A rock is dropped in a pond, causing circular ripples. The radius increased with a rate 1 foot per second. When the radius is 4 feet, the area is increasing by 8π square feet per second.1. True2. False

Answer:

Cart 1 = 4 m/s

Cart 2 = 4 m/s

Explanation:

See attachment

Answer: The total energy created by the Alpha decay.

Explanation: The sum total of the kinetic energy of the alpha particle and the new nucleus is the total energy created by the alpha decay.

Consider the decay of a radioactive nuclide by the spontaneous emission from its nuclei of alpha particles. An alpha particle which is composed of two protons and two neutrons and has a charge of +2. With an appreciable mass and its ejection from the nuclide creates a certain amount of recoil energy in the nucleus. The total energy (Ex) created by alpha decay is therefore the sum of the kinetic energy of the particle, the recoil energy given to the new nucleus, and the total energy of any emitted gamma rays.

The sum of the kinetic energies of an alpha particle and the new nucleus after alpha decay equals the initial energy (Q-value) of the reaction, most of which is carried by the alpha particle due to mass differences.

The sum of the kinetic energies of the alpha particle and the new nucleus after an alpha decay can be determined by considering the conservation of energy and momentum. The energy released during the decay, known as the Q-value, is primarily carried away by the alpha particle due to its relatively smaller mass compared to the daughter nucleus.

The energy of the alpha particle can be measured experimentally, which then allows us to determine the energy of the new nucleus. According to conservation of energy, the sum of the kinetic energies of the alpha particle and the new nucleus is equal to the Q-value of the reaction. If the Q-value (Qa) is known to be 4.3 MeV, and assuming the potential energy is zero in the final state, this energy will be distributed between the alpha particle and the new nucleus.

Using the example values provided, if the kinetic energy of the new nucleus (KEnucleus) is calculated to be 23.3 eV, then the remainder of the Q-value minus the kinetic energy of the new nucleus will represent the kinetic energy of the alpha particle. Since the alpha particle carries away most of the kinetic energy, the sum of the kinetic energies will be very close to the initial Q-value.

Explanation:

The number of subshell present are s, p, d, and f

The number of orbitals in each are as follows -

The number of orbitals can be calculated by the degeneracy,  2 l + 1 , where l denoted is angular momentum quantum number that determines the shape of an orbital. For s, p, d, and f the angular momentum quantum number is 0, 1, 2 3 respectively.

So, maximum number of f orbitals that are possible can be calculated as -

2 ×  l + 1  =  2  × 3  + 1  =  7

Answer:

The time taken by the personal computer to 'surf' the internet is 11.13 h.

Explanation:

The expression for the energy in terms of current and time is as follows;

E= Vit

Here, V is the potential, i is the current and t is the time.

According to question, in doing a load of clothes, a clothes drier uses 18 A of current at 240 V for 41 min.

Convert time from minute to second.

[tex]t=\frac{41}{60}s[/tex]

Calculate the energy used by the clothes drier.

Put V= 240 V, [tex]t=\frac{41}{60}s[/tex] and i=18 A in the expression for the energy.

[tex]E= (240)(18)\frac{41}{60}[/tex]

E'= 2937.6 W

Therefore, the energy of a clothes drier is E'= 2937.6 W.

It is given in the problem that a personal computer, in contrast, uses 2.2 A of current at 120 V. With the energy used by the clothes drier, this computer is used to surf the internet.

Calculate the time taken by the computer to 'surf' the internet.

E'=V'i't'

Here, V' is the voltage used by the a personal computer, i' is the current and t' is the time taken by the personal computer.

Put E'= 2937.6 W, V= 120 V and i'= 2.2 A.

2937.6 = (120)(2.2)t'

[tex]t'=\frac{2937.6}{264}[/tex]

t'= 11.13 h

Therefore, the time taken by the personal computer to 'surf' the internet is 11.13 h.

