A device is rated at 1.3kW when connected to a 120 V source. The equivalent resistance of this device in ohm is:

a- 18.3
b- 12.0
c- 11.1
d- 14.4

(a) Velocity with which the mug leaves the counter is approximately 5.02 m/s.

(b) The direction of velocity of mug just before it hits the floor is downwards, since mug is falling under influence of gravity.

Velocity is a quantity that designates how fast and also in what direction a certain point is moving.

(a) As we know, PE = m g h

\(\mathrm{PE = mgh }\)

\(\mathrm{= (m)(9.81 m/s^2)(1.36 m) }\)

= 13.4mJ

\(\mathrm{KE =\frac{1}{2} mv^2}\)

PE = KE

\(\mathrm{mgh = \frac{1}{2}mv^2}\)

\(\mathrm{v = \sqrt{2gh}}\)

\(\mathrm{v = \sqrt{2 \times 9.81 \times 1.36 m}}\)

v = 5.02 m/s

Therefore, the velocity with which the mug leaves the counter is approximately 5.02 m/s.

(b) The direction of the velocity of mug just before it hits the floor is downwards, since mug is falling under the influence of gravity. Velocity vector has a vertical component that points downwards and horizontal component that is parallel to counter.

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Answer:

Option B period

Explanation:

Time period is the time taken to complete a cycle of any function .

The net force on particle q₂, located between particles q₁ and q₃, is approximately 189000 N. The force exerted by particle q₁ on q₂ is positive and equals 252000 N, while the force exerted by particle q₃ on q₂ is negative and equals -63000 N.

To find the net force on particle q₂, we need to calculate the individual forces exerted on q₂ by particles q₁ and q₃ and then determine their sum.

The force between two charged particles can be calculated using Coulomb's law:

F = k * |q₁ * q₂| / r²

Where F is the force between the particles, k is the electrostatic constant (k ≈ 9.0 x \(10^9\) Nm²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them.

First, let's calculate the force exerted on q₂ by q₁:

F₁₂ = k * |q₁ * q₂| / r₁₂²

F₁₂ = (9.0 x \(10^9\) Nm²/C²) * |(8.0 μC) * (3.5 μC)| / (0.10 m)²

F₁₂ ≈ 252000 N

The force is positive because q₁ and q₂ have opposite charges.

Next, let's calculate the force exerted on q₂ by q₃:

F₂₃ = k * |q₂ * q₃| / r₂₃²

F₂₃ = (9.0 x \(10^9\)Nm²/C²) * |(3.5 μC) * (-2.5 μC)| / (0.15 m)²

F₂₃ ≈ -63000 N

The force is negative because q₂ and q₃ have the same charge.

Finally, we can find the net force on q₂ by summing the individual forces:

Net force = F₁₂ + F₂₃

Net force = 252000 N + (-63000 N)

Net force ≈ 189000 N

The net force on particle q₂ is approximately 189000 N.

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Answer:

Work done, W = 2 J

Explanation:

Given that,

Weight of a book, W = F = 1 N

It is lifted to a height of 2 m

We need to find the work done. It can be calculated using the formula as follows :

W = F d

Put all the values,

W = 1 N × 2 m

W = 2 J

So, 2J of work was done.

Answer:

It should be C

Explanation:

It depends on the mass of each ball

Remember the formula for momentum, mass X velocity

Momentum depends on the mass of the object

The momentum of the billiard balls after the collision is 3 Kgm/s.

Given the following data:

To find the momentum of the balls after the collision:

Momentum is simply a multiplication (product) of the mass of an object with its velocity.  Also, momentum is a vector quantity because it has both magnitude and direction.

Mathematically, momentum is given by the formula;

\(Momentum = Mass\) × \(Velocity\)

\(Total \; momentum = Momentum \; B + Momentum \;of \;the \;other\; balls.\)

Since the other billiard balls were at rest (not experience any motion), there velocities would be zero (0) m/s.

Substituting the values, we have:

\(Total \; Momentum = 3 + 0\)

Total momentum = 3 Kgm/s.

Therefore, the momentum of the billiard balls after the collision is 3 Kgm/s.

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Answer:

49 N (d)

Explanation:

w= mg = 5 kg * 9.8 m/s^2 = 49 N

The weight of a 5.0-kilogram object at the surface of Earth is 49 N. Hence, option (C) is correct.

Mass is a fundamental quantity in physics and the most fundamental attribute of matter. Mass can be defined as the amount of matter contained in a body. Kilogram is the SI unit of mass (kg).

