Find the net work W done on the particle by the external forces during the motion of the particle in terms of the initial and final kinetic energies.Express your answer in terms of Kinitial and Kfinal.W=

Answers

Answer 1

Answer:

[tex]W=K_f-K_i[/tex]

Explanation:

The work done on a particle by external forces is defined as:

[tex]W=\int\limits^{r_f}_{r_i} {F\cdot dr} \,[/tex]

According to Newton's second law [tex]F=ma[/tex]. Thus:

[tex]W=\int\limits^{r_f}_{r_i}{ma\cdot dr} \,\\[/tex]

Acceleration is defined as the derivative of the speed with respect to time:

[tex]W=m\int\limits^{r_f}_{r_i}{\frac{dv}{dt}\cdot dr} \,\\\\W=m\int\limits^{r_f}_{r_i}{dv \cdot \frac{dr}{dt}} \,[/tex]

Speed is defined as the derivative of the position with respect to time:

[tex]W=m\int\limits^{v_f}_{v_i} v \cdot dv \,[/tex]

Kinetic energy is defined as [tex]K=\frac{mv^2}{2}[/tex]:

[tex]W=m\frac{v_f^2}{2}-m\frac{v_i^2}{2}\\W=K_f-K_i[/tex]


Related Questions

Consider a current carrying a wire coming out of your computer screen towards you. Which statement below correctly describes the magnetic field created by the current in the wire?
1. The magnetic field encircles the wire in a counterclockwise direction
2. The magnetic field encircles the wire in a clockwise direction

Answers

Answer:

The magnetic field encircles the wire in a reversal or counterclockwise direction

Explanation:

Lenz's law states that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field which produced it. According to Lenz law, the magnetic field encircles the wire in a reversal or counterclockwise direction.

Therefore, the first option is the correct answer.

In Millikan's experiment, an oil drop of radius 2.342 μm and density 0.816 g/cm3 is suspended in chamber C when a downward-pointing electric field of 1.92 ✕ 105 N/C is applied. Find the charge on the drop, in terms of e. (Include the sign of the value in your answer.)

Answers

Answer:

-14 e

Explanation:

Assuming oil drop is spherical then V = 4pi.r^3/3

density = 0.816 g/cm^3= 0.816 x 10^-3kg/cm^3= 0.816 x 10^-3/10^-6 kg/m^3= 0.816 x 10^3 kg/m^3

mass =(4 x 3.142 x (2.342 x 10^-6)^3 x 0.816 x 10^3)/3 kg

mass = (12.568 x 12.85 x 10^-18 x 0.816 x 10^3)/3 kg

m= 4.39 x 10^-14 kg

F=qE…. Eqn. 1

F=mg… Eqn. 2

Compare both eqn.1 and eqn. 2

qE=mg

q=mg/E

q = (4.39 x 10^-14 x 9.81)/1.92 x 10^5

q = 2.24 x 10^-18 C

Number of charges, n = 2.24 x 10^-18/1.62 x 10^-19

n=13.827

Charges come in integer values, nearest is 14

Number of charges is 14.

The direction of the field (downwards) is the direction a positive test charge would move. This means a positive charge would move downwards and repelled by the top plate which must be positive.

Since mg acts downwards then the other force must act up if the oil drop is suspended. This means that the charge is being attracted to the top plate which we have already determined is positive. for the charge to be attracted to the positive top plate then the charge must be negative.

Charge is electron hence the sign is minus.

-14 e

Assume that a uniform magnetic field is directed into the monitor you are reading this on. If an electron is released with an initial velocity directed from the bottom edge to the top edge of the screen, which of the following describes the direction of the resultant force acting on the electron?a. out of the page
b. to the right
c. to the left
d. into the page

Answers

Answer:

b. to the right

Explanation:

In the given condition we have the magnetic field lines perpendicular to the direction of moving charges then here in this case we can apply the Fleming's left-hand rule to determine the force acting on the charges (here electrons).As the direction of magnetic  field lines is into the screen and the electrons move form bottom of the screen towards up then we apply the Fleming's left-hand rule and find that the deviation will be towards right.We spread the index finger, thumb and the middle finger of our left hand mutually perpendicular to each other then we align the pointing of the index finger in the direction of the magnetic field and the middle finger in the direction of the current or the direction of the motion of the positive charge and if we have a negative charge then we take the direction to be opposite. Now the direction of the thumb pointing tells us the direction of the force.

Final answer:

Using the left-hand rule for a negatively charged particle like an electron, the force on an electron moving upward with the magnetic field directed into the page is to the left. The correct answer is option c, to the left.

Explanation:

To determine the direction of the resultant force acting on an electron as it moves within a magnetic field, one can use the right-hand rule or, in the case of negatively charged particles like an electron, the left-hand rule. Considering that an electron is negatively charged, we apply the left-hand rule, with the thumb in the direction of the electron's velocity (from the bottom to the top edge of the screen), and the index finger in the direction of the magnetic field (into the page). The middle finger then points in the direction of the force experienced by the electron.

By this rule, for a magnetic field directed into the page and an electron moving upward, the resultant force will be to the left of the electron's initial direction of travel. The correct answer to the question is option c, to the left. This force will cause the electron to move in a circular path due to the magnetic Lorentz force.

Consider two uniform solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is:_________.a) 2b) 8c) 4d) 10e) 6

Answers

Answer:

The ratio of moment of inertia of larger sphere to that of smaller sphere = 4

Explanation:

The moment of inertia of solid sphere is given by I = 2/5MR² where M = mass of sphere and R = radius of sphere.