Final answer:

The most appropriate biomaterials for artificial tendons are polymers, due to their high toughness, elasticity, and ability to mimic natural extracellular matrices.

Explanation:

For fabricating an artificial tendon, which requires the capacity to sustain substantial deformation at low forces and quickly return to its original dimensions after stress release, polymers would be the most appropriate class of biomaterials. Biopolymers like collagen are noted for high toughness and elasticity, vital properties for mimicking the natural structure and function of tendons. Modern bioengineering strategies also involve creating synthetic extracellular matrices (ECM) which utilize peptides and polymer conjugates to mimic natural ECM, providing both structural support and facilitating tissue integration and regeneration.

Metals and ceramics, while being strong and rigid, do not offer the same flexibility and elastomeric properties required by tissues such as tendons that undergo repeated and significant strain. Semi-flexible polymers and polymer gels on the other hand, have been engineered to possess a balance of strength and flexibility, similar to that of natural tendon tissue.

Final answer:

To find the initial speed of the car, we use the work-energy principle and the equation μk × g × d = ½ × v². By substituting the given coefficient of kinetic friction (0.29) and skid mark distance (23.74 meters), we calculate the initial speed to be approximately 11.68 m/s.

Explanation:

The question involves calculating the initial speed of a car at the moment the driver applied the brakes, which resulted in skid marks on the road. The length of the skid marks and the coefficient of kinetic friction (μk) between the tires and the road are known.

To calculate the initial speed of the car, we use the work-energy principle, which states that the work done by the friction force is equal to the change in kinetic energy of the car:

Work done by friction = Change in kinetic energy

μk × m × g × d = ½ × m × v²

Since mass (m) cancels out and gravitational acceleration (g) is a constant (9.81 m/s²), we can simplify the equation to:

μk × g × d = ½ × v²

Now we can solve for the initial velocity (v):

v = √(2 × μk × g × d)

Plugging in the given values, μk = 0.29 and d = 23.74 meters, we have:

v = √(2 × 0.29 × 9.81 m/s² × 23.74 m)

v ≈ √(2 × 0.29 × 9.81 × 23.74)

v ≈ √(136.4)

v ≈ 11.68 m/s (approximately)

Thus, the initial speed of the car when the brakes were applied was approximately 11.68 meters per second.

Answer:

(a) 0.1134 L

(b) 2.009 L

(c) 0.07 cm from the top

Explanation:

The volume of the aluminum container and the turpentine is 2.000 L at  23 °C.

(a) When the entire system is heated to from 23 °C to 91 °C. The volume of the aluminum container is:

Vf = Vi*(1 + 3α*ΔT)

where:

Vi is the initial volume, Vf the final volume, α is the linear expansion coefficient and ΔT is the temperature change.

Vf = 2*[1 + 3*2.4 *10^-5*(91 - 23)] = 2.009 L

The volume of the turpentine is

Vf = Vi*(1 + β*ΔT)

where:

β is the  volume expansion coefficient

Vf = 2*[1 + 9.0*10^-4*(91 - 23)] = 2.1224 L

The overflow is:

2.1224  - 2.009 = 0.1134 L

(b) the volume of turpentine remaining in the cylinder at 91 °C is the same volume of the hollow aluminum cylinder, that is, 2.009 L

(c) Cooling the system back to 23 °C means the aluminum container is back to 2.000 L. The  volume of turpentine is:

Vf = 2.1224*[1 + 9.0*10^-4*(23-91)] = 1.9925 L

The following proportion must be  satisfied:

Volume of turpentine / Volume of container = deep turpentine / deep of container

1.9925 / 2.000 = deep turpentine/19

deep turpentine = (1.9925 / 2.000)*19 = 18.93 cm

This is 19 - 18.93 = 0.07 cm from the top

Answer:

The answer to the question is

A 100 lb person would weigh 300.33 lbf at the upper atmosphere of Jupiter

Explanation:

