Two point charges, initially 2.0 cm apart, experience a 1.0 N force. If they are moved to a new separation of 0.25 cm, what is the electric force between them (in N)?

Answer:

The 500 watts motor

Explanation:

Power is the workdone per unit time, it can be expressed as;

P = VI

P = I^2 × R

Where;

P = power

V = potential difference

I = current

R = resistance

Making current the subject of formula;

I = P/V

I^2 = P/R

Since they are both connected to the same standard home outlet. The potential difference across them is thesame( V is constant). Therefore the higher the power the higher the current.

I ∝ P

So the electrical motors with higher power 500 watts draws greater current.

Answer:

Check the explanation

Explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

Vertex: Point where the principal axis and mirror meet

Focal point: Point we are reflected light converges or appears to diverge

Focal length: distance from the center of a mirror to the focal point

Principal axis: line that runs to the center of curvature to a mirror

Center of curvature: sensor of spherical mirror from which a curved mirror was cut

Explanation:

Just did the assignment on Edge.

A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex.

A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are two types of spherical mirrors: concave, and convex. These are illustrated in.

The most commonly occurring examples of concave mirrors are shaving mirrors and makeup mirrors.

As is well-known, these types of mirrors magnify objects placed close to them. The most commonly occurring examples of convex mirrors are the passenger-side wing mirrors of cars.

These types of mirrors have wider fields of view than equivalent flat mirrors, but objects which appear in them generally look smaller

The answers to the given questions are:

Vertex: Point where the principal axis and mirror meet

Focal point: Point we are reflected light converges or appears to diverge

Focal length: distance from the centre of a mirror to the focal point

Principal axis: line that runs to the centre of curvature of a mirror

Center of curvature: sensor of spherical mirror from which a curved mirror was cut

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The initial speed of the bullet was determined by utilizing the principles of conservation of energy and momentum. The final velocity of the bullet and bob was first determined from the given height and the known conversion of kinetic to potential energy. This final velocity was then input into the conservation of momentum equation to find the initial speed of the bullet.

The ballistic pendulum is a classic example of a problem in physics which can be solved either by using the principles of work and energy or the principles of impulse and momentum. For this problem, we will utilize conservation of momentum. We know that the momentum before the collision is equal to the momentum after the collision.

Therefore, we can create the following equation: (m1×v1) + (m2×v2) = (m1+m2)×V, where m1 and v1 represent the mass and velocity of the bullet, m2 and v2 represent the mass and velocity of the block, and V is the final velocity of the bullet-block system. We know that the block was initially at rest, hence v2 = 0.

After the bob reaches maximum height, there's no kinetic energy (because the speed is zero), so all that original kinetic energy has been converted into potential energy, m×g×h, where m is the total mass (mass of bullet + mass of bob), g is the acceleration due to gravity, and h is the height the bob was raised. From here we can solve for V, then substitute back into the momentum equation to solve for v1, which represents the initial speed of the bullet.

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Using conservation of momentum and energy, the initial speed of an 8.0 g bullet fired into a 2.5 kg ballistic pendulum bob, which rises 6.0 cm, is approximately 339.9 m/s. The key steps involve converting units, applying conservation laws, and solving for the initial speed. Therefore, the bullet's speed is determined to be 339.9 m/s.

For solving this problem, we will use the principle of conservation of momentum and the principle of conservation of energy.

Step-by-Step Solution

Convert the masses into common units:

mass of bullet, [tex]m_{bullet[/tex] = 8.0 g = 0.008 kg

mass of pendulum bob = 2.5 kg.

Convert the rise height into meters:

h = 6.0 cm = 0.06 m.

Determine the final velocity of the combined bullet and pendulum system at the lowest point (right after the collision) using energy conservation:

At maximum height, all kinetic energy is converted to potential energy:

mgh = 0.5 (M + m) v²

Using v = √(2gh) since M includes the bullet:

v = √(2 * 9.8 m/s² * 0.06 m)

v = √(1.176)

v ≈ 1.084 m/s

Use conservation of momentum to find the initial speed of the bullet:

Initial momentum = [tex]m_{bullet[/tex] * [tex]v_{bullet[/tex]

Final momentum = (M + m) * v = (2.5 kg + 0.008 kg) * 1.084 m/s

So, p = (2.508 kg) * 1.084 m/s

p = 2.719 kg·m/s

Initial speed of the bullet:

[tex]v_{bullet[/tex] = p / [tex]m_{bullet[/tex]

[tex]v_{bullet[/tex] = 2.719 kg·m/s / 0.008 kg

[tex]v_{bullet[/tex] ≈ 339.9 m/s

Therefore, the initial speed of the bullet is approximately 339.9 m/s.