Radius of smaller sphere = D/2

Radius of larger sphere = 2D/2 = D.

Moment of inertia of smaller sphere I₁ = 2/5M × D²/4 = MD²/10

Moment of inertia of larger sphere I₂ = 2/5M × D² = 2MD²/5

The ratio of moment of inertia of larger sphere to that of smaller sphere = I₂/I₁ = 2MD²/5 ÷ MD²/10 = 10 × 2/5 = 4

A new class of objects can be created conveniently by ________; the new class (called the ________) starts with the characteristics of an existing class (called the ________), possibly customizing them and adding unique characteristicsof its own. Group of answer choices

Answers

Answer:

Option A is correct.

Inheritance, superclass, subclass

A new class of objects can be created conveniently by **inheritance**; the new class (called the **superclass**) starts with the characteristics of an existing class (called the **subclass**), possibly customizing them and adding unique characteristics of its own.

Explanation:

A class is a term in object oriented programming that is extensible program code used to create, name and implement what you want the objects to do.

Inheritance is used to describe the making of new classes from already existing classes. The general properties of the old classes remain in the new classes created from them.

Hence, the new classes (because they're usually an improvement on the old classes as they hold on to the wanted properties of the old classes and additional great ones are added or modified) are called superclasses and the old, already existing ones are called subclasses.

The missing words from the given paragraph are inheritance, superclass and subclass respectively.

The given problem is based on the concept of Object Oriented Programming (OOPs). A class is a term in object oriented programming that is extensible program code used to create, name and implement what you want the objects to do.

Inheritance is used to describe the making of new classes from already existing classes. The general properties of the old classes remain in the new classes created from them.

Hence, the new classes (because they're usually an improvement on the old classes as they hold on to the wanted properties of the old classes and additional great ones are added or modified) are called super classes and the old, already existing ones are called subclasses.

So, the complete paragraph will be,

A new class of objects can be created conveniently by inheritance; the new class (called the superclass) starts with the characteristics of an existing class (called the subclass), possibly customizing them and adding unique characteristics of its own.

Thus, we can conclude that the missing words from the given paragraph are inheritance, superclass and subclass respectively.

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Nearly all conventional piston engines have flywheels on them to smooth out engine vibrations caused by the thrust of individual piston firings. Why does the flywheel have this effect

Answers

Answer:

This is because, the flywheel has a very large moment of Inertia and hence sudden piston torques have negligible effect on the flywheel, but every piston combined has a significant torque. This smoothens out the vibrations.

Explanation:

Final answer:

A flywheel reduces engine vibrations by utilizing its angular momentum to smooth out the intermittent power delivery from piston firings, thus ensuring steady rotation of the crankshaft and maintaining engine speed during periods when power is not supplied.

Explanation:

The primary reason why a flywheel reduces engine vibrations in conventional piston engines is due to its ability to store rotational energy. When the pistons fire, they impart energy to the crankshaft, causing the engine to turn. This energy, however, is delivered in pulses rather than smoothly, which can lead to uneven rotation and vibrations. The flywheel, being a heavy rotating disk, has significant angular momentum. This momentum ensures that the flywheel continues to spin between these pulses of power, effectively smoothing out the rotation of the engine's crankshaft. This results in a reduction of the vibrations that occur due to the intermittent nature of power delivery from individual piston firings.

Flywheels also help maintain engine speed during the periods when no power is supplied, such as between combustion events in a four-stroke engine. This steady rotation is crucial for the engine's performance and longevity. Additionally, flywheels play a role in energy conservation, as they can store energy and release it when needed, which is particularly important in stopping and starting scenarios.

Tech A says that the solenoid on the starter motor switches the high current on and off. Tech B says that the solenoid engages the starter motor with the ring gear. Who is correct

Answers

Tech B is correct.

Explanation:

Generally the electromagnet for a coil of wire, which allow the  system to transform electric energy into mechanical energy is understood as a solenoid, by generating  magnetic field from electric current and induces linear motion by utilizing the magnetic field. Every modern starters depend on the solenoid to use the flywheel ring gear to enable the start drive. When the solenoid is rejuvenated, a plunger or lever is controlled which pushes the ring gear into mesh with the pinion. A standard starter solenoid has one small adapter for the starter control wire and two major terminals: one for the positive battery cable, and another one for the thick wire that drive the starter motor by its own.

The correct answer is that both Tech A and Tech B are correct.

In a vehicle's starting system, the solenoid serves two main functions:

1. Switching High Current: When the ignition key is turned to start the engine, a small current flows through the solenoid coil, creating an electromagnetic field that pulls the solenoid plunger inward. This action closes a pair of heavy contacts, allowing a high current to flow from the battery to the starter motor. This is what Tech A is referring to when they mention that the solenoid switches the high current on and off.

2. Engaging the Starter Motor with the Ring Gear: The movement of the solenoid plunger also pushes a lever that engages the starter motor's pinion gear with the ring gear on the engine's flywheel. This engagement is necessary to turn the engine over during the starting process. This is the function that Tech B is describing.

Therefore, the solenoid is responsible for both switching the high current to the starter motor and engaging the starter motor with the ring gear. Both technicians are correct in their statements about the functions of the solenoid in the starting system.

A uniform cylindrical grindstone has a mass of 15.0 kg and a radius of 18.6 cm. The grindstone reaches a rotational velocity of 1.83 rev/min before its motor turns off. After the grindstone motor is turned off, a knife blade is pressed against the outer edge of the grindstone with a perpendicular force of 8.82 N. The coefficient of kinetic friction between the grindstone and the blade is 0.80. Use the work energy theorem to determine how many turns the grindstone makes before it stops.