To solve the question we note that

Mass of object = 100 lb =‪ 45.35924‬ kg

Mass of Jupiter = 300×Mass of Earth = 300×5.972 × 10²⁴ kg =1.7916×10²⁷ kg

Radius of Jupiter = 10× Radius of Earth = 10×6,371 km = 63710 km

Gravitational constant, G = 6.67408 × 10⁻¹¹ m³ kg-1 s-2

Gravitational force is given by [tex]F_G= \frac{Gm_1m_2}{r^2}[/tex]

Plugging in the values we get

[tex]F_G[/tex] = [tex]\frac{6.67408*10^{-11}*45.35924*1.7916*10^{27}}{63710^2}[/tex] = 1335.93 N

Converting into lbf gives 1335.93 N *0.2248 lbf/N = 300.33 lbf

On Jupiter, you would weigh 2.5 times more than on Earth due to its stronger gravity. Therefore, if you weighed 100 lb on Earth, you would weigh approximately 250 lb in the upper atmosphere of Jupiter though your weight may slightly vary with altitude. It is important to note that while weight changes with location, mass remains constant.

If you weighed 100 lb on Earth, it is interesting to calculate what you would weigh in the upper atmosphere of Jupiter. Since gravitational force is what we perceive as weight, and gravity varies with the mass of the planet and the distance from its center, we can determine the comparative weight. Jupiter has a mass approximately 318 times that of Earth and a radius about 11 times greater. However, for simplicity, the student question references Jupiter's mass as 300 times that of Earth and a radius 10 times that of Earth. This would normally impact the surface gravity calculation significantly.

Now, since it's stated that on Jupiter you would weigh 2.5 times more than on Earth, if you weigh 100 lb on Earth, you would weigh 250 lb on Jupiter. But note that in the upper atmosphere, your weight might be slightly less than this because you would not be at Jupiter's surface, and gravity decreases with altitude.

Lastly, remember the important conceptual distinction: While your weight changes depending on the gravity of the celestial body you are on, your mass remains constant. Your mass represents the amount of matter within you and does not change with location.

Answer:

a) The force between the two wires is attractive.

b) (F/L) = (μ₀I²)/(2πd)

Explanation:

a) According to Ampere's law, current in the same direction attract, while current in opposite directions repel. So, for this case of two wires carrying curremt in the same direction, the force between the wires is attractive.

b) The force of attraction between two current carrying wires carrying currents of magnitude I₁ and I₂ respectively, at some distance d, apart is given as

F = (μ₀ I₁ I₂ L)/(2πd)

(F/L) = (μ₀ I₁ I₂)/(2πd)

I₁ = I₂ = I

(F/L) = (μ₀I²)/(2πd)

Hope this Helps!!

(a) The force between the two wires is attractive.

(b) The force per unit length between the two wires is (μ₀I²)/(2πd)

(a) It is given that two wires carry current in the same direction, so the force between the wires will be attractive.

(b) The magnetic force between the two wires carrying currents I₁ and I₂ separated by a distance d, is given by:

dF = I₁dl × B₂ force on wire with current I₁ due to magnetic field of the wire with current I₂

dF = I₁dl ×  (μ₀I₂)/(2πd)

F = (μ₀ I₁ I₂ L)/(2πd)

(F/L) = (μ₀ I₁ I₂)/(2πd)

since I₁ = I₂ = I

(F/L) = (μ₀I²)/(2πd)

Learn more about magnetic force:

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Explanation:

As we know that

time = distance/speed

The time used for firs half of the trip was

(1 mi)(12 mi/hour) = 1/12 hours = 5 minutes

The last half of the trip will took 10 minutes, 1/6 hour.

Speed = distance/ time

(1 mil) = (1/6h) = 6 mil/h

so the speed for last half of the trip was = 6mph

the average speed was

(2mil)(1/4 hour) = 8 mil/hour

So the ling's average speed was 8mph.