Answer:

(a) the input force is 36.56 N

(b) the input force is 37.49 N

Explanation:

Given;

density of hydraulic oil, ρ =  8.53 x 10² kg/m³

radius of plunger, r₁ = 0.135 m

radius of piston, r₂ = 5.43 x 10⁻³ m

Part (a) The input force needed to support 22600-N weight, when the bottom surfaces of the piston and plunger are at the same level;

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

Where;

P is pressure

F is force

A is circular area = πr²

[tex]\frac{F_1}{A_1} =\frac{F_2}{A_2} \\\\F_2 = \frac{F_1*A_2}{A_1} =\frac{F_1* \pi r_2^2}{\pi r_1^2} = \frac{F_1* r_2^2}{ r_1^2} \\\\F_2 = \frac{22600*(5.43*10^{-3})^2 }{(0.135)^2}\\\\F_2 = 36.56 \ N[/tex]

Part (b) The input force needed to support 22600-N weight, when the  bottom surface of the output plunger is 1.20 m above that of the input plunger

[tex]P_2 = P_1 + \rho gh[/tex]

But, F = PA  and  A = πr²

[tex]F_2 = F_1(\frac{A_2}{A_1} ) + \rho gh*A_2\\\\F_2 = F_1(\frac{r_2^2}{r_1^2} )+\rho gh(\pi r_2^2)\\\\F_2 = 22600(\frac{5.43*10^{-3}}{0.135})^2 \ + 853*9.8*1.2*\pi (5.43*10^{-3})^2\\\\F_2=36.56 + 0.93\\\\F_2 = 37.49 \ N[/tex]

The solution of this problem involves the use of Pascal's principle and a concept known as hydrostatic pressure.

First, let's identify the given parameters:
- The density (ρ) of the hydraulic oil is 8.53 x 10ˆ2 kg/m³
- The radius of the input piston is 5.43 x 10ˆ-3 m
- The radius of the output plunger is 0.135 m
- The total weight (W) being lifted is 22600 N
- The acceleration due to gravity (g) is approximately 9.81 m/s²
- The height difference (Δh) between the pistons is 1.2 m

We will use these in our calculations.

We begin by determining the areas of the input piston and the output plunger using the formula for the area of a circle A = πr². We denote the area of the input piston as Ain and the area of the output plunger as Aout.

Let's now focus on when the pistons are at the same level.
Part (a) requires us to find the input force (F) needed to support the weight of the car and output plunger. This is governed by Pascal's principle, which states that for an incompressible, non-viscous fluid in a hydraulic system, pressure is transmitted undiminished throughout the fluid and acts with equal force on all areas. Using Pascal's principle, the force required on the input piston is equal to the weight divided by the ratio of the areas. F = W * (Ain / Aout). After performing the calculation, we find that F equivales to approximately 36.562893827160494 N.

Next, let's turn to when the bottom surface of the output plunger is 1.2 m above the input piston.
Part (b) of the problem asks us to calculate the input force needed in this scenario. We must consider not only Pascal's principle but the additional hydrostatic pressure due to the height difference between the pistons. Firstly, we calculate the hydrostatic pressure difference (ΔP): ΔP = ρ * g * Δh. We then add this pressure difference to the force required when pistons were at the same level. Remember that pressure is force divided by area, thus when we add pressure we need to multiply it by the area of the input piston to maintain the units consistent. F = F_same_level + ΔP * Ain. The result of this calculation yields an input force of approximately 37.49208673165364 N.

In conclusion, the input force required to support the specified weight when the bottom surfaces of the pistons are at the same level is about 36.56 N. This force increases to roughly 37.49 N when the output plunger is pushed 1.2 m above the input piston due to the added hydrostatic pressure.

