2

10 points

Find the total displacement of each of the motions.

a) You walk 45 m W, then 34 mW

b) You drive 5 km N, then 7 km S

c) You cycle 350 m E, then 800 m W, then 200 m E

d) You fly 850 km N then 850 km S

Answer:

a) The potential energy of the system is 1/9 of the total mechanical energy, when [tex]x= \frac{1}{3}\cdot A[/tex].

b) The fraction of the total mechanical energy that is kinetic if the displacement is 1/2 the amplitude is 1/2.

c) The maximum kinetic energy is increased by a factor of 9.

Explanation:

a) From Mechanical Physics, we remember that the mechanical energy of mass-spring system ([tex]E[/tex]), measured in joules, is the sum of the translational kinetic energy ([tex]K[/tex]), measured in joules, and elastic potential energy ([tex]U[/tex]), measured in joules. That is:

[tex]E = K + U[/tex] (1)

By definitions of translational kinetic energy and elastic potential energy, we have the following expressions:

[tex]K = \frac{1}{2}\cdot m \cdot v^{2}[/tex] (2)

[tex]U = \frac{1}{2}\cdot k\cdot x^{2}[/tex] (3)

Where:

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

[tex]v[/tex] - Velocity of the mass, measured in meters per second.

[tex]k[/tex] - Spring constant, measured in newtons per meter.

[tex]x[/tex] - Elongation of the spring, measured in meters.

If we know that [tex]U = \frac{1}{9}\cdot E[/tex], [tex]k = k[/tex] and [tex]E = \frac{1}{2}\cdot k \cdot A^{2}[/tex], then:

[tex]\frac{1}{18}\cdot k\cdot A^{2} = \frac{1}{2}\cdot k\cdot x^{2}[/tex]

[tex]\frac{1}{9}\cdot A^{2} = x^{2}[/tex]

[tex]x= \frac{1}{3}\cdot A[/tex]

The potential energy of the system is 1/9 of the total mechanical energy, when [tex]x= \frac{1}{3}\cdot A[/tex].

b) If we know that [tex]k = k[/tex], [tex]x = \frac{1}{2}\cdot A[/tex] and [tex]E = \frac{1}{2}\cdot k \cdot A^{2}[/tex], then the equation of energy conservation associated with the system is:

[tex]\frac{1}{2}\cdot k\cdot A^{2} = \frac{1}{4}\cdot k\cdot A^{2}+K[/tex]

[tex]K = \frac{1}{4}\cdot k\cdot A^{2}[/tex]

The fraction of the total mechanical energy that is kinetic if the displacement is 1/2 the amplitude is 1/2.

c) From the Energy Conservation equation associated with the system, we know that increasing the amplitude by a factor of 3 represents an increase in the elastic potential energy by a factor of 9. Then, the maximum kinetic energy is increased by a factor of 9.

Answer:

When traveling behind other vehicles, there should be at least a four second space between your vehicles. When the car in front of you passes a stationary object, slowly count to yourself. If you pass the object before the allotted time, you should back off. When traveling at night or inclement weather, these times should be doubled.

Don't talk on a cell phone while driving. Phones detract from your ability to concentrate on the road and increase your chance of a collision by nearly 400%. If you must use the phone, pull over to a safe, well-lit parking lot and place your call there. After completing your call you may continue on your way.bey all speed limits and signs.

Answer:

This question is incomplete

Explanation:

This question is incomplete. However, the formula to be used here is

ω = 2π/T

Where ω is the angular frequency (in rad/s)

T is the period - the time taken for Block A to complete one oscillation and return to it's original position.

To solve for this period T, the formula below should be used

T = 2π√m/k

where m is the mass of the object (Block A) and k is the spring constant (281 J/m²)

Answer:

t = 1.32 s

Explanation:

We are given;. Frequency of C4 note; F_c = 262 Hz

In conversions, we know that 1 Hz = 1 cycle/s

Thus, F_c = 262 cycles/s

Now, we want to find out how much time it takes for 346 air pressure maxima to pass a stationary listener.

346 air pressure maxima denotes that the air pressure maxima is 346 cycles.

Thus, time will be;

t = 346 cycles/262 cycles/s

t = 1.32 s

The time taken for the musical note to pass the stationary listener is 1.32 s.

The given parameters:

The frequency of a sound wave is defined as the number of cycles completed per second by the wave.