Answers

Answer:

[tex]n \approx 5.778\times 10^{-4}\,rev[/tex]

Explanation:

The Work-Energy Theorem is applied herein:

[tex]-\frac{1}{4}\cdot m_{cyl}\cdot R^{2}\cdot \omega^{2} = - \mu_{k}\cdot N\cdot r \cdot 2\pi \cdot n[/tex]

The number of turns needed to stop the grindstone is:

[tex]n = \frac{m_{cyl}\cdot R^{2}\cdot \omega^{2}}{4\cdot \mu_{k}\cdot N \cdot r\cdot 2\pi}[/tex]

[tex]n = \frac{(15\,kg)\cdot (0.186\,m)^{2}\cdot [(1.83\,\frac{rev}{min} )\cdot (\frac{2\pi\,rad}{1\,rev} )\cdot (\frac{1\,min}{60\,s} )]^{2}}{4\cdot (0.80)\cdot (8.82\,N)\cdot(0.186\,m)\cdot 2\pi}[/tex]

[tex]n \approx 5.778\times 10^{-4}\,rev[/tex]

What kind of friction occurs when moving parts have ball bearings

Answers

Answer: Rolling friction

Explanation:

Rolling friction is said to act when an object rolls over a surface. Machines often have moving parts. These moving parts roll over each other as the machine works. Ball bearings are commonly used to reduce friction between the two surfaces in contact as the machine parts roll over each other. This is a typical example of rolling friction as applied to machine parts.

Answer:

Rolling friction.

Explanation:

Rolling friction is the force resisting the motion when a body ( such as a ball, tires, wheel) rolls on a surface. It is applicable for bodies whose point of contact keeps changing. It is the force that opposes the motion of a body which is rolling over the surface of another.

Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy needed for deformation of the wheel, roadbed, etc. is recovered when the pressure is removed.

A basketball with a mass of 0.61 kg falls vertically to the floor where it hits with a velocity of −7 m/s. (We take the positive direction to be upward here.) The ball rebounds, leaving the floor with a velocity of 4.6 m/s. (Indicate the direction with the signs of your answers.)

Answers

Answer:

a. What impulse act on the ball during its collision with the floor?

b. If the ball is in contact with the floor for 0.04 s, what is the average force of the ball on he floor?

The answers to the question are

a. The impulse acting on the ball during its collision with the floor is

7.076 kg·m/s

b. The average force of the ball on the floor with contact of 0.04 s is

176.9 N

Explanation:

Mass of the ball = 0.61 kg

Initial velocity = -7 m/s

Final velocity = 4.6 m/s

Impulse = Δp = FΔt = mΔv

Where Δt =change in time

m = mass of Average force of he the ball

Δv = velocity change

Therefore impulse = m×(Final velocity - initial velocity)

= 0.61 × (4.6-(-7)) = 0.61×11.6

= 7.076 kg·m/s

b. Average force of the ball on the floor is given by

[tex]F_{Average}[/tex]×Δt = mΔv = 7.076 kg·m/s

where Δt = change in time = 4.6 m/s

Therefore [tex]F_{Average}[/tex] =mΔv /Δt = 7.076/0.04 = 176.9 kg·m/s²

= 176.9 N

You heat a 5.2 gram lead ball (specific heat capacity = 0.128 Joules/g-deg) to 183. ∘ C. You then drop the ball into 34.5 milliliters of water (density 1 g/ml; specific heat capacity = 4.184 J/g-deg ) at 22.4 ∘ C. What is the final temperature of the water when the lead and water reach thermal equilibrium?

Answers

Answer:

The final temperature when the lead and water reach thermal equilibrium is [tex]23.14^{o} C[/tex]

Explanation:

Using the law of conservation of energy the heat lost by the lead ball is gained by the water.

[tex]-q_{L} =+q_{w}[/tex] .............................1

where

[tex]q_{L}[/tex] is the heat energy of the lead ball;

[tex]q_{w}[/tex] is the heat energy of water;

but q = msΔ

T...............................2

substituting expression in equation 2 into the equation 1;

Δ

T =Δ

T .............................3

where [tex]m_{L}[/tex] is the mass of the lead ball = 5.2 g

[tex]s_{L}[/tex] is the specific heat capacity of the lead ball = 0.128 Joules/g-deg

[tex]m_{w}[/tex] is the mass of water = volume x density = 34.5 ml x 1 g/ml = 34.5 g

[tex]s_{w}[/tex] is the specific heat capacity of water = 4.184 J/g-deg

Δ

T is the temperature changes encountered by the lead ball and water   respectively

inputting the values of the parameters into equation 3

5.2 g x 0.128 Joules/g-deg x (183-22.4) = 34.5 g x 4.184 J/g-deg x ([tex]T_{2}[/tex] -22.4)

[tex]T_{2}[/tex] -22.4 = [tex]\frac{106.9}{144.3}[/tex]

[tex]T_{2}[/tex] -22.4 = 0.7408

[tex]T_{2}[/tex] = [tex]23.14^{o} C[/tex]

Therefore the final temperature  when the lead and water reach thermal equilibrium is [tex]23.14^{o} C[/tex]

A concrete highway curve of radius 60.0 m is banked at a 19.0 ∘ angle. what is the maximum speed with which a 1400 kg rubber-tired car can take this curve without sliding? (take the static coefficient of friction of rubber on concrete to be 1.0.)