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Answer:

Length of the pipe = 53.125 cm

Explanation:

given data

harmonic frequency f1  = 800 Hz

harmonic frequency f2  = 1120 Hz

harmonic frequency f3  = 1440 Hz

solution

first we get here fundamental frequency that  is express as

2F = f2 - f1    ...............1

put here value

2F = 1120 - 800

F = 160 Hz

and

Wavelength is express as

Wavelength  = Speed ÷ Fundamental frequency    ................2

here speed of waves in air  = 340 m/s

so put here value

Wavelength  =340 ÷ 160

Wavelength   = 2.125 m

so

Length of the pipe will be

Length of the pipe = 0.25 × wavelength    ......................3

put here value

Length of the pipe = 0.25 × 2.125

Length of the pipe = 0.53125 m

Length of the pipe = 53.125 cm

Final answer:

The length of the pipe, which resonates at odd harmonics and has successive frequencies of 800 Hz, 1120 Hz, and 1440 Hz, is calculated to be approximately 32.2 centimeters. This calculation assumes that the pipe is closed at one end, and uses the relationship between the harmonics and the fundamental frequency.

Explanation:

The student is inquiring about determining the length of a pipe based on the frequencies of its successive harmonics. Since the successive harmonics are at 800 Hz, 1120 Hz, and 1440 Hz, and these frequencies are not direct multiples of each other, it suggests that we're dealing with a pipe that is closed at one end. Such pipes produce odd harmonics only. The given frequencies thus correspond to the fundamental (first harmonic), the third harmonic, and the fifth harmonic, respectively.

The frequency of the nth harmonic in a pipe closed at one end is given by:

fn = n(f1), where n is an odd integer and f1 is the fundamental frequency, which in this case is 800 Hz. So, the third harmonic would be 3(800 Hz) = 2400 Hz, which is incorrect given our second frequency is 1120 Hz. The provided frequencies imply that 800 Hz is, in fact, the third harmonic (800 Hz = 3f1). Hence, the fundamental frequency (f1) is 800 Hz / 3 = 266.67 Hz.

The wavelength (λ1) of the fundamental frequency in a tube closed at one end is given by λ1 = 4L. Using the formula for frequency (
f = v / λ), where v is the velocity of sound in air (approximately 343 m/s), we can calculate the length of the pipe by rearranging it to L = v / (4f1).

Therefore, L = 343 m/s / (4 * 266.67 Hz) = 0.322 meters or 32.2 cm.

Complete Question

An oil tanker has collided with a smaller vessel, resulting in an oil spill in a large, calm-water bay of the ocean. You are investigating the environmental effects of the accident and need to know the area of the spill. The tanker captain informs you that 18000 liters of oil have escaped and that the oil has an index of refraction of n = 1.1. The index of refraction of the ocean water is 1.33. From the deck of your ship you note that in the sunlight the oil slick appears to be blue. A spectroscope confirms that the dominant wavelength from the surface of the spill is 485 nm. Assuming a uniform thickness, what is the largest total area oil slick

Answer:

The  largest total area of the oil slick  [tex]A = 8.257 *10^{9} \ m^2[/tex]

Explanation:

From the question we are told that

     The volume of oil the escaped is  [tex]V = 18000 \ L[/tex]

    The refractive index of oil is [tex]n_o = 1.1[/tex]

     The refractive index of water is [tex]n_w = 1.33[/tex]

      The wavelength of the light  is [tex]\lambda = 485 \ nm = 485 * 10^{-9} \ m[/tex]

Generally the thickness of the oil for condition of constructive interference between the oil and the water is mathematically represented as

          [tex]d = m *\frac{\lambda}{2n_w}[/tex]

Where is the order of interference of the light and it value ranges from 1, 2, 3,...n

It is usually take as 1 unless stated otherwise by the question

substituting value

      [tex]d = 1 * \frac{485 *10^{-9}}{2 * 1.1}[/tex]    

      [tex]d = 218 nm[/tex]    

The are can be mathematically evaluated as

        [tex]A = \frac{V}{d}[/tex]

Substituting values

        [tex]A = \frac{18000}{218*10^{-8}}[/tex]

        [tex]A = 8.257 *10^{9} \ m^2[/tex]

Answer:

Explanation:4meters

Work=10J

Force=2.5N

Distance=work ➗ force

Distance=10 ➗ 2.5

Distance=4meter

Final answer:

Given that the work done on a book was 10 J and the force required to move the book was 2.5 N, we use the formula Work = Force x Distance to find that the book was moved a distance of 4 meters.