A body's mass does not alter at any time. Only in severe instances where a massive amount of energy is provided or removed from the body.

The force of gravity acting on a body is measured by weight. The weight formula is as follows: w = mg. Because weight is a force, it has the same SI unit as force; the SI unit of weight is Newton (N).

The weight of the  object is = 5.0 × 9.8 N

= 49.0 N.

Hence, option (B) is correct.

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Answer:

False

Explanation:

A contact force is any force that requires contact to occur. Contact forces are ubiquitous and are responsible for most visible interactions between macroscopic collections of matter. Pushing a car up a hill or kicking a ball across a room are some of the everyday examples where contact forces are at work. 

Answer:

false

Explanation:

Answer:

A

Explanation: took the test

Answer:

visualizing

Explanation:

You are imagining yourself doing it, using the image in your head and the steps you read to figure out what to do first, next, last.

A miniature quadcopter is located at xi = −1.75 m and yi = 2.70 m at t = 0, so the x-coordinate of the quadcopter's position at t = 2.10 s is -0.185 m, and the y-coordinate is -3.175 m.

The equation that is used here is the kinematic equations to find the position of the quadcopter at time t,

x = xi + vav, x × t

y = yi + vav, y × t

Substituting the given values, one can get:

x = -1.75 m + 1.70 m/s × 2.10 s = -0.185 m

y = 2.70 m - 2.50 m/s × 2.10 s = -3.175 m

Hence, the x-coordinate of the quadcopter's position at t = 2.10 s is -0.185 m, and the y-coordinate is -3.175 m.

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Changing the green sum of forces arrow involves manipulating applied forces, frictional forces, and normal forces, allowing for adjustments in magnitude and direction through various means.

To change the green sum of forces arrow, you can employ the following three strategies:

Adjusting Applied Forces: By modifying the magnitude or direction of the applied forces, you can alter the green sum of forces arrow. If the applied forces are increased or directed in a different way, the green sum of forces arrow will change accordingly. For instance, increasing the magnitude of a pushing force will result in a larger green sum of forces arrow in that direction.

Modifying Frictional Forces: Frictional forces play a crucial role in determining the green sum of forces. By changing the coefficient of friction or applying lubricants, you can affect the magnitude of frictional forces acting on an object. Reducing friction will decrease the green sum of forces arrow, while increasing friction will have the opposite effect.

Varying Normal Forces: The green sum of forces arrow can be influenced by adjusting the normal forces acting on an object. Normal forces are perpendicular to the surface and counteract the weight of an object. By changing the angle or surface on which an object rests, you can modify the normal forces. This alteration will subsequently impact the green sum of forces arrow.

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Answer:

6bar

Explanation:

According to pressure law;

P1/T1 = P2/T2

Given the following;

P1 = 1bar

T1  = 20oC

P2 = ?

T2 = 120oC

Substitute

1/20 = P2/120

20P2 = 120

P2 = 120/20

P2 = 6bar

Hence the new pressure will be 6bar

Answer:

B,C,D

Explanation:

Ap3X

The ions are;

S^2- Gained 2 electrons

Li^+ - Lost one electron

Al^3+ - Lost 3 electrons

Cl^- gained one electron

Sr^2+ Lost two electrons

P^3- gained 3 electrons

As an atom or molecule acquires or loses one or more electrons, ions are created. Protons and neutrons make up the positively charged nucleus of an atom, which is encircled by negatively charged electrons. An atom typically has a neutral charge because the amount of electrons and protons in it equals one.

The balance between the negatively charged electrons and positively charged protons is upset when an atom receives or loses an electron, creating an ion with a positive or negative charge.

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Answer:

α = θ^(-1/2)

Explanation:

The angular acceleration α is the derivative of angular velocity ω with respect to time, and it can be found by taking the derivative of ω with respect to θ.

Given: ω = 2√θ

To find α, we differentiate ω with respect to θ:

α = dω/dθ

Using the power rule of differentiation, we can differentiate 2√θ with respect to θ:

α = d/dθ (2√θ)

Using the chain rule, we can differentiate 2√θ with respect to θ:

α = 2 * (1/2) * θ^(-1/2) * dθ/dθ

Simplifying, we get:

α = θ^(-1/2)

So, the angular acceleration α as a function of θ is given by α = θ^(-1/2).

Answer:

The equivalent resistance is 2 ohms.