Answer 62.78mph

Explanation:

Answer:

The returning speed = 70 miles per hour (mph)

Explanation:

Explanation:

∴  The Correct option is (b)

Answer:

684J

Explanation:

So basically the formula for gravitational potential energy is Mass X Gravity X height. That is G.p.e = mgh

We don't have the mass but since we have the height, we multiply directly with the height since the quantity of weight is already given.

so G.p.e = 360 X 1.9 = 684J

Note that; The answer is in joules because g.p.e is work done.

Hope that was helpful!!

Answer:

Explanation:

The package had the same velocity as the plane when it was dropped. Newton's 1st Law says that "an object in motion tends to stay in motion, at the same velocity, in a straight line unless acted on by an outside force".

There only outside force acting on the package was its weight -- that force is straight down. The horizontal velocity that the plane gave the package continued (as Newton said it would), so as it fell, horizontally it kept pace with the plane.

Answer:

The minimum friction coefficient required is 0.3

(friction coefficients have no units)

Explanation:

To find a force we need to know something about a mass, and we haven't been told the mass of the car. Let's just call it 'm' and leave it at that for the moment, because it will cancel out in the end.

The centripetal force is given by F = ma = mv2/r

We have values for the velocity and the radius, so:

Fcent=m×6 × 6/13.5 = 2. 667m N

The frictional force must be equal to or greater than this force in order for the car to successfully make it around the curve without sliding out.

The frictional force will be given by:

Ffrict = μFnorm

Where Fnorm is the normal force, equal to mg.

We can equate these two forces, the frictional force and the centripetal force:

Fcent = Ffrict

2.667m=μmg

We can cancel out a factor of m in both sides and rearrange to make μ the subject:

μ = 2.667g

Substituting in the value g=9.8 ms−2,

μ = 2.667/9.8 = 0.27

Approximately = 0.3

Explanation:

Below is an attachment containing the solution.

Answer:

Explanation:

Given that,

The initial point A=(0,-2)

And the final point B=(3,6)

O is a reference point (0,0)

OA=r1=(0,-2)

OB=r2=(3,6)

Then we want to find their combination vector i.e AB.

AB is given as position vector B - position vector A

So, AB=OB-OA

AB=r2-r1

AB=(3,6)-(0,-2). Note -×-=+

Then, AB=(3-0,6--2)

AB=(3,6+2)

AB=(3,8)

In vector form

AB=3•i +8•j

Answer:

Torque = 882Nm

Explanation:

Torque = Mg×distance

But plank's is pivoted ,therefore distance=3/2=1.5m

Mass of Nancy=60jg

Acceleration due to gravity, g=9.8m/s^2

Torque= 60×9.8×1.5

Torque= 882Nm

Answer:

Conservation

Explanation:

She has observation conservation because If the temperature of the liquids stays constant and the container is insulated and not heat or cool the liquid much would not change the density of the liquid very much so that it's original volume could remain constant.

The interesting thing is not that the child assumes the taller glass holds more liquid but that they fail to understand conservation: the fact that the water from one glass is going to be the same amount after being poured into any other container. It's as if they did not realize the water came from the same glass.

Answer:

4,5

Explanation:

The resulting swing converts potential energy to kinetic energy and kinetic energy to potential energy when the swinging stops. This is line with the law of conservation of mechanical energy which deals with inter conversion of energy forms and energy not being able to get lost.

The conservation of momentum is most suited to the collision. This law states that when a collision occurs the initial momentum before and after the collision is the same(without any external force).

Answer:

The magnitude of the other force is 43.75 N.

Explanation:

Given that,

Mass of the object, m = 8.5 kg

Force 1, [tex]F_1=14\ N[/tex]

Acceleration of the object, [tex]a=3.5\ m/s^2[/tex]

To find,

The greatest possible magnitude of the other force.