Explanation:

The question asks to calculate the distance a book was moved given that the work done on the book was 10 J and the force required to move the book was 2.5 N.

To find the distance, we can use the formula for work, which is:

Work (W) = Force (F) * Distance (d)

From the formula, we can solve for distance (d) by rearranging the equation:

Distance (d) = Work (W) / Force (F)

Plugging in the given values:

d = 10 J / 2.5 N

This calculation yields:

d = 4 m

Therefore, the book was moved a distance of 4 meters.

Answer:

The wavelength of the laser, λ = 5.625 * 10⁻⁷ m

Explanation:

Separation of the narrow slits, d = 7.5 * 10⁻⁵ m

The distance between the screen and the two slits, d = 4m

The distance between the bright spot and the center of the pattern, Y = 1.5 cm

Y = 1.5 * 10⁻² m

To calculate the wavelength, λ, of the laser we will use the relationship:

[tex]Y = \frac{\lambda L}{2d} \\1.5 * 10^{-2} = \frac{\lambda * 4}{2*7.5*10^{-5} }\\\lambda = \frac{1.5 * 10^{-2} * 15 * 10^{-5} }{4}[/tex]

λ = 5.625 * 10⁻⁷ m

Final answer:

Destructive interference between two waves occurs when their phase difference is [tex]\pi + 2\pi n[/tex], for any integer n, resulting in a minimized or zero resultant amplitude.

Explanation:

The full criterion for destructive interference between two waves is when the phase difference between the waves is [tex]\pi + 2\pi n[/tex] for any integer n. This occurs because two waves are exactly half a wavelength out of phase [tex]\pi[/tex] radians phase difference), resulting in the peaks of one wave aligning with the troughs of the other, canceling each other out. Unlike constructive interference, where the waves reinforce each other leading to increased amplitude, destructive interference leads to a decrease in amplitude, potentially down to zero in the case of perfect destructive interference with identical waves.

Expressed mathematically, for pure destructive interference, the phase difference must fulfill the condition: phase difference = [tex]\pi + 2\pi n[/tex] for any integer n. This means that the path length difference between the two waves must be an odd multiple of half the wavelength. The result is that at the points of destructive interference, the amplitude of the resultant wave is minimized or even becomes zero, eliminating the wave at that point.

Answer:the object is not accelerating

Explanation:

There object is not accelerating since there's no increase in velocity

Final answer:

Based on the descriptions of graphical data, we can conclude that the object has negative acceleration because its velocity is decreasing over time while it is moving in the positive direction, or its negative velocity is increasing over time. Also, since the object is moving in the negative direction, it experiences a negative displacement.

Explanation:

The question asks about the motion of an object based on different graphical representations. To determine the nature of this motion, we can analyze the provided diagrams. In this case, we have descriptions of how the velocity changes over time, which allows us to infer acceleration, and acceleration is defined as the change in velocity over time. According to the information, the object experiences a decrease in positive velocity, which indicates a negative acceleration, as acceleration is in the opposite direction to the velocity. Furthermore, it is mentioned that the object has a negative velocity which increases in magnitude, coherently resulting in negative acceleration as well.

Acceleration is a vector quantity, meaning it has both direction and magnitude. Since we are discussing a coordinate system where to the right is considered positive, any acceleration towards the left will be considered negative. The graphs that indicate an object having a constant negative velocity also imply that the object has negative displacement over the time period, because it's moving in the negative direction of the coordinate system.

Answer:

7350 J

Explanation:

Gravitational Potential Energy: This is defined as the energy possessed by a body due to it's position in the gravitational field. The S.I unit is Joules(J).

Applying,

E.p = mgh..................... Equation 1

Where E.p = Gravitational potential Energy, m = mass of the object, h = height of the object above the surface of the earth, g = acceleration due to gravity.

Given: m = 2.5 kg, h = 300 m

Constant: g = 9.8 m/s²

Substitute these values into equation 1

E.p = 2.5(300)(9.8)

E.p = 7350 J.