Explanation:

let the first resistance = R₁ = 10 ohm

let the second resistance = R₂ = 10 ohm

let the third resistance = R₃ = 10 ohm

let the fourth resistance = R₄ = 10 ohm

let the fifth resistance = R₃ = 10 ohm

The equivalent resistance is calculated as;

\(\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} + \frac{1}{R_5} \\\\\frac{1}{R_T} = \frac{(R_2R_3R_4R_5)+(R_1R_3R_4R_5)+(R_1R_2R_4R_5) +(R_1R_2R_3R_5)+(R_1R_2R_3R_4)}{R_1R_2R_3R_4R_5} \\\\R_T = \frac{R_1R_2R_3R_4R_5}{(R_2R_3R_4R_5)+(R_1R_3R_4R_5)+(R_1R_2R_4R_5) +(R_1R_2R_3R_5)+(R_1R_2R_3R_4)} \\\\R_T = \frac{(10^5)}{(10^4)+(10^4)+(10^4)+(10^4)+(10^4)} \\\\R_T = \frac{10^5}{5(10^4)} \\\\R_T = \frac{10}{5} \\\\R_T = 2 \ ohms\)

Therefore, the equivalent resistance is 2 ohms.

For two runners  running in a 500 meter dash and runner, the speeds of both runners  is mathematically given as

v1=25m/s

v2=20m/s

and the first runner is faster

Generally, the equation for the speed  is mathematically given as

v=d/t

Therefore, for first runner

v=500/20

v1=25m/s

For 2nd runner

v=500/25

v2=20m/s

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\(\bold{\huge{\underline{ Solution }}}\)

Here,

Here, we have

We have to find the time of flight

We know that,

Time of flight

\(\sf{ = }{\sf{\dfrac{ 2uSin{\theta}}{g}}}\)

Subsitute the required values,

\(\sf{ = }{\sf{\dfrac{ 2{\times}100{\times}Sin30{\degree}}{9.8}}}\)

\(\sf{ = }{\sf{\dfrac{ 200{\times}{\frac{1}{2}}}{9.8}}}\)

\(\sf{ = }{\sf{\dfrac{ 100}{9.8}}}\)

\(\bold{ = 10.20 \: s }\)

Hence, The time of flight is 10.20 sec .

Here, We have

We have to find the maximum height attained by the body

We know that,

Maximum height

\(\sf{ = }{\sf{\dfrac{ u^{2}Sin^{2}{\theta}}{2g}}}\)

Subsitute the required values,

\(\sf{ = }{\sf{\dfrac{ (100)^{2}{\times}Sin^{2}30{\degree}}{2{\times} 9.8}}}\)

\(\sf{ = }{\sf{\dfrac{ 10000{\times}{\frac{1}{2}}{\times}{\frac{1}{2}}}{19.6}}}\)

\(\sf{ = }{\sf{\dfrac{ 5000{\times}{\frac{1}{2}}}{19.6}}}\)

\(\sf{ = }{\sf{\dfrac{ 2500}{19.6}}}\)

\(\sf{ = 127.5 \: m}\)

Hence, The maximum height attained by the body is 127.5 .

Here, we have

We have to find the horizontal range

We know that,

Horizontal range

\(\sf{ = }{\sf{\dfrac{ u^{2}Sin2{\theta}}{g}}}\)

Subsitute the required values,

\(\sf{ = }{\sf{\dfrac{ (100)^{2}{\times}Sin2{\times}30{\degree}}{9.8}}}\)

\(\sf{ = }{\sf{\dfrac{ 10000{\times}Sin{\times}60{\degree}}{9.8}}}\)

\(\sf{ = }{\sf{\dfrac{ 10000{\times}{\frac{\sqrt{3}}{2}}}{9.8}}}\)

\(\sf{ = }{\sf{\dfrac{ 5000{\times}\sqrt{3}}{9.8}}}\)

\(\sf{ = }{\sf{\dfrac{ 5000{\times}1.732}{9.8}}}\)

\(\sf{ = }{\sf{\dfrac{ 8660}{9.8}}}\)

\(\sf{ = 883.67 \: or 883.7 m}\)

Hence, The range of the body is 883.67 or 883.7 m.

Answer:

(a) 10.20 s (nearest hundredth)

(b) 127.55 m (nearest hundredth)

(c) 883.70 m (nearest hundredth)

Explanation:

Part (a)

At the end of the projectile's flight, its vertical displacement will be zero.