Answers

Final answer:

The student's question involves calculating the maximum speed a car can take a banked curve without sliding, using physic principles of circular motion and the coefficient of static friction.

Explanation:

The student's question revolves around determining the maximum speed at which a 1400 kg car can navigate a banked highway curve without sliding, given a static coefficient of friction between rubber and concrete. To solve this, we need to use principles of circular motion and friction.

To find the maximum speed (v), we can use the following equation that balances gravitational, frictional, and centripetal forces:

F_{friction} = μ_s × N

N = m × g × cos(θ)

F_{centripetal} = m × v^2 / r

Where μ_s is the static coefficient of friction (1.0), N is the normal force, m is the mass of the car (1400 kg), g is the acceleration due to gravity (9.8 m/s^2), θ is the banking angle (19.0 degrees), v is the maximum speed, and r is the radius of the curve (60.0 m). The forces due to friction and centripetal need to equal for the car to navigate the curve without sliding.

After applying trigonometry and mechanics principles, we can solve for v which gives us the maximum speed without sliding.

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Two cylindrical solenoids, A and B, each have lengths that are much greater than their diameters. The two solenoids have the same density of turns in their windings. Solenoid A has a diameter that is twice the diameter of solenoid B, but solenoid B has a length that is twice the length of solenoid A. How do their inductances compare with one another

Answers

Answer:

The inductance of solenoid A is twice that of solenoid B

Explanation:

The inductance of a solenoid L is given by

L = μ₀n²Al where n = turns density, A = cross-sectional area of solenoid and l = length of solenoid.

Given that d₁ = 2d₂ and l₂ = 2l₁ and d₁ and d₂ are diameters of solenoids A and B respectively. Also, l₁ and l₂ are lengths of solenoids A and B respectively.

Since we have a cylindrical solenoid, the cross-section is a circle. So, A = πd²/4.

Let L₁ and L₂ be the inductances of solenoids A and B respectively.

So  L₁ = μ₀n²A₁l₁ = μ₀n²πd₁²l₁/4

L₂ = μ₀n²A₂l₂ = μ₀n²πd₂²l₂/4

Since d₁ = 2d₂ and l₂ = 2l₁, sub

L₁/L₂ = μ₀n²πd₁²l₁/4 ÷ μ₀n²πd₂²l₂/4 = d₁²/d₂² × l₁/l₂ = (2d₂)²/d₂² × l₁/2l₁ = 4d₂²/d₂²  × l₁/2l₁ = 4 × 1/2 = 2

L₁/L₂ = 2

L₁ = 2L₂

So, the inductance of solenoid A is twice that of solenoid B

What enables humans to see light in the infrared range of the electromagnetic spectrum

Answers

Answer: night vision goggles

Explanation: These goggles use technology to enhance all light, including the infrared rays, which aren't normally visible to the naked eye. This way you can see any type of light that is surrounding you.

please give brainliest!

Nothing does. That's why we can't see it without some sort of external imaging device.

If we instead connect this headlight and starter in series with the 12.0 V battery, how much total power in W would the headlight and starter consume? (You may neglect any other resistance in the circuit and any change in resistance in the two devices.)

Answers

Answer:

If [tex]\large{P_{H}}[/tex] and [tex]\large{P_{S}}[/tex] be the power consumed by the headlight and starter respectively, then the total power consumed will be [tex]\large{P = \dfrac{P_{H}P_{S}}{P_{H} + P_{S}}}[/tex]

Explanation:

We know that electric power ([tex]P[/tex]) is given by

[tex]\large{P = \dfrac{V^{2}}{R}}[/tex]

where '[tex]V[/tex]' is the applied voltage and '[tex]R[/tex]' is the resistance.

If we consider that '[tex]\large{P_{H}}[/tex]' and '[tex]\large{P_{S}}[/tex]' be the power consumed by the headlight and starter respectively, then the resistance ([tex]\large{R_{H}}[/tex]) of the headlight and the resistance ([tex]\large{R_{S}}[/tex]) of the starter can be written as

[tex]&&\large{R_{H} = \dfrac{V^{2}}{P_{H}} = \dfrac{12^{2}}{P_{H}}}\\&and,& \large{R_{S} = \dfrac{V^{2}}{P_{S}} = \dfrac{12^{2}}{P_{S}}}[/tex]

If the headlight and the starter in connected in series, then equivalent resistance ([tex]\large{R_{eq}}[/tex]) will be

[tex]\large{R_{eq} = R_{H} + R_{S} = 12^{2}(\dfrac{1}{P_{H} + P_{S}})}[/tex]

So the total power ([tex]P[/tex]) consumed will be given by

[tex]\large{P = \dfrac{12^{2}}{R_{eq}} = \dfrac{1}{(\dfrac{1}{P_{H}} + \dfrac{1}{P_{S}})} = \dfrac{P_{H}P_{S}}{P_{H} + P_{S}}}[/tex]

When the 30.0-W headlight and the 2.40-kW starter are connected in series to a 12.0-V battery, they consume a total power of 2430 W.

The total power consumed by the headlight and starter when connected in series to a 12.0-V battery can be calculated by adding the individual powers.

Power of headlight = 30.0 WPower of starter = 2.40 kW = 2400 WTotal power = 30.0 W + 2400 W = 2430 W

Imagine that you take a beam of monochromatic light and start to reduce the power of this beam of light. As you get the power (intensity) lower and lower, what will happen to your observations of the beam of light with regards to observing individual photons?

Answers

Answer:

No change in velocity of photons...