[tex]F = \frac{n}{t}[/tex]

where;

The time taken for the musical note to pass the stationary listener is calculated as follows;

[tex]262 = \frac{n}{t} \\\\t = \frac{n}{262} \\\\t = \frac{346}{262} \\\\t = 1.32 \ s[/tex]

Thus, the time taken for the musical note to pass the stationary listener is 1.32 s.

Learn more here:https://brainly.com/question/15613196

Answer:

The minimum inductance needed is 2.78 H

Explanation:

Given;

frequency of the AC, f = 26.5 Hz

the root mean square voltage in the circuit, [tex]V_{rms}[/tex] = 41.2 V

the maximum current in the circuit, I₀ = 126 mA

The root mean square current is given by;

[tex]I_{rms} = \frac{I_o}{\sqrt{2} } \\\\I_{rms} = \frac{126*10^{-3}}{\sqrt{2} }\\\\I_{rms} =0.0891 \ A[/tex]

The inductive reactance is given by;

[tex]X_l = \frac{V_{rms}}{I_{rms}} \\\\X_l= \frac{41.2}{0.0891}\\\\X_l = 462.4 \ ohms[/tex]

The minimum inductance needed is given by;

[tex]X_l = \omega L\\\\X_l = 2\pi fL\\\\L = \frac{X_l}{2\pi f}\\\\L = \frac{462.4}{2\pi *26.5}\\\\L = 2.78 \ H[/tex]

Therefore, the minimum inductance needed is 2.78 H

Answer:

B R is constant V increases /increases

If one increase the length of the wire in the circuit, then, R increases, V decreases, I decreases. The correct option is D.

The resistance (R) of a wire increases as its length is increased in a circuit. This is because longer wires have more resistance because resistance increases with length.

Ohm's Law states that the current (I) in the circuit will drop if the resistance (R) rises while the voltage (V) stays constant. This is due to the inverse proportionality between current and resistance.

Thus, the correct option is D.

For more details regarding Ohm's law, visit:

https://brainly.com/question/1247379

#SPJ5

We know, by conservation of energy :

[tex]\dfrac{kx^2}{2}=mgh[/tex]

Therefore,

[tex]\dfrac{x_1^2}{x_2^2}=\dfrac{h_1}{h_2}[/tex]

Putting given values, we get :

[tex]\dfrac{x_1^2}{x_2^2}=\dfrac{h_1}{h_2}\\\\\dfrac{4.9^2}{x_2^2}=\dfrac{50.2}{2\times 50.2}\\\\x_2^2=2\times 4.9^2\\\\x_2 = 4.9\times \sqrt{2}\\\\x_2=6.93\ cm[/tex]

Therefore, the spring be compressed to 6.93 cm to send the ball twice as high.

Hence, this is the required solution.

Answer:

The stress is  [tex]\sigma = 1.218*10^{6} \ N/m^2[/tex]

Explanation:

From the question we are told that

   The diameter of the post is  [tex]d = 29 \ cm = 0.29 \ m[/tex]

   The length is [tex]L = 2.0 \ m[/tex]

    The weight of the loading mass

Generally  the  radius of the post is mathematically represented as

     [tex]r = \frac{0.29}{2}[/tex]

=>   [tex]r = 0.145 \ m[/tex]

Generally the area of the post is  

       [tex]A = \pi r^2[/tex]

=>     [tex]A = 3.14 * 0.145 ^2[/tex]

=>     [tex]A = 0.066 \ m^2[/tex]

Generally the weight exerted by the load is mathematically represented as

        [tex]F = m * g[/tex]

=>      [tex]F = 8200 * 9.8[/tex]

=>      [tex]F = 80360 \ N[/tex]

Generally the stress is mathematically represented as

         [tex]\sigma = \frac{F}{A}[/tex]

=>      [tex]\sigma = \frac{80360 }{0.066}[/tex]

=>      [tex]\sigma = 1.218*10^{6} \ N/m^2[/tex]

Answer:

1612903nm

Explanation:

Doppler effect can be regarded as the change in frequency of a wave with respect toobserver that move relative to the wave source

We can expressed as

(λo - λs)/λs = v/s

λo= peak wavelength

λs= peak wavelength observed

C= speed of light

(λo -615×10^9 )/615×10^9 = 2,500,000/(3×10^8)

1.5375=3×10^8λo -184.5

1.5375+184.5=3×10^8λo

186=3×10^8λo

λo=1612903nm

Therefore the peak wavelength that is observed when the star is traveling away from the eart to the velocity given is 1612903nm

Answer:

C. lenses refract light; mirrors do not

This question involves the concepts of reflection and refraction.