Solution,

Let [tex]F_2[/tex] is the magnitude of other force that is acting on the object. For the greatest force, the two forces must be act in opposite direction such that :

[tex]F_2-F_1=ma[/tex]

[tex]F_2=ma+F_1[/tex]

[tex]F_2=14+8.5\times 3.5[/tex]

[tex]F_2=43.75\ N[/tex]

So, the magnitude of the other force is 43.75 N.

Answer:

The angular frequency of oscillation w = 21

Explanation:

To solve the question, we note that x(t) is the point in the motion of the object. Therefore to find the angular frequency of oscillation, we find the relationship between the angular velocity and time

The angular frequency, ω is a scalar quantity used to depict the rate of rotation per unit time

When there is a function in simple harmonic motion (SHM) with the following equation then ω is the angular frequency

x(t) = A·cos (2πft) = A·cos(ωt)  which is similar to 42.5*cos(21t)

then 21 = angular frequency

The fundamental frequency of a piano wire can be calculated using the formula f = sqrt(T/(4L^2*m)). Plugging in the given values, the fundamental frequency of the piano wire is 116.6 Hz.

The fundamental frequency of a piano wire can be calculated using the formula:

f = √(T/(4L2m))

Where f is the fundamental frequency, T is the tension, L is the length, and m is the mass per unit length.

Plug in the given values:

T = 2030 N

L = 1.3 m

m = 0.003 kg/m

f = √(2030/(4*1.32*0.003))

Solving this equation gives the fundamental frequency f = 116.6 Hz.

To find out after how many years the activity level of a sample with a half-life of 10 years decreases from 2 curies to 0.25 curie, we calculate that it takes 30 years.

The question asks, "A sample of radioactive waste has a half-life of 10 years and an activity level of 2 curies. After how many years will the activity level of this sample be 0.25 curie?" To solve this problem, we follow the basic principle of half-lives, which states that the amount of a radioactive substance decreases to half its initial amount after one half-life period.

In this example, the activity decreases from 2 curies to 0.25 curies. To go from 2 curies to 1 curie, it takes one half-life (10 years). To go from 1 curie to 0.5 curies takes another half-life (adding up to 20 years in total). Finally, to decrease from 0.5 curies to 0.25 curies requires a third half-life period, adding another 10 years, for a total of 30 years.

Therefore, it will take 30 years for the activity level of the sample to reduce to 0.25 curie.

Answer:

The ball travels at a speed of 11.662 m/s, making a 30.96° angle from the horizontal ground.

Explanation:

If the ball is thrown horizontally with a speed of 10.0 m/s and the hot air balloon is rising at a speed of 6.0 m/s then we can make the following deductions:

1. The ball is ALSO rising at a speed of 6.0 m/s

2. The vertical speed of the ball is 6.0 m/s

Thus the ball travels with 10 m/s horizontal and 6 m/s vertical speed relative to the ground.

To find the total speed and direction:

Total speed = [tex]\sqrt{(V_X)^2+(V_Y)^2}[/tex]

Total speed = [tex]\sqrt{10^2 + 6^2}[/tex]

Total speed = 11.662 m/s

Angle from the horizontal:

Tan( Angle ) = Perpendicular / Base

Tan (Angle) = Vertical Speed / Horizontal Speed

Tan (Angle) = 6/10

Angle = 30.96°

The initial velocity of the ball thrown horizontally from the basket of a hot-air balloon relative to a person on the ground is 10.0 m/s in the horizontal direction.

The initial velocity of the ball relative to a person standing on the ground can be found by adding the velocities of the ball and the hot-air balloon together. Since the ball is being thrown horizontally outward, its initial velocity in the horizontal direction will be 10.0 m/s. The vertical velocity of the balloon is 6.0 m/s, but since the ball is not thrown vertically, this velocity does not affect its horizontal velocity.