Explanation:

The reason speed of light is constant is that is doesn't depend upon intensity of light as produced by the source. This is the main reason why the wave function (psi)* in Einstein's Photoelectric experiment remains unaffected by intensity. The monochromatic beam of light will glow lower and lower as the power decreases and eventually vanishes from visible range as the emission from the power source has been stopped...

Two 5.0 mm × 5.0 mm electrodes are held 0.10 mm apart and are attached to 7.5 V battery. Without disconnecting the battery, a 0.10-mm-thick sheet of Mylar is inserted between the electrodes.A) What is the capacitor's potential difference before the Mylar is inserted?
B) What is the capacitor's electric field before the Mylar is inserted?
C) What is the capacitor's charge before the Mylar is inserted?
D) What is the capacitor's potential difference after the Mylar is inserted?
E) What is the capacitor's electric field after the Mylar is inserted?
F) What is the capacitor's charge after the Mylar is inserted?

Answers

Answer:

A) V = 7.5 V

B) E = 75,000 V/m

C) Q = 16.6 pC

D) V = 7.5 V

E) E = 24,000 V/m

F) Q = 52 pC

Explanation:

Given:

- The Area of plate A = ( 5 x 5 ) mm^2

- The distance between plates d = 0.10 mm

- The thickness of Mylar added t = 0.10 mm

- Voltage supplied by battery V = 7.5 V

Solution:

A) What is the capacitor's potential difference before the Mylar is inserted?

- The potential difference across the two plates is equal to the voltage provided by the battery V = 7.5 V which remains constant throughout.

B) What is the capacitor's electric field before the Mylar is inserted?

- The Electric Field E between the capacitor plates is given by:

                                E = V / k*d

k = 1 (air)                  E = 7.5 / 0.10*10^-3

                                E = 75,000 V/m

C) What is the capacitor's charge Q before the Mylar is inserted?

                                C = k*A*ε / d

k = 1 (air)                   C = ( 0.005^2 * 8.85*10^-12 ) / 0.0001

                                C = 2.213 pF

                                Q = C*V

                                Q = 7.5*(2.213)

                                Q = 16.6 pC

D) What is the capacitor's potential difference after the Mylar is inserted?

- The potential difference across the two plates is equal to the voltage provided by the battery V = 7.5 V which remains constant throughout.

E) What is the capacitor's electric field after the Mylar is inserted?    

- The Electric Field E between the capacitor plates is given by:

                                E = V / k*d

k = 3.13                     E = 7.5 / (3.13)0.10*10^-3

                                E = 24,000 V/m              

F) What is the capacitor's charge after the Mylar is inserted?      

                                C = k*A*ε / d

k = 3.13                    C = 3.13*( 0.005^2 * 8.85*10^-12 ) / 0.0001

                                C = 6.927 pF

                                Q = C*V

                                Q = 7.5*(6.927)

                                Q = 52 pC                                      

Here, we are required to evaluate parameters relating to the capacitor.

A) V = 7.5 V

B) E = 75,000 V/m

C) Q = 16.6 pC

D) V = 7.5 V

E) E = 24,000 V/m

F) Q = 52 pC

Data:

The Area of plate A = ( 5 x 5 ) mm^2 = 2.5 × 10^(-5)m²

The distance between plates d = 0.10 mm = 0.1 × 10^(-3)

The thickness of Mylar added t = 0.10 mm = 0.1 × 10^(-3)

Voltage supplied by battery V = 7.5 V

A) The potential difference across the two plates is equal to the voltage provided by the battery prior to the insertion of the Mylar, V = 7.5 V which remains constant throughout.

The potential difference across the two plates is equal to the voltage provided by the battery prior to the insertion of the Mylar, V = 7.5 V which remains constant throughout.B) The capacitor's Electric Field E between the capacitor plates is given as:

The potential difference across the two plates is equal to the voltage provided by the battery prior to the insertion of the Mylar, V = 7.5 V which remains constant throughout.B) The capacitor's Electric Field E between the capacitor plates is given as: E = V / k*d

The potential difference across the two plates is equal to the voltage provided by the battery prior to the insertion of the Mylar, V = 7.5 V which remains constant throughout.B) The capacitor's Electric Field E between the capacitor plates is given as: E = V / k*dwhere dielectric constant , k(air) = 1

The potential difference across the two plates is equal to the voltage provided by the battery prior to the insertion of the Mylar, V = 7.5 V which remains constant throughout.B) The capacitor's Electric Field E between the capacitor plates is given as: E = V / k*dwhere dielectric constant , k(air) = 1 E = 7.5 /(1 × 0.10*10^-3)

E = 75,000 V/m

C) The capacitor's charge Q before the Mylar is inserted can be evaluated as follows;

C = k × A × ε /d

ε /d

ε /d C =

ε /d C = (1×2.5×10^(-5)×8.85*10^-12)/0.0001

ε /d C = (1×2.5×10^(-5)×8.85*10^-12)/0.0001 C = 2.213 × 10^(-12) = 2.213 pF

ε /d C = (1×2.5×10^(-5)×8.85*10^-12)/0.0001 C = 2.213 × 10^(-12) = 2.213 pF Q = C × V

Q = 7.5*(2.213)

Q = 16.6 pC

D) The potential difference across the two plates, after the mylar has been inserted, V = 7.5 V which remains constant throughout.