Answer:

The speed of the clay immediately before the impact is 91.23 m/s

Explanation:

Given;

mass of clay, m₁ = 12g = 0.012 kg

mass of wooden block, m₂ = 100g = 0.1 kg

initial velocity of the wooden block, u₂ = 0

distance moved by the wooden block, d = 7.5 m

coefficient of friction, μk = 0.65

Apply the principle of conservation of linear momentum;

Total momentum before collision = Total momentum after collision

m₁u₁ + m₂u₂ = v(m₁ +m₂)

where;

u₁ is the initial velocity of the clay immediately before the impact

v is the common velocity of clay-block system after impact

u₂ = 0

m₁u₁ = v(m₁ +m₂)

[tex]U_1 = \frac{(m_1 + m_2)V}{m_1}[/tex] ------- equ. (i)

Apply the principle of conservation of energy after the impact

ΔK + ΔU = 0

where;

ΔK is change in kinetic energy

ΔU is change in internal energy of the system due to frictional force

[tex](K_f -K_i) + (F_k*d) = 0\\\\-K_i +F_k*d = 0\\\\K_i = F_k*d \\\\\frac{1}{2} (m_1+m_2)v_i^2 = \mu_k (m_1 +m_2)gd\\\\\frac{1}{2}v_i^2 = \mu_kgd\\\\v_i^2 = 2 \mu_kgd\\\\v_i = \sqrt{2 \mu_kgd}[/tex]

[tex]v_i[/tex] is the common velocity of the clay-block system immediately after the impact, which is equal to V in equation (i)

[tex]U_1 = \frac{(m_1+m_2)V}{m_1} = \frac{(m_1+m_2)v_i}{m_1}\\\\U_1 = \frac{m_1+m_2}{m_1}(\sqrt{2 \mu_kgd})\\\\U_1 = \frac{0.012+0.1}{0.012}(\sqrt{2 *0.65*9.8*7.5})\\\\U_1 = 9.3333(9.77497)\\\\U_1 = 91.23 \ m/s[/tex]

Therefore, the speed of the clay immediately before the impact is 91.23 m/s

Answer:b-The person and the earth

Explanation:

The best system will be the person and earth as a system

It is so because whatever the energy required by the person is derived from earth resource and thus by depleting the earth resource person is getting is required form of energy .

for example person want thermal energy , for this he need coal which is earth resource and thus all the energy is derived from earth and is being converted into some other form of energy.

Answer:

1.333 cm/s

Explanation:

The formula for the volume of the cube V in term of its edge s is:

[tex]V = s^3[/tex]

By using chain rule we have the following equation between the rate of change of the volume and the rate of change of the edge:

[tex]\frac{dV}{dt} = \frac{dV}{ds}\frac{ds}{dt}[/tex]

[tex]100 = \frac{d(s^3)}{ds}\frac{ds}{dt}[/tex]

[tex]100 = 3s^2\frac{ds}{dt}[/tex]

[tex]\frac{ds}{dt} = \frac{100}{3s^2}[/tex]

We can substitute s = 5 cm:

[tex]\frac{ds}{dt} = \frac{100}{3*5^2} = 100 / 75 = 1.333 cm/s[/tex]

Answer:B

Explanation:

Power=p

Voltage=v

Resistance=r

Voltage for both:110v

For 60 watts bulb:

Resistance=v^2/p

Resistance=110^2/60

Resistance=(110x110)/60

Resistance=12100/60

Resistance=201.7 ohms

Current=power/voltage

Current=60/110

Current=0.55 amperes

For 100watts bulb:

Resistance=v^2/p

Resistance=110^2/100

Resistance=(110 x 110)/100

Resistance=(12100)/100

Resistance =121 ohms

Current=power/voltage

Current=100/110

Current=0.91

The 60W bulb has greater resistance and smaller current than the 100W bulb, based on calculations from the power, voltage and Ohm's Law.

In the case of light bulbs, power (P) is given by the formula P = IV, where I is the current and V is the voltage. Bulb A is rated at 60W and Bulb B at 100W, both functioning at a voltage (V) of 110V. To find the current (I) for each bulb, you would divide the power (P) by the voltage (V). This shows that Bulb B, with a higher wattage, has a greater current.

The resistance (R) of the bulbs can be found using Ohm's Law, which states R = V/I. This shows that Bulb A, with a smaller current, has a greater resistance.

Therefore, option B-'The 60W bulb has a greater resistance and smaller current than the 100 W bulb' is the correct statement.

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The plants that are typically the first to live in soil are known as pioneer plants or pioneer species.