Resolving vertically, taking up as positive:

\(s=0\quad u=100 \sin30^{\circ} \quad v=v, \quad a=-9.8, \quad t=t\)

\(\begin{aligned}\textsf{Using }\:s & =ut+\dfrac12at^2:\\ 0 & =100 \sin 30^{\circ}t+\dfrac12(-9.8)t^2\\ 0 & = 50t-4.9t^2\\ 4.9t^2 & = 50t\\ 4.9t & = 50\\ t & = \dfrac{50}{4.9}\\ t & = 10.20\:\sf s\:(nearest\:hundredth)\end{aligned}\)

Part (b)

At the maximum height, vertical velocity will be zero.

Resolving vertically, taking up as positive:

\(s=0\quad u=100 \sin30^{\circ} \quad v=0, \quad a=-9.8, \quad t=t\)

\(\begin{aligned}\textsf{Using }\:v^2 & = u^2+2as :\\ 0^2 & = (100 \sin 30^{\circ})^2+2(-9.8)s\\ 0 & = 2500-19.6s\\ 19.6s & = 2500\\ s & = \dfrac{2500}{19.6}\\ s & = 127.55\: \sf m\:(nearest\:hundredth) \end{aligned}\)

Part (c)

The horizontal velocity of a projectile is always constant, so u = v.

The horizontal component of acceleration is zero.

Resolving horizontally, taking right as positive (and using the value for t we found in part a):

\(s=s\quad u=100 \cos30^{\circ} \quad v=100 \cos30^{\circ} , \quad a=0, \quad t=\dfrac{50}{4.9}\)

\(\begin{aligned}\textsf{Using }\:s & =ut+\dfrac12at^2 : \\ s & =(100 \cos 30^{\circ})\left(\dfrac{50}{4.9}\right)+\dfrac12(0)\left(\dfrac{50}{4.9}\right)^2\\ s & =50\sqrt{3}\left(\dfrac{50}{4.9}\right)+0\\ s & =883.70\: \sf m\:(nearest\:hundredth)\end{aligned}\)

One important takeaway from Dan Ariely's talk is that our decision-making processes are frequently irrational and influenced by variables outside of our conscious consciousness.

Social norms, emotional states, and cognitive biases, for example, can all influence our choices. As a result, one method to put this knowledge to use is to become more aware of these influences and actively consider them when making decisions.

This may entail devoting more time to decision-making, seeking out diverse views, and being aware of our own biases and tendencies.

Another key takeaway from the talk is the significance of considering the long-term consequences of our choices rather than focusing solely on short-term gains or losses.

This may entail weighing the risks and benefits of various options, as well as considering the effect of decisions on others as well as ourselves.

Overall, the information presented by Dan Ariely can be used to make more thoughtful and informed decisions by becoming more aware of our own biases and tendencies, considering diverse viewpoints, and thinking critically about the potential repercussions of our decisions.

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Nuclear power is a clean energy source that emits no emissions. Fission, which is the splitting of uranium atoms to release energy, is how it generates energy.

The operational risks and safety concerns that go along with them, risks associated with uranium mining, financial and regulatory risks, unresolved waste management issues, concerns about nuclear weapons proliferation, and unfavorable public perception are all obstacles to and risks associated with an increase in the use of nuclear energy.

The generation of radioactive wastes such spent (used) reactor fuel, uranium mill tailings, and other radioactive wastes is a significant environmental hazard associated with nuclear power.

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Answer:

A capacitor is formed from two square plates of edge length a and separation d, with d <

Explanation:

A capacitor is formed from two square plates of edge length a and separation d, with d <

The magnitude of the displacement is 1,097.7 mi, and the angle is 89.9°

To find the displacement from Dallas to Chicago, we can break down the vectors representing the distances and directions into their x and y components. Since the Earth is modeled as flat, we can use basic trigonometry to calculate the components.

Let's start by considering the vector from Dallas to Atlanta. The magnitude of this vector is given as 730 miles, and the direction is 5.00° north of east. To calculate the x and y components, we can use the following equations:

Substituting the values:

x = 730 * cos(5.00°)

y = 730 * sin(5.00°)

Similarly, for the vector from Atlanta to Chicago, with a magnitude of 560 miles and a direction 21.0° west of north:

x = magnitude_AC * sin(angle_AC)

y = magnitude_AC * cos(angle_AC)

Substituting the values:

x = 560 * sin(21.0°)

y = 560 * cos(21.0°)

To find the displacement from Dallas to Chicago, we can sum the x and y components:

Now, we can calculate the magnitude and direction of the displacement using these x and y components:

magnitude_displacement = √(x_displacement² + y_displacement²)

angle_displacement = atan(y_displacement / x_displacement)

Finally, we can substitute the calculated values and solve for the magnitude and direction:

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The hiker travelled 4.02 km North/South and 4.74 km East/West during her hike.