E) The Electric Field, E between the capacitor plates is given by:

where the dielectric constant of the mylar = 3.13

E = V / k × d

E = 7.5 / (3.13)0.10*10^-3

E = 24,000 V/m

F) C = k×A×ε / d

C = 3.13×( 0.005^2 × 8.85×10^-12 ) / 0.0001

C = 6.927pC

Q = C × V

Q = 7.5 × (6.927)

Q = 52 pC

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MIT’s robot cheetah can jump over obstacles 46. cm high and has speed of 12.0 km/h. a) If the robot launches itself at an angle of 60.° at this speed, what is its maximum height? b) What would the launch angle have to be to reach a height of 46. cm?

Answers

Answer:

(a)  [tex]y_{max}=0.423m[/tex]

(b)  [tex]\alpha =64.3^{o}[/tex]

Explanation:

Given data

[tex]v_{i}=12km/h=3.33m/s\\\alpha =60^{o}\\g=9.8m/s^{2}\\Required\\(a)y_{max}\\(b)Angle[/tex]

Solution

For Part (a)

As the velocity component in direction of y is given by:

[tex]v_{yi}=v_{i}Sin\alpha \\v_{yi}=3.33Sin60\\v_{yi}=2.88m/s[/tex]

The maximum displacement is given by:

[tex]v_{yf}^{2}=v_{yi}^{2}-2gy_{max}\\ y_{max}=\frac{(2.88)^{2}}{2(9.8)}\\ y_{max}=0.423m[/tex]

For Part (b)

To reach y=46cm =0.46m apply:

[tex]0=v_{yi}^{2}-2(9.8)(0.46)\\v_{yi}=3m/s\\As\\Sin\alpha =\frac{v_{yi}}{v_{i}}\\\alpha =Sin^{-1}(\frac{v_{yi}}{v_{i}})\\\alpha =Sin^{-1}(\frac{3}{3.33} )\\\alpha =64.3^{o}[/tex]

a) When launched at a 60° angle with a speed of 3.33 m/s, the robot cheetah can reach a maximum height of about 0.715 meters.

b) To reach a height of 0.46 meters, the launch angle needs to be approximately 31.74 degrees.

a) To find the maximum height (h_max) when the robot cheetah launches at a 60-degree angle with a speed of 3.33 m/s, we can use the following formula:

h_max = (u^2 * sin^2(θ)) / (2 * g)

Where:

u is the initial speed (3.33 m/s)

θ is the launch angle (60 degrees)

g is the acceleration due to gravity (9.8 m/s²)

First, calculate sin(60 degrees):

sin(60 degrees) = √3 / 2 ≈ 0.866

Now, plug in the values and calculate h_max:

h_max = (3.33^2 * (0.866)^2) / (2 * 9.8) ≈ 0.715 meters

b) To determine the launch angle (θ) required to reach a height of 0.46 meters (46 cm), we'll rearrange the same formula:

sin^2(θ) = (2 * g * h_desired) / u^2

Plug in the values:

sin^2(θ) = (2 * 9.8 * 0.46) / (3.33^2)

Now, find sin(θ):

sin(θ) ≈ √(0.2794) ≈ 0.5289

Finally, calculate θ:

θ ≈ arcsin(0.5289) ≈ 31.74 degrees

So, the launch angle required to reach a height of 0.46 meters is approximately 31.74 degrees.

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In 50 words or more, describe the scientific process that led to the development of the big bang theory. Include the key ideas and observations of the various scientists you've learned about.

Answers

Answer:

Explanation:

The Big Bang theory is a cosmological model of the observable universe from the earliest known periods through its subsequent large-scale evolution.

These theories were based on the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past.

What led to big bang theory was that free electrons would have caused light (photons) to scatter the way sunlight scatters from the water droplets in clouds," NASA stated. Over time, however, the free electrons met up with nuclei and created neutral atoms. This allowed light to shine through about 380,000 years after the Big Bang.

The best-supported theory of our universe's origin centers on an event known as the big bang. This theory was born of the observation that other galaxies are moving away from our own at great speed in all directions, as if they had all been propelled by an ancient explosive force.

Origins of the universe, explained

The most popular theory of our universe's origin centers on a cosmic cataclysm unmatched in all of history—the big bang.

The best-supported theory of our universe's origin centers on an event known as the big bang. This theory was born of the observation that other galaxies are moving away from our own at great speed in all directions, as if they had all been propelled by an ancient explosive force.

A Belgian priest named Georges Lemaître first suggested the big bang theory in the 1920s, when he theorized that the universe began from a single primordial atom. The idea received major boosts from Edwin Hubble's observations that galaxies are speeding away from us in all directions, as well as from the 1960s discovery of cosmic microwave radiation—interpreted as echoes of the big bang—by Arno Penzias and Robert Wilson.

Further work has helped clarify the big bang's tempo. Here’s the theory: In the first 10^-43 seconds of its existence, the universe was very compact, less than a million billion billionth the size of a single atom.

It's thought that at such an incomprehensibly dense, energetic state, the four fundamental forces—gravity, electromagnetism, and the strong and weak nuclear forces—were forged into a single force, but our current theories haven't yet figured out how a single, unified force would work. To pull this off, we'd need to know how gravity works on the subatomic scale, but we currently don't.

A pole-vaulter just clears the bar at 5.31 m and falls back to the ground. The change in the vaulter's potential energy during the fall is -3900 J. What is his weight?

Answers

Answer:

Weight = 734.46 N

Explanation:

Given:

Initial height of the pole-vaulter is, [tex]h_i=5.31\ m[/tex]

Final height of the pole-vaulter is, [tex]h_f=0\ m[/tex]

Change in the vaulter's potential energy is, [tex]\Delta U=-3900\ J[/tex]

We know that, change in potential energy is given as:

[tex]\Delta U=mg(h_f-h_i)[/tex]

Where, 'm' is the mass of the object, 'g' is acceleration due to gravity and has a value of 9.8 m/s².