Pioneer plants or pioneer species are the plants that are often the first to live in soil. These plants are distinguished by their propensity to colonize bare or disturbed soil, such as on newly formed land or in the wake of a natural disaster.

The process of primary succession, which is the gradual formation of plant and animal communities in a region devoid of soil or organic matter, depends critically on pioneer plants.

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Answer:

The separation distance between the parallel planes of an atom is hc/2sinθ(EK - EL)

Explanation:

The relationship between energy and wavelength is expressed below:

E = hc/λ

λ = hc/EK - EL

Considering the condition of Bragg's law:

2dsinθ = mλ

For the first order Bragg's law of reflection:

2dsinθ = (1)λ

2dsinθ = hc/EK - EL

d = hc/2sinθ(EK - EL)

Where 'd' is the separation distance between the parallel planes of an atom, 'h' is the Planck's constant, 'c' is the velocity of light, θ is the angle of reflection, 'EK' is the energy of the K shell and 'EL' is the energy of the K shell.

Therefore, the separation distance between the parallel planes of an atom is hc/2sinθ(EK - EL)

Answer:

It is perceived as louder.

Explanation:

Amplitude affects the loudness of sound.

Frequency and wavelength affect the pitch of the sound.

The slope of the line is calculated by dividing the change in distance over the change in time.

Answer:3m/s

Explanation:

mass(m)=50kg

Kinetic energy =225 joules

Kinetic energy=(m x (velocity)^2)/2

225=(50 x (velocity)^2)/2

Cross multiplying we get

225x2=50x(velocity)^2

450=50x(velocity)^2

Divide both sides by 50

450/50=(50x(velocity)^2)/50

9=(velocity)^2

Taking the square root of both sides we get

√9=velocity

3=velocity

Velocity=3m/s

Answer:

(D) Decrease in width of 2.18 x [tex]10^{-6[/tex]m

Explanation:

Given:

force 'F'= 60,000 N

elastic modulus 'E' = 207 GPa => 2.07 x  [tex]10^{11[/tex]N/m²

cross section area ' [tex]A_{0}[/tex]'= 20 mm x 40 mm => 800mm² =>8 x [tex]10^{-4}[/tex] m²

∈z = б/E => (F/ [tex]A_{0}[/tex])/E => F/ [tex]A_{0}[/tex]E

∈z = 60,000/(8 x [tex]10^{-4}[/tex] x 2.07 x  [tex]10^{11[/tex])

∈z =3.62 x  [tex]10^{-4}[/tex]

Lateral strain is given by,

∈x= -v∈z => -(0.30)(3.62 x  [tex]10^{-4}[/tex])

∈x=1.09  x  [tex]10^{-4}[/tex]

Next is to calculate the change in width

ΔW= Wo x ∈x =>20 x 1.09  x  [tex]10^{-4}[/tex]

ΔW= -2.18 x  [tex]10^{-6[/tex] m

Therefore, the correct option is 'D'

The steel specimen, when pulled in tension, will experience a decrease in width. This decrement is calculated to be about 1.75*10^-7 m, closest to option (D) decrease in width of 2.18  10−6 m.

The change in the width of a steel specimen being pulled in tension can be found using the formula for strain in the lateral direction = -Poisson's ratio * (stress/Young's modulus). Here, the stress (force/area) is 60,000N/(20mm*40mm), the Young's modulus is 207 GPa, and the Poisson's ratio is 0.30. Plugging these values in, we get a lateral strain of -8.74*10^-6. The change in width, which is this lateral strain times the original width (20mm), will thus be a decrease of about 1.75*10^-4 mm, or 1.75*10^-7 m. Amongst the given options, this is closest to (D) decrease in width of 2.18  10−6 m.

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Answer:

Either repel or attract.

Explanation:

Answer:

Explanation:

Let r be the radius of circular top and h be the height of the cylinder

Given

π r² h = 1000

Let cost of making side of can be p per unit area , the cost of making top and bottom will be 2p per unit area.

total cost

C = 2 x π r² x 2p + 2πrh x p

= 2(1000 / h) x 2p + 2π x (1000 / π) x  [tex]\frac{1}{\sqrt{h} }[/tex] x h x p

= 2(1000 / h) x 2p + 2π x (1000 / π) x √h x p

differenciating

dC / dh =  2(- 1000 / h²) x 2p + 2π x (1000 / π) x [tex]\frac{1}{2\sqrt{h} }[/tex] x p  = 0 for minimum cost

- 4 / h² + 1 / √h = 0

h³ = 16

h = 2.519 cm .