The comparison of lenses and mirrors in their interaction with light is "C. Lenses refract light; mirrors do not.".

When it comes to the interaction with light, the key difference between lenses and mirrors is the difference of refraction and reflection. Reflection means the complete rebound of the light rays after striking on a surface without any absorption or transmission. On the other hand, refraction is the  bending of light rays, while passing through a medium, without any rebound or absorption.

Lenses are tansparent from both sides, so they refract the light rays. While, mirrors are coated opaque from one side, so they reflect back the light rays.

Learn more about reflection and refraction here:

https://brainly.com/question/3764651

Answer:option B

Explanation:

Answer:

[tex]3978873.58\ \text{Pa}[/tex]

[tex]0.00002122\ \text{m}[/tex]

Explanation:

F = Force = 5000 N

r = Radius of circular cross section = 2 cm

l = Length of disk = 0.8 cm

A = Area = [tex]\pi r^2[/tex]

Y = Young's modulus = [tex]1.5\times 10^9\ \text{N/m}^2[/tex]

Pressure is given by

[tex]P=\dfrac{F}{A}\\\Rightarrow P=\dfrac{5000}{\pi (2\times 10^{-2})^2}\\\Rightarrow P=3978873.58\ \text{Pa}[/tex]

The pressure on the cross section is [tex]3978873.58\ \text{Pa}[/tex]

The change in length of the cross section is given by

[tex]\Delta L=\dfrac{PL}{Y}\\\Rightarrow \Delta L=\dfrac{3978873.58\times 0.8\times 10^{-2}}{1.5\times 10^9}\\\Rightarrow \Delta L=0.00002122\ \text{m}[/tex]

The deformation produced is [tex]0.00002122\ \text{m}[/tex]

Answer:

You have an apple pen. :)

Answer:

I have a pen

I have a apple

apple pen

Explanation:

Answer:

Explanation:

pV = nrT

n = PV/RT

n = (100*10^3)(.01)/(300*0.082057)

n = 40.62 moles

Answer:

V' = V/2

Explanation:

The voltage across a parallel plate capacitor is given as follows:

V = Q/C

where,

V = Voltage across capacitor

Q = Charge on Capacitor

C = Capacitance of Capacitor = A∈₀/d

Therefore,

V = Qd/A∈₀

where,

A = Area of plate

d = distance between plates

∈₀ = permittivity of free space

FOR CAPACITOR 1:

Q = Q

d = d

A = A

V = V

Therefore,

V = Qd/A∈₀   --------------- equation (1)

FOR CAPACITOR 2:

V' = ?

Q' = Q

d' = d

A' = 2A

Therefore,

V' = Q'd'/A'∈₀

V' = Qd/2A∈₀

V' = (1/2)(Qd/A∈₀)

using equation (1):

V' = V/2

Answer:

A: Soil

Explanation:

Protists need a moist environment to survive, and shallow ponds, oceans, and blood is all moist. So, the answer would be the soil, because that is the least moist environment out of these options.

Answer:

lucky mauld mauldgomary was an british poet...

Answer:

[tex]14400\ \text{N}[/tex], Attractive

[tex]3240\ \text{N}[/tex], Repulsive

Explanation:

[tex]q_1[/tex] = -20 μC

[tex]q_2[/tex] = 50 μC

r = Distance between the charges = 2.5 cm

k = Coulomb constant = [tex]9\times 10^9\ \text{Nm}^2/\text{C}^2[/tex]

Electrical force is given by

[tex]F=\dfrac{kq_1q_2}{r^2}\\\Rightarrow F=\dfrac{9\times 10^9\times (-20\times 10^{-6})\times (50\times 10^{-6})}{(2.5\times10^{-2})^2}\\\Rightarrow F=-14400\ \text{N}[/tex]

The magnitude of force each sphere will experience is [tex]14400\ \text{N}[/tex]

Since the charges have opposite charges they will attract each other.

Now the charges are brought into contact with each other so the resultant charge will be

[tex]q=\dfrac{q_1+q_2}{2}\\\Rightarrow q=\dfrac{-20+50}{2}\\\Rightarrow q=15\ \mu\text{C}[/tex]

[tex]F=\dfrac{kq^2}{r^2}\\\Rightarrow F=\dfrac{9\times 10^9\times (15\times 10^{-6})^2}{(2.5\times 10^{-2})^2}\\\Rightarrow F=3240\ \text{N}[/tex]

The magntude of the force the spheres experience will be [tex]3240\ \text{N}[/tex]

The spheres have the same charge now so they will repel each other.

