rest is given as:

s = s₁ + s₂

s = 10 m + 20 m

s = 30 m

Now, the distance between deer and car, when it comes to rest, can be calculated as:

Distance between deer and car = 35 m - s = 35 m - 30 m

Distance between deer and car = 5 m

b.

Since, the distance covered by the car in total must be equal to 35 m at maximum. Therefore,

s₁ + s₂ = 35 m

using equation 1 and equation 2 from previous part:

Vi t + (Vf² - Vi²)/2a = 35 m

Vi(0.5 s) + [(0 m/s)² - Vi²]/2(-10 m/s²) = 35 m

0.5 Vi + 0.05 Vi² = 35

0.05 Vi² + 0.5 Vi - 35 = 0

solving this quadratic equation, we get:

Vi = - 31.92 m/s  (OR)  Vi = 21.92 m/s

For maximum velocity:

Vmax = 21.92 m/s

Answer:

θ₀ = 84.78° (OR) 5.22°

Explanation:

This situation can be treated as projectile motion. The parameters of this projectile motion are:

R = Range of Projectile = 150 m

V₀ = Launch Speed of Projectile = 90 m/s

g = 9.8 m/s²

θ₀ = Launch angle (OR) Angle of Elevation = ?

The formula for range of a projectile is given as:

R = V₀² Sin 2θ₀/g

Sin 2θ₀ = Rg/V₀²

Sin 2θ₀ = (150 m)(9.8 m/s²)/(90 m/s)²

2θ₀ = Sin⁻¹ (0.18)

θ₀ = 10.45°/2

θ₀ = 5.22°

Also, we know that for the same launch velocity the range will be same for complementary angles. Therefore, another possible value of angle is:

θ₀ = 90° - 5.22°

θ₀ = 84.78°

Answer:

The wavelength will be 33.9 cm

Explanation:

Given;

frequency of the wave, F = 1200 Hz

Tension on the wire, T = 800 N

wavelength, λ = 39.1 cm

[tex]F = \frac{ \sqrt{\frac{T}{\mu} }}{\lambda}[/tex]

Where;

F is the frequency of the wave

T is tension on the string

μ is mass per unit length of the string

λ is wavelength

[tex]\sqrt{\frac{T}{\mu} } = F \lambda\\\\\frac{T}{\mu} = F^2\lambda^2\\\\\mu = \frac{T}{F^2\lambda^2} \\\\\frac{T_1}{F^2\lambda _1^2} = \frac{T_2}{F^2\lambda _2^2} \\\\\frac{T_1}{\lambda _1^2} = \frac{T_2}{\lambda _2^2}\\\\T_1 \lambda _2^2 = T_2\lambda _1^2\\\\[/tex]

when the tension is decreased to 600 N, that is T₂ = 600 N

[tex]T_1 \lambda _2^2 = T_2\lambda _1^2\\\\\lambda _2^2 = \frac{T_2\lambda _1^2}{T_1} \\\\\lambda _2 = \sqrt{\frac{T_2\lambda _1^2}{T_1}} \\\\\lambda _2 = \sqrt{\frac{600* 0.391^2}{800}}\\\\\lambda _2 = \sqrt{0.11466} \\\\\lambda _2 =0.339 \ m\\\\\lambda _2 =33.9 \ cm[/tex]

Therefore, the wavelength will be 33.9 cm

Answer:

the two beams must travel paths that differ by one-half of a wavelength.

Answer:

he correct answers are a, b

Explanation:

In the two-slit interference phenomenon, the expression for interference is

          d sin θ= m λ                       constructive interference

          d sin θ = (m + ½) λ             destructive interference

in general this phenomenon occurs for small angles, for which we can write

           tanθ = y / L

           tan te = sin tea / cos tea = sin tea

           sin θ = y / La

un

derestimate the first two equations.

Let's do the calculation for constructive interference

         d y / L = m λ

the distance between maximum clos is and

         y = (me / d) λ

this is the position of each maximum, the distance between two consecutive maximums

         y₂-y₁ = (L   2/d) λ - (L 1 / d) λ₁          y₂ -y₁ = L / d λ

examining this equation if the wavelength decreases the value of y also decreases

the same calculation for destructive interference

         d y / L = (m + ½) κ

         y = [(m + ½) L / d] λ

again when it decreases the decrease the distance

the correct answers are a, b

Answer:

F' = F/4

Thus, the magnitude of electrostatic force will become one-fourth.

Explanation:

The magnitude of force applied by each charge on one another can be given by Coulomb's Law:

F = kq₁q₂/r²   -------------- equation 1

where,

F = Force applied by charges

k = Coulomb's Constant

q₁ = magnitude of first charge

q₂ = magnitude of 2nd charge

r = distance between the charges

Now, in the final state the charges on both spheres are halved. Therefore,

q₁' = q₁/2

q₂' = q₂/2

Hence, the new force will be:

F' = kq₁'q₂'/r²

F' = k(q₁/2)(q₂/2)/r²

F' = (kq₁q₂/r²)(1/4)

using equation 1:

F' = F/4

Thus, the magnitude of electrostatic force will become one-fourth.