π r² h = 1000

π r²  x 2.519 = 1000

r = 11.24 cm

The cylinder will have height of 2.519 cm and radius of 11.24 cm.

Wyatt should design the can with a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm to minimize cost. This considers the volume constraint of 1000 cm³ and the different material costs for the top/bottom and side. Detailed steps involve deriving these dimensions mathematically.

Let's denote the radius of the base of the cylinder by r and the height by h. The volume V of the cylinder is given by V = πr²h. Given that the volume is 1000 cm³, we have:

Step 1: V = πr²h = 1000 cm³

Therefore, h = 1000 / (πr²).

Step 2: Next, we need to express the cost of the material. The cost for the top and bottom parts is double the cost of the side. The surface area A of the can is:

Area of the top and bottom (each): [tex]A_t[/tex] = πr²

Area of the side: [tex]A_s[/tex] = 2πrh

Total area A:

A = 2πr² + 2πrh

Considering the cost factor, the effective cost area C is:

C = 2(2πr²) + 2πrh

C = 4πr² + 2πrh

Step 3: Substitute h from the volume equation:

C = 4πr² + 2πr(1000 / (πr²))

C = 4πr² + 2000 / r

Step 4: To minimize the cost, take the derivative of C with respect to r and set it to zero:

[tex]\frac{dC}{dr}[/tex] = 8πr - 2000 / r² = 0

8πr = 2000 / r²

8πr³ = 2000

r³ = 250 / π

r ≈ 3.4198 cm

Step 5: Calculate the height h:

h = 1000 / (πr²)

h ≈ 1000 / (π * (3.4198)²)

h ≈ 27.2837 cm

In summary, Wyatt should design the can with a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm to minimize the cost.

Wyatt should choose a radius of approximately 3.4198 cm and a height of approximately 27.2837 cm for the metal can to minimize the cost, given the volume constraint of 1000 cm³.

Answer:

1, 2, and 5

Explanation:

Answer:

1, 2 and 5

Explanation:

Answer:

The required power by the engine is 33.0 hp

Explanation:

Solution

Newton's second law says that, the net force Fnet on an object of mass m will accelerates the object

Where

Fnet = ma

a = acceleration

θ = angle of incline,

m = mass of the 30 skiers,

f = frictional force

N = normal force

mg sinθ, mg cos θ are components of weight skier

F = the force applied by engine

Now,

The skier mass  is 65 kg

We calculate the mass of the 30 skier

m = 30 (65kg) = 1950 kg

Calculate the net force acting on the skiers along the x-axis

Fnet, x=ma

Now,

F-mg sin θ - f = 0

F= mg sin θ + f -----(1)

The kinetic frictional force is denoted by

f = μk N ------(2)

μk = The coefficient of the kinetic friction

We now, calculate the net force acting on the skiers along y axis

Fnet, y = ma

N- mg cos θ = 0

so,

N = mg cos θ

This value is  substituted in equation (2)

f = μk mg cos θ

we substitute the value for equation (1)

F = mg sin θ + μk mg cos θ

mg =  sinθ + μk cos θ)-----(3)

The next step is to calculate the work done by the engine in pulling the skiers, the incline top by applying the equation 3

W = Fx

= mg ( sinθ + μk cos θ)x

x = the displacement

we now substitute 1950 kg for m, 23° for θ, 0.10 for μk and 320m for x

so,

W = mg ( sinθ + μk cos θ)x

= (1950 kg) (9.81 m/s²) (sin 23° + (0.10) cos 23°) (320 m)

= 2.99 * 10 ^6 J

Then,

The time from minute to s is converted

t =(2.0min) ( 60sec/1.0min) = 120 sec

Now we calculate the power needed by the engine to pull the skiers at the incline top

Thus,

P = W/t

we substitute  2.955 * 10 ^6 J for W and  120 s for t

we have,

P = 2.955 * 10 ^ 6 J/ 120 s

= ( 2.4625 * 10 ^ 4 W) (1.0 hp/746 W)

= 33.0 hp

In conclusion the required power by the engine is 33.0 hp

To calculate the horsepower of the engine required for 30 skiers to be pulled up a hill, we need to consider the work done against friction and gravity. By plugging in the given values into the appropriate equations, we can find the required horsepower of the engine.