Now, weight of the object is given as the product of its mass and acceleration due to gravity. So, replace 'mg' by weight 'w'. So, the equation becomes,

[tex]\Delta U = w(h_f-h_i)[/tex]

Now, rewriting in terms of 'w', we get:

[tex]w=\dfrac{\Delta U}{(h_f-h_i)}[/tex]

Now, plug in all the given values and solve for 'w'. This gives,

[tex]w=\dfrac{-3900\ J}{(0-5.31)\ m}\\\\\\w=\dfrac{3900}{5.31}\ N\\\\\\w=734.46\ N[/tex]

Therefore, weight of the vaulter is 734.46 N.

Final answer:

The weight of the pole-vaulter is calculated using the principle of conservation of mechanical energy and the equation for gravitational potential energy, resulting in a value of approximately 734.46 Newtons.

Explanation:

The question asked concerns the calculation of the weight of a pole-vaulter given a change in potential energy as the vaulter falls. The calculation can be made using the principle of conservation of mechanical energy, and the equation for gravitational potential energy: PE = mgh, where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is the change in height.

The change in the vaulter's potential energy is given in the problem as -3900 J, which is negative because potential energy decreases as height decreases. Assuming that the entire change in potential energy is converted into kinetic energy, we can arrange the equation: -PE = mgh = weight * h for the weight of the vaulter, giving: weight = -PE / h.

Substituting the given values into this equation gives weight = (-(-3900 J)) / (5.31 m) = 734.46 N. So, the weight of the pole-vaulter is approximately 734.46 Newtons.

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A wire of length 8x is bent into the shape of a circle. A. Express the circumference of the circle as a function of x. B. Express the area of the circle as a function of x.

Answers

Answer:

[tex]a. C=8X\\\\b. A=\frac{16x^2}{\pi}[/tex]

Explanation:

Given length is [tex]8x[/tex]

Circumference of a circle is given as:

[tex]C=2\pi r[/tex]

a.But the circumference is equal to length of the wire. Therefore circumference as a function of [tex]x[/tex] is:

[tex]C=8x[/tex]

b.Area as function of [tex]x[/tex]

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

Rewrite the circumference equation to make r the subject of the formula.

[tex]2\pi r=8x\\r=\frac{4x}{\pi}[/tex]

To express area as a function of [tex]x[/tex]:-

[tex]A=\pi r^2\\=\pi (\frac{4x}{\pi})^2\\=\frac{16x^2}{\pi}[/tex]

Therefore area of circle as a function of [tex]x[/tex] is [tex]\frac{16x^2}{\pi}[/tex]

Final answer:

The circumference of the circle, represented as function of x, is C(x) = 8x. The area of the circle, represented as function of x, is A(x) = (16x²) / π.

Explanation:

The given length of the wire bent into a circle is 8x. This is equivalent to the circumference of this circle because a circle's circumference is the distance around it.

So, the function of the circumference, C, in terms of x is C(x) = 8x.

For the area of the circle, we must understand that the formula for the area of a circle is πr² where r is the radius of the circle. The radius is half the diameter, and since the circumference of a circle is πD where D is the diameter, we can find that r = circumference / (2π), or r = 8x / (2π).  

So, substituting r into the formula for the area, we get A(x) = π(8x / (2π))² = π(4x / π)² = π((4x)² / π²) = (16x²) / π.

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A satellite system that has unique properties is the ____ satellite, which is used by governments for spying and by scientific agencies for observing celestial bodies

Answers

Answer: Highly-elliptical-earth-orbit (heo)

Explanation: Highly-elliptical-earth-orbit (heo) satellite system has unique properties

which is used by governments for spying and by scientific agencies for observing celestial bodies. It is an extremely elongated orbit that is useful for communication satellites which creates signals between a source transmitter and a receiver at different locations on earth. They are used by government for spying, scientific agencies for observing celestial bodies, for the internet and telephone communications.

Answer:

Highly elliptical satellite orbit.

Explanation:

Highly elliptical satellite orbit is used to provide coverage over any point on the globe. The HEO is not limited to equatorial orbits like the geostationary orbit and the resulting lack of high latitude and polar coverage.

As a result of its ability to provide high latitude and polar coverage, countries such as Russia which need coverage over polar and near polar areas make significant use of highly elliptical orbits, HEO. With two satellites in any orbit, they are able to provide continuous coverage.

An ice cream machine produced 44 ice creams per minute. After reconditioning, its speed increase to 55 ice creams per minute. By what percent did the speed of the machine increase

Answers

Answer:

an ice cream machine produced 44 ice cream per minute.

Now, after reconditioning it  speeds up to 55 ice cream per minute.

=> 55 - 44 = 11

=> 11 / 44 = 0.25

=> 0.25 * 100% = 25%.

thus it increased it production to 25%.

Explanation:

Answer:

25%

Explanation:

The way to find this answer is to:

Subtract 44 from 55 (11)

Then, you can put 11 over 44

Simplified, this is equal to 1/4.

1/4 as a percentage is 25%.

Good luck with your RSM work!

geography Which nation in the region has seen its growth rate accelerate, while the majority of the region has seen a decline in growth rates?

Answers

Answer:

For further investigation see also the most recent World Population Data ... and Latin America and the Caribbean, and the regions of Melanesia, ... While Germany's death rate exceeds its birth rate, its population ... Population growth accelerated.

When Dr. Hewitt immerses an object in water the second time and catches the water that is displaced by the object, how does the weight lost by the object compare to the weight of the water displaced?