The magnitude of the electrostatic force will be F' = F/4

Here we used Coulomb's Law:

F = kq₁q₂/r²   -------------- equation 1

Here

F = Force applied by charges

k = Coulomb's Constant

q₁ = magnitude of first charge

q₂ = magnitude of 2nd charge

r = distance between the charges

Now

q₁' = q₁/2

q₂' = q₂/2

So, the new force should be

F' = kq₁'q₂'/r²

F' = k(q₁/2)(q₂/2)/r²

F' = (kq₁q₂/r²)(1/4)

So,

F' = F/4

Learn more about force here: https://brainly.com/question/14282312

Answer:

3) Transmitted intensity of light if unpolarized light passes through a single polarizing filter = 40 W/m²

- Transmitted intensity of light if an additional polarizer is added perpendicular to the first polarizer in the setup described = 7.5 W/m²

Explanation:

Complete Question

3) What is the transmitted intensity of light if unpolarized light passes through a single polarizing filter and the initial intensity is 80 W/m²?

- What is the transmitted intensity of light if an additional polarizer is added perpendicular to the first polarizer in the setup described in Question 3 (the setup)? Show all work in your answer.

The image of this setup attached to this question as obtained from online is attached to this solution.

Solution

3) When unpolarized light passes through a single polarizer, the intensity of the light is cut in half.

Hence, if the initial intensity of unpolarized light is I₀ = 80 W/m²

The intensity of the light rays thay pass through the first single polarizer = I₁ = (I₀/2) = (80/2) = 40 W/m²

- According to Malus' law, the intensity of transmitted light through a polarizer is related to the intensity of the incident light and the angle at which the polarizer is placed with respect to the major axis of the polarizer before the current polarizer of concern.

I₂ = I₁ cos² θ

where

I₂ = intensity of light that passes through the second polarizer = ?

I₁ = Intensity of light from the first polarizer that is incident upon the second polarizer = 40 W/m²

θ = angle between the major axis of the first and second polarizer = 30°

I₂ = 40 (cos² 30°) = 40 (0.8660)² = 30 W/m²

In the same vein, the intensity of light that passes through the third/additional polarizer is related to the intensity of light that passes through the second polarizer and is incident upon this third/additional polarizer through

I₃ = I₂ cos² θ

I₃ = intensity of light that passes through the third/additional polarizer = ?

I₂ = Intensity of light from the second polarizer that is incident upon the third/additional polarizer = 30 W/m²

θ = angle between the major axis of the second and third/additional polarizer = 60° (although, it is 90° with respect to the first polarizer, it is the angle it makes with the major axis of the second polarizer, 60°, that matters)

I₃ = 30 (cos² 60°) = 30 (0.5)² = 7.5 W/m²

Hope this Helps!!!

Answer:

The speed will be "3.4×10⁴ m/s²".

Explanation:

The given values are:

Angular speed,

w = 7200 rpm

i.e.,

  = [tex]7200 \times \frac{2 \pi}{60}[/tex]

  = [tex]753.6 \ rad/s[/tex]

Speed from the center,

r = 6.0 cm

As we know,

⇒  Linear speed, [tex]v=wr[/tex]

On putting the estimated values, we get

                               [tex]=753.6\times 0.06[/tex]

                               [tex]=45.216 \ m[/tex]

Now,

Acceleration on disk will be:

⇒  [tex]a=\frac{v^2}{r}[/tex]

       [tex]=34074 \ m/s^2[/tex]

       [tex]=3.4\times 10^4 \ m/s^2[/tex]

Answer:

The number of bright spot is  m =4

Explanation:

From the question we are told that

    The number of lines is  [tex]s = 500 \ lines / mm = 500 \ lines / 10^{-3} m[/tex]

     The wavelength of the laser is  [tex]\lambda = 480 nm = 480 *10^{-9} \ m[/tex]

Now the the slit is mathematically evaluated as

        [tex]d = \frac{1}{s} = \frac{1}{500} * 10^{-3} \ m[/tex]

Generally the diffraction grating is mathematically represented as

        [tex]dsin\theta = m \lambda[/tex]

Here m is the order of fringes (bright fringes) and at maximum m  [tex]\theta = 90^o[/tex]

    So

          [tex]\frac{1}{500} * sin (90) = m * (480 *10^{-3})[/tex]

=>        [tex]m = 4[/tex]

This  implies that the number of bright spot is  m =4

Answer:

The distance between the two charges is =4.4mm

Answer:

I think it is the 4th answer choice

Explanation:

Heat is thermal energy that flows in the direction of high temp to low temp, and internal energy is the "energy contained in a system", and thermal energy is a part of that.