This question involves vector addition, the resolution of vectors, the use of bearings, and trigonometry in the calculation of the hiker's movement.

This may appear to be a difficult problem, but with some visual aid and the proper use of mathematical formulas, the issue can be addressed correctly.

Resolution of VectorThe resolution of a vector is the process of dividing it into two or more components.

The angle between the resultant and the given vector is equal to the inverse tangent of the two rectangular components.

Angles will always be expressed in degrees in the solution.

The sine, cosine, and tangent functions in trigonometry are denoted by sin, cos, and tan.

The tangent function can be calculated using the sine and cosine functions as tan x = sin x/cos x. Also, in right-angled triangles, Pythagoras’ theorem is used to find the hypotenuse or one of the legs.

Distance Travelled North/SouthThe hiker traveled North for the first part of the hike and South for the second.

The angles that the hiker traveled in the first part and second parts are 53 degrees and 17 degrees, respectively.

The angle between the two is (180 - 53 - 17) = 110 degrees.

The angle between the resultant and the Northern direction is 110 - 53 = 57 degrees.

Using sine and cosine, we can calculate the north/south distance traveled to be 5 sin 57 = 4.02 km, and the east/west distance to be 5 cos 57 = 2.93 km.

Distance Travelled East/WestThe hiker walked East for the second part of the hike.

To calculate the distance travelled East/West, we must first calculate the component of the first part that was East/West.

The angle between the vector and the Eastern direction is 90 - 53 = 37 degrees.

Using sine and cosine, we can calculate that the distance travelled East/West for the first part of the hike is 5 cos 37 = 3.88 km.

To determine the net distance travelled East/West, we must combine this component with the distance travelled East/West in the second part of the hike.

The angle between the second vector and the Eastern direction is 17 degrees.

Using sine and cosine, we can calculate the distance traveled East/West to be 3 sin 17 = 0.86 km.

The net distance traveled East/West is 3.88 + 0.86 = 4.74 km.

Therefore, the hiker travelled 4.02 km North/South and 4.74 km East/West during her hike.

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Never put a weight directly on the balance pan. Always cover it with a piece of weight paper. Never add chemicals to a container or piece of weighing paper while it is on the scale. Never weigh something that is hot or cold.

The amount of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, a chair, your bed, a football, a glass, and even air. Whether anything is light or heavy depends on its mass.

Mass is independent of place. Using a formula, can one estimate an object's mass based on its weight.  corresponds to mass dividing weight by gravitational acceleration Determine the weight in pounds that is equivalent in Newtons. The formula used to determine mass based on weight expresses mass in Newtons.

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Answer:

4.47

Explanation:

Given data

vector 1 = 2m/s

vector 2= 4 m/s

The expression for the magnitude of two vectors is

|a| = √v1^2+ v2^2

substitute

|a| = √2^2+ 4^2

|a| = √4+ 16

|a| = √20

|a| = 4.47

Hence the magnitude of the two vectors is 4.47

Answer:

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Using the formula F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them, we can calculate the gravitational force between Jupiter and the sun.

Plugging in the values, we get:

F = (6.674 x 10^-11 N * (m^2 / kg^2)) * ((1.9 x 10^27 kg) * (2 x 10^30 kg)) / (78 x 10^6 m)^2

Simplifying this, we get:

F = 1.98 x 10^27 N

Therefore, the gravitational force between Jupiter and the sun is approximately 1.98 x 10^27 Newtons.

The gravitational force between Jupiter and the sun, calculated using Newton's law of gravitation with their masses and distance, is \(1.95 * 10^{22} N.\)

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The new gravitational force between the two planets, when they are moved to two million miles apart, is 250,000 N

The gravitational force between two objects can be calculated using Newton's Law of Universal Gravitation, which states that the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Given:

Initial distance between the planets = 1 million miles

Initial gravitational force = 1,000,000 N

Final distance between the planets = 2 million miles

To determine the new gravitational force, we need to compare the ratios of the distances and apply the inverse square law.

Let's denote the initial distance as d1, the initial gravitational force as F1, the final distance as d2, and the unknown final gravitational force as F2.

According to the inverse square law, the ratio of the gravitational forces is the square of the ratio of the distances:

(F2/F1) = (d1/d2)²

Substituting the given values:

(F2/1,000,000 N) = (1 million miles / 2 million miles)²

Simplifying:

(F2/1,000,000 N) = (1/2)²

(F2/1,000,000 N) = 1/4

F2 = (1/4) * 1,000,000 N

F2 = 250,000 N

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