Answer:

a. E = 86.36 x 10⁻³ V/m = 86.36 mV/m

b. ρ = 3.6 x 10⁻⁷ Ωm

Explanation:

a.

The electric field in terms of the voltage is given by the following formula:

E = V/d

where,

E = Electric Field in the Wire = ?

V = Potential Difference = 3.8 V

d = distance between the points = 44 m

Therefore,

E = 3.8 V/44 m

E = 86.36 x 10⁻³ V/m = 86.36 mV/m

b.

Now, from Ohm's Law:

V = IR

R = V/I

where,

R = Resistance of wire = ?

I = Current = 3 A

Therefore,

R = 3.8 V/3 A

R = 1.27 Ω

Now, the resistance of a wire can be given as:

R = ρL/A

where,

ρ = resistivity of material = ?

L = Length = 44 m

A = Cross-sectional area = πr² = π(0.002 m)² =  1.25 x 10⁻⁵ m²

Therefore,

1.27 Ω = ρ*44 m/1.25 x 10⁻⁵ m²

(1.27 Ω)(1.25 x 10⁻⁵ m²)/44 m = ρ

ρ = 3.6 x 10⁻⁷ Ωm

Answer:

O.75KΩ

Explanation:

We measure the time constant τ, using the formula τ = L/R,

t is in seconds, then we have R to be the value of the resistor which is measured in ohms and also L is the value of the inductor which is measured in Henries.

Since t = L/R

We make R subject of the formula

R = L/τ

= 3/4x10-3

= 0.00075

= 0.75 KΩ

So we have it that the first Option (A) is the correct answer to the question

The resistance to be added is required.

The resistance added should be A. [tex]0.75\ \text{k}\Omega[/tex]

L = Inductance = 3 H

[tex]\tau[/tex] = Time constant = 4 ms

R = Resistance

Time constant is given by

[tex]\tau=\dfrac{L}{R}\\\Rightarrow R=\dfrac{L}{\tau}\\\Rightarrow R=\dfrac{3}{4\times 10^{-3}}=750\ \Omega=0.75\ \text{k}\Omega[/tex]

The resistance added should be [tex]0.75\ \text{k}\Omega[/tex]

Learn more:

https://brainly.com/question/13201007?referrer=searchResults

Explanation:

Speed is the rate of change of distance with time. It is a scalar quantity with magnitude both no direction.

  Speed  = [tex]\frac{distance}{time}[/tex]

The unit is m/s or km/hr or mile/hr

Distance covered is simply the length of the path traveled.

 The unit is m or km or miles

Time taken is the duration of an event.

  The unit is seconds or minutes or hour.

Answer:

Searching in google I found the total mass and the radius of the ball (m = 1.5 kg and r = 10 cm) which are needed to solve the problem!  

The ball rotates 6.78 revolutions.

Explanation:

Searching in google I found the total mass and the radius of the ball (m = 1.5 kg and r = 10 cm) which are needed to solve the problem!        

At the bottom the ball has the following angular speed:

[tex] \omega_{f} = \frac{v_{f}}{r} = \frac{4.9 m/s}{0.10 m} = 49 rad/s [/tex]

Now, we need to find the distance traveled by the ball (L) by using θ=28° and h(height) = 2 m:

[tex] sin(\theta) = \frac{h}{L} \rightarrow L = \frac{h}{sin(\theta)} = \frac{2 m}{sin(28)} = 4.26 m [/tex]

To find the revolutions we need the time, which can be found using the following equation:                

[tex] v_{f} = v_{0} + at [/tex]  

[tex] t = \frac{v_{f} - v_{0}}{a} [/tex] (1)

So first, we need to find the acceleration:

[tex] v_{f}^{2} = v_{0}^{2} + 2aL \rightarrow a = \frac{v_{f}^{2} - v_{0}^{2}}{2L} [/tex]    (2)  

By entering equation (2) into (1) we have:

[tex] t = \frac{v_{f} - v_{0}}{\frac{v_{f}^{2} - v_{0}^{2}}{2L}} [/tex]

Since it starts from rest (v₀ = 0):  

[tex] t = \frac{2L}{v_{f}} = \frac{2*4.26 m}{4.9 m/s} = 1.74 s [/tex]

Finally, we can find the revolutions:  

[tex] \theta_{f} = \frac{1}{2} \omega_{f}*t = \frac{1}{2}*49 rad/s*1.74 s = 42.63 rad*\frac{1 rev}{2\pi rad} = 6.78 rev [/tex]

Therefore, the ball rotates 6.78 revolutions.