Answer:

Explanation:

Heat absorbed by oil

= mass x specific heat x rise in temperature

= 30 x 10⁻³ x 950 x 2.2 x 10³ x ( 50-10 )

= 25.08 x 10⁵ J  

Heat absorbed by air

= 50 x 1.2 x 1.0054 x 10³ x ( 20-10 )

= 6.03 x 10⁵ J

Total heat absorbed = 31.11 x 10⁵ J

If time required = t

heat lost from room

= .35 x 10³ t

Total heat generated in time t

= 1.8 x 10³ t

Heat generated = heat used

1.8 x 10³ t =  .35 x 10³ t  + 31.11 x 10⁵

1.45 x 10³ t = 31.11 x 10⁵

t = 31.11 x 10⁵ / 1.45 x 10³

t = 2145.5 s

Answer:

B: I2>I1

Explanation:

See attached file

Complete Question

A very large sheet of a conductor carries a uniform charge density of [tex]4.00\ pC/mm^2[/tex]  on its surfaces. What is the electric field strength 3.00 mm outside the surface of the conductor?

Answer:

The electric field is  [tex]E = 4.5198 *10^{5} \ N/C[/tex]

Explanation:

From the question we are told that

    The charge density is  [tex]\sigma = 4.00pC /mm^2 = 4.00 * 10^{-12 } * 10^{6} = 4.00 *10^{-6}C/m[/tex]

    The position outside the surface is  [tex]a = 3.00 \ mm = 0.003 \ m[/tex]

Generally the electric field is mathematically represented as

          [tex]E = \frac{\sigma}{\epsilon _o }[/tex]

Where  [tex]\epsilon_o[/tex] is  the permitivity of free space with values  [tex]\epsilon _o = 8.85 *10^{-12} F/m[/tex]

substituting values  

           [tex]E = \frac{4.0*10^{-6}}{8.85 *10^{-12} }[/tex]

           [tex]E = 4.5198 *10^{5} \ N/C[/tex]

Answer:

From the image, the force as shown in option A will exert the biggest torque on the cylinder about its central axes.

Explanation:

The image is shown below.

Torque is the product of a force about the center of rotation of a body, and the radius through which the force acts. For a given case such as this, in which the cylinders are identical, and the forces are of equal magnitude, the torque at the maximum radius away from the center will exert the maximum torque. Also, the direction of the force also matters. To generate the maximum torque, the force must be directed tangentially away from the circle formed by the radius through which the force acts away from the center. Option A satisfies both condition and hence will exert the most torque on the cylinder.

Given info

d = 0.000250 meters = distance between slits

L = 302 cm = 0.302 meters = distance from slits to screen

[tex]\theta_8 = 1.12^{\circ}[/tex] = angle to 8th max (note how m = 8 since we're comparing this to the form [tex]\theta_m[/tex])

[tex]x_n = x_5 = 3.33 \text{ cm} = 0.0333 \text{ meters}[/tex] (n = 5 as we're dealing with the 5th minimum )

---------------

Method 1

[tex]d\sin(\theta_m) = m\lambda\\\\0.000250\sin(\theta_8) = 8\lambda\\\\8\lambda = 0.000250\sin(1.12^{\circ})\\\\\lambda = \frac{0.000250\sin(1.12^{\circ})}{8}\\\\\lambda \approx 0.000 000 61082633\\\\\lambda \approx 6.1082633 \times 10^{-7} \text{meters}\\\\ \lambda \approx 6.11 \times 10^{-7} \text{ meters}\\\\ \lambda \approx 611 \text{ nm}[/tex]

Make sure your calculator is in degree mode.

-----------------

Method 2

[tex]\Delta x = \frac{\lambda*L*m}{d}\\\\L*\tan(\theta_m) = \frac{\lambda*L*m}{d}\\\\\tan(\theta_m) = \frac{\lambda*m}{d}\\\\\tan(\theta_8) = \frac{\lambda*8}{0.000250}\\\\\tan(1.12^{\circ}) = \frac{\lambda*8}{0.000250}\\\\\lambda = \frac{1}{8}*0.000250*\tan(1.12^{\circ})\\\\\lambda \approx 0.00000061094306 \text{ meters}\\\\\lambda \approx 6.1094306 \times 10^{-7} \text{ meters}\\\\\lambda \approx 611 \text{ nm}\\\\[/tex]

-----------------

Method 3

[tex]\frac{d*x_n}{L} = \left(n-\frac{1}{2}\right)\lambda\\\\\frac{0.000250*3.33}{302.0} = \left(5-\frac{1}{2}\right)\lambda\\\\0.00000275662251 \approx \frac{9}{2}\lambda\\\\\frac{9}{2}\lambda \approx 0.00000275662251\\\\\lambda \approx \frac{2}{9}*0.00000275662251\\\\\lambda \approx 0.00000061258279 \text{ meters}\\\\\lambda \approx 6.1258279 \times 10^{-7} \text{ meters}\\\\\lambda \approx 6.13 \times 10^{-7} \text{ meters}\\\\\lambda \approx 613 \text{ nm}\\\\[/tex]

There is a slight discrepancy (the first two results were 611 nm while this is roughly 613 nm) which could be a result of rounding error, but I'm not entirely sure.

Answer:

The angular speed of the ball will increase

Explanation:

the angular speed of the ball will increase because the force of hit by the players will sum up in opposite direction to increase the angular speed