Therefore, the initial velocity (magnitude and direction) of the ball relative to a person on the ground will be the same as its initial velocity when thrown from the basket, which is 10.0 m/s horizontally.

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Answer:

The correct answer is Can be pronounced in many ways.

Explanation:

Typically a consultant is hired to solve a major business problem, carry out a major change and increase sales. The consultant, with experience of other companies, with methodology resources listens to the client's need, - the current situation and design an effective plan to implement, thus creating a positive impact on the business in a short time.

Answer:

C

Explanation:

- Let acceleration due to gravity @ massive planet be a = 30 m/s^2

- Let acceleration due to gravity @ earth be g = 30 m/s^2

Solution:

- The average time taken for the ball to cover a distance h from chin to ground with acceleration a on massive planet is:

                                 t = v / a

                                 t = v / 30

- The average time taken for the ball to cover a distance h from chin to ground with acceleration g on earth is:

                                 t = v / g

                                 t = v / 9.81

- Hence, we can see the average time taken by the ball on massive planet is less than that on earth to reach back to its initial position. Hence, option C

Answer:

a) 2.4×10^4N/C

b) 2.9 ×10^3V

Explanation:

Correct ststement: An electric force of 3.9×10^-15N acts on the electron if it is placed anywhere between the two plates.

a) The electric field magnitude is given by E= F/e

Where F = electric force

e= elementary charge carried by a single proton e= 1.6×10^-19C

E= (3.9×10^-15)/(1.6×10^-19)

E= 2.4×10^4NC

b) Ptential difference is given by:

Change in V= E×change in distance

Potential difference= (2.4×10^4)× (0.12)

Potential difgerence= 2.9×10^3V

Answer:

0.08kg

Explanation:

K.E = 1/2 mv^2

v = 970m/s

K.E = 3.9x 10^3J= 3900J

K.E = 1/2 mv^2

3900 = 1/2 m x 970x 970

3900 = 1/2 ×940900m

3900 = 470450m

m = 3900/470450 = 0.00828993516 = 0.008kg

I think the Answer is 0.08kg

Answer with Explanation:

We are given that

Diameter of coil=d=0.115mm

Radius, r=[tex]\frac{d}{2}=\frac{0.115}{2}=0.0575mm=0.0575\times 10^{-3} m[/tex]

Using [tex]1mm=10^{-3} m[/tex]

Electric field=E=0.235V/m

T=55 degree C

[tex]T_0=20^{\circ} C[/tex]

[tex]\rho_0=2.82\times 10^{-8}\Omega m[/tex]

[tex]\alpha=3.9\times 10^{-3}/C[/tex]

(a).We know that

[tex]\rho=\rho_0(1+\alpha(T-T_0))[/tex]

Substitute the values

[tex]\rho=2.82\times 10^{-8}(1+3.9\times 10^{-3}(55-20))[/tex]

[tex]\rho=3.2\times 10^{-8}\Omega m[/tex]

(b).Current density,[tex]J=\frac{E}{\rho}[/tex]

Using the formula

[tex]J=\frac{0.235}{3.2\times 10^{-8}}=7.3\times 10^6A/m^2[/tex]

c.Total current,I=JA

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

[tex]\pi=3.14[/tex]

Using the formula

[tex]I=7.3\times 10^6\times 3.14\times (0.0575\times 10^{-3})^2[/tex]

I=0.076A

d.Length of wire=l=2m

[tex]V=El[/tex]

Substitute the values

[tex]V=0.235\times 2=0.47 V[/tex]

Radiative energy

Explanation:

The light from polaris travels through space in the form of energy is called  

Radiative energy.

This energy is transferred by means of electromagnetic radiation like X-rays, gamma rays, light, heat radiation and so on. It can travel through space in the form of radiation. For instance, we get the heat through the sun, that is located far away from the Earth by means of radiation. Through the electromagnetic waves,  sun's heat is transmitted and not  through any kind of solid medium, but by means of vacuum.