Answers

Answer:

The weight loss of object is equal to the weight of water displaced.

Explanation:

- When the object is immersed the force of Buoyancy acts against the weight and reducing the scale weight.

- The amount of Buoyancy Force is proportional to the fraction of Volume of object immersed in water; hence, the same amount is spilled/lost.

- The amount of water is proportional to the volume of object of fraction of object immersed in water will lead to the same fraction of water displaced and caught by Dr. Hewitt.  

A good baseball pitcher can throw a baseball toward home plate at 93 mi/h with a spin of 1510 rev/min. How many revolutions does the baseball make on its way to home plate? For simplicity, assume that the 60 ft path is a straight line.

Answers

Answer:

[tex]\Delta \theta =11.073\ rev[/tex]

Explanation:

Given,

Speed of baseball = 93 mi/h

spin = 1510 rev/min

[tex]\Delta x = 60\ ft[/tex]

[tex]v =93\times  \dfrac{88}{60} = 136.4 ft/s[/tex]

[tex]\omega = 1510\times \dfrac{1}{60}= 25.167\ rad/s[/tex]

[tex]\Delta t = \dfrac{\Delta x}{v}[/tex]

[tex]\Delta t = \dfrac{60}{136.4 }[/tex]

[tex]\Delta t = 0.44\ s[/tex]

Revolutions of ball

[tex]\Delta \theta = \omega t[/tex]

[tex]\Delta \theta = 25.167\times 0.44[/tex]

[tex]\Delta \theta =11.073\ rev[/tex]

Revolution of the ball is equal to [tex]\Delta \theta =11.073\ rev[/tex].

f we apply an electrical stimulus to a muscle cell to cause it to contract, the magnitude of that stimulus must be strong enough to reach a critical value that is essential to initiate contraction. This critical value is known as __________.

Answers

Answer:

critical value is known as threshold

Explanation:

solution

when we apply electrical stimulus to the cell of muscle

then magnitude of stimulus will be strong enough for reaching the critical value

and this critical value is threshold because when the size of an stimulus change in requirement for the detection, this is called the threshold

but if change is done by without stimulation then there threshold stimulus is absolute threshold

so correct answer is threshold

To answer this question, suppose that each vehicle is moving at 7.69 m/s and that they undergo a perfectly inelastic head-on collision. Each driver has mass 82.6 kg. The total vehicle masses are 810 kg for the car and 4280 kg for the truck. Note that these values include the masses of the drivers. If the collision time is 0.129 s, (a) what force does the seat belt exert on the truck driver?

Answers

Answer:

Force(F) = -80,955.01 N

Explanation:

We need to first determine the impulse that the truck driver received from the car during the collision

So; m₁v₁ - m₂v₂ = (m₁m₂)v₀

where;

m₁ = mass of the truck = 4280 kg

v₁ = v₂ =  speed of the each vehicle = 7.69 m/s

m₂ = mass of the car = 810 kg

Substituting our data; we have:

(4280×7.69) - (810×7.69) = (4280+810)v₀

32913.2 - 6228.9 = (5090)v₀

26684.1 =  (5090)v₀

v₀ = [tex]\frac{26684.1}{5090}[/tex]

v₀ = 5.25 m/s

NOW, Impulse on the truck = m (v₀ - v)

= 4280 × (5.25 - 7.69)

= 4280 ×  (-2.44)

= -10,443.2 kg. m/s

Force that the seat belt exert on the truck driver can be calculated as:

Impulse = Force × Time

-10,443.2 kg. m/s = F (0.129)

F = [tex]\frac{-10,443.2}{0.129}[/tex]

Force(F) = -80,955.01 N

Thus, the Force that the seat belt exert on the truck driver = -80,955.01 N

Because the block is not moving, the sum of the y components of the forces acting on the block must be zero. Find an expression for the sum of the y components of the forces acting on the block, using coordinate system b.

Answers

Answer:

Incomplete questions

Completed question, check attachment for diagram

Because the block is not moving, the sum of the y components of the forces acting on the block must be zero. Find an expression for the sum of the y components of the forces acting on the block, using coordinate system shown. Express your answer in terms of some or all of the variables

Fn, Ff, Fw and θ.

Explanation:

Check attachment for solution

Final answer:

The sum of the y components of forces on a stationary block must be zero due to Newton's second law, which results in the normal force being equal to the weight of the block.

Explanation:

In physics, when analyzing the forces acting on a stationary block, we apply Newton's second law, which implies that the net force in the y-component must be zero because the block is not moving vertically. An expression for the sum of the y components of the forces acting on the block can be deduced by considering all the vertical forces, including the weight of the block (acting downward) and the normal force (acting upward).

For a block on a frictionless surface attached to a spring, we consider the spring force and gravitational force. If the block is in equilibrium, these forces satisfy the equation mg = k Δy, where m is the mass of the block, g is the acceleration due to gravity, k is the spring constant, and Δy is the displacement from the equilibrium position. Therefore, the sum of the y components equates to zero: normal force - weight = 0, which also indicates that the normal force is equal to the weight.

why the sun emits most of its energy in the form of visible light?

Answers

Human eye could perceive this visible light and used it to look at the objects.

Explanation:

There are 3 forms of radiation emitted by the sun. They are Infrared radiation, Ultra Violet radiation as well as visible radiation.

Visible light is the type of light can perceive by the human eye and utilizes to see the objects.  

Since the sun is hotter (5800 K) than the earth, it emits mostly the radiation energy in the form of this visible light.

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