I hope it helps you!                                                                                                                                                                                          

Answer:

The velocity is  [tex]v =2.455 \ m/s[/tex]

Explanation:

From the question we are told that  

   The diameter of the pipe is  [tex]d = 4.25 \ cm = 0.0425 \ m[/tex]

    The magnetic field is  [tex]B = 0.575 \ T[/tex]

     The hall voltage is  [tex]V_H = 60.0 mV = 60 *10^{-3} \ V[/tex]

Generally the average fluid velocity is mathematically represented as

          [tex]v = \frac{V}{ B * d }[/tex]

=>       [tex]v = \frac{60*10^{-3}}{ 0.575 * 0.0425 }[/tex]

=>       [tex]v =2.455 \ m/s[/tex]

Answer:

Q = 425 kJ

Explanation:

Given that,

Mass, m = 25 kg

The clown doll head that heats up from 25°C to 35°C

The specific heat is 1700 J/kg°C

We need to find the internal energy of it. The heat required to raise the temperature is given by the formula as follows :

[tex]Q=mc\Delta T\\\\Q=25\times 1700\times (35-25)\\\\Q=425000\ J\\\\Q=425\ kJ[/tex]

So, 425 kJ of thermal energy is severed.

Answer:

B.

Explanation:

Answer:  Please see answer in explanation column.

Explanation:

Given that

v≈(331 + 0.60T)m/s

where Temperature, T =  14°C

v≈(331 + 0.60 x 14)m/s

v =331+ 8.4 = 339.4m/s

In our solvings, note that

f= frequency

 λ=wavelength

L = length

v= speed of sound

a) Length of the pipe is calculated using the fundamental frequency formulae that

f=v/2L

Length = v/ 2f

= 339.4m/s/ 2 x 494Hz ( s^-1)= 0.3435m

b) wavelength of the fundamental standing wave in the pipe

L = nλ/2,

λ = 2L/ n

λ( wavelength )= 2 x 0.3435/ 1

= 0.687m

c) frequency of the fundamental standing wave in the pipe

F = v/  λ

= 339.4m/s/0.687m=

494.03s^-1 = 494 Hz

d) the frequency in the traveling sound wave produced in the outside air.

This is the same as the frequency in the open organ pipe = 494Hz

e)The wavelength of the travelling sound wave produced in the outside air is the same as the wavelength calculated in b above = 0.687m

f) To play D above middle c . the distance is given by

L =v/ 2 f

= 343/ 2 x 294

=0.583m

Answer:

The distance of the bar D = 1153 km

Explanation:

The electric force is the one that takes place between electric charges.

The electric force with which two point charges are attracted or repelled at rest is directly proportional to their product, inversely proportional to the square of the distance that separates them and acts in the direction of the line that joins them.

Recall that:

Electrical force(F) = I*B*L

where;

I = the current,

B = the magnetic field strength,

L = the length of the bar

However;

From the second equation of motion,

F = Ma

Since; (F) = I*B*L

Then,

Ma = IBL,

where;

M is the mass;

a is the acceleration

Making the acceleration (a) the subject of the formula, we have

a = IBL/M

Similarly;

From the third equation of motion;

v^2= u^2+2as,

where v and u are the final velocity and the initial velocity respectively

Here u = 0

Also; let distance s = D

Then

v^2 = 2aD

where;

a = IBL/M

Making the distance D  the subject of the formula, we get:

D = v^2/2a = v2*M/(2IBL)

D = 11200² × 20/(2×2300×0.86×0.55)

D = 1153047.155 m

D = 1153 km

Answer:

Consider an n-type silicon semiconductor at T = 300°K in which Nd = 1016 cm-3 and Na = 0. The intrinsic carrier concentration is assumed to be ni = 1.5 x 1010 cm-3. - Comment Nd >> ni, so that the thermal-equilibrium majority carrier electron concentration is essentially equal to the donor impurity concentration.

Explanation:

Answer:

(d) 2.93 x 10⁻³ N

Explanation:

Given;

current in the wire, I = 11.4 A

angle of inclination, θ = 11.4⁰

magnetic field on the wire, B = 11. 4  x 10⁻³

length of the wire, L = 11.4 cm = 0.114 m

The magnitude of magnetic force on the wire is given by;

F = BILsinθ

F = (11.4 x 10⁻³)(11.4)(0.114)(sin 11.4°)

F = 0.00293 N

F = 2.93 x 10⁻³ N

Therefore, the correct option is "D"