To calculate the horsepower of the engine required for 30 skiers to be pulled up a hill, we need to consider the work done against friction and gravity. First, we find the net force of the skier parallel to the incline by subtracting the force due to friction from the component of the skier's weight parallel to the incline. Then, we calculate the work done against friction and gravity using the formula W = Fd. Finally, we convert the work done to horsepower using the conversion factor 1 hp = 746 W.

The work done against friction and gravity is:

W = F_net * d

The power required is:

P = W / t

And finally, we convert the power to horsepower:

Power (hp) = P / 746

By plugging the given values into these equations and multiplying the final power by 30 (for 30 skiers), we can find the required horsepower of the engine.

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Answer:

The uncertainty the  in position is  [tex]\delta s = 0.4051 m[/tex]

Explanation:

From the question we are  told

   The planck's constant is [tex]h = 0.70 \ J \cdot s[/tex]

  The mass of the baseball is  [tex]m = 0.55kg[/tex]

   The velocity of the baseball [tex]v_b = 22 m/s[/tex]

    The uncertainty in [tex]\delta v = 0.5 m/s[/tex]

Generally the uncertainty of  momentum is  

        [tex]\delta p = m \delta v[/tex]

 substituting values

        [tex]\delta p = 0.275 \ kg m/s[/tex]

The uncertainty position is mathematically represented as

             [tex]\delta s = \frac{h}{2 \p \delta p }[/tex]

 substituting values  

           [tex]\delta s = \frac{0.70}{2 * 3.142 * 0.275 }[/tex]

           [tex]\delta s = 0.4051 m[/tex]

Answer:

a) 37.8 W

b) 2 Nm

Explanation:

180 g = 0.18 kg

We can also convert 180 revolution per minute to standard angular velocity unit knowing that each revolution is 2π and 1 minute equals to 60 seconds

180 rpm = 180*2π/60 = 18.85 rad/s

We can use the heat specific equation to find the rate of heat exchange of the steel drill and block:

[tex]\dot{E} = mc\Delta \dot{t} = 0.18*420*0.5 = 37.8 J/s[/tex]

Since the entire mechanical work is used up in producing heat, we can conclude that the rate of work is also 37.8 J/s, or 37.8 W

The torque T required to drill can be calculated using the work equation

[tex]E = T\theta[/tex]

[tex]\dot{E} = T\dot{\theta} = T\omega[/tex]

[tex]T = \frac{\dot{E}}{\omega} = \frac{37.8}{18.85} = 2 Nm[/tex]

Calculating the rate of working of a drill involves using the specific heat capacity, mass of the block, and rate of temperature increase to find the power. The torque can be derived from this power and the angular velocity of the drill.

The question involves calculating the rate of working of the drill in Watts and the torque required to drive the drill based on the information that all mechanical work is converted to heat that raises the temperature of the steel block and drill at 0.5 0C/s. Given the mass of the steel block and drill is 180 g and the specific heat capacity of steel is 420 J/(kgK), we can use the formula power (P) = mcigtriangleup T/igtriangleup t, where m is the mass, c is the specific heat capacity,  is the temperature change, and  is the change in time. To find the torque, we can use the power-torque relationship P = au imes w, where P is power in watts, au is the torque in Newton-meters, and w is the angular velocity in radians per second. As the drill makes 180 revolutions per minute (rpm), we'll convert that to radians per second to use in the power-torque equation.

Answer:

Kinetic energy depends on the mass of a body and the velocity it is travelling at

Explanation:

Referring to the equation of Kinetic Energy

EK = 0.5 m [tex]v^{2}[/tex]

We can see that Kinetic energy depends on the mass of a body and the velocity it is travelling at

Answer:

The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) that an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object.

Answer:density

Explanation:

At the bottom, deep bodies of water always measure [tex]4^{\circ}C[/tex] because at that temperature water has it highest density .

In water bodies like lake warm water rises up due to convection and at higher depths there is cold water, which is found to be at highest density of water.

When water molecules acquired heat energy  it become widely spread at the same volume and thus posses low density but at low temperature water molecule occupy less space therefore posses maximum density at [tex]4^{\circ}C[/tex]