The bullseye of a dart board is directly across from the dart being thrown, S. / maway. If the dart is released at 21.3 m/s horizontally. Does the dart hit within 1.00cm of the bullseye? It not, how should the shot be adjusted?

The maximum angle at which an object will not slip on an incline can be calculated using the coefficient of friction (μ).

When an object is on an inclined plane, there are two main forces acting on it: the gravitational force pulling it downward (mg) and the normal force (N) exerted by the inclined plane perpendicular to its surface. Additionally, there is a frictional force (F) acting parallel to the surface of the incline.

To prevent slipping, the frictional force must be equal to or greater than the force component pulling the object down the incline. This force component is given by the equation F = mg sin(θ), where θ is the angle of inclination.

The maximum frictional force that can be exerted between two surfaces is given by the equation F = μN, where μ is the coefficient of friction.

For an object not to slip, the maximum frictional force (F) must be equal to or greater than the force component pulling the object down the incline (mg sin(θ)). Therefore, we have:

F ≥ mg sin(θ)

Substituting F = μN, we get:

μN ≥ mg sin(θ)

Since N = mg cos(θ) (the normal force is equal to the component of the gravitational force perpendicular to the incline):

μmg cos(θ) ≥ mg sin(θ)

μ cos(θ) ≥ sin(θ)

Now, divide both sides of the equation by cos(θ):

μ ≥ tan(θ)

Taking the inverse tangent (arctan) of both sides, we get:

θ ≤ arctan(μ)

Therefore, the maximum angle at which an object will not slip on an incline is given by θ = arctan(μ).

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Answer: False

Explanation:

Took the test.

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Rationale:

Ideal mechanical advantage is the ratio of input to output distance moved.

The distance travelled by the body is determined as 9 m.

The distance travelled by the body is calculated by applying the following kinematic equation as shown below.

Mathematically, the kinematic equation is given as;

v² = u² + 2as

where;

The given parameters include the following;

the initial velocity of the body = 0

the final velocity of the = 6 m/s

the constant acceleration of the body = 2 m/s²

the distance travelled by the body = ?

The distance travelled by the body is calculated as follows;

v² = u² + 2as

v² = 0 + 2as

v² =  2as

s = v² / 2a

s = ( 6² ) / ( 2 x 2 )

s = 9 m

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The complete question is below:

A body started from rest at constant acceleration of 2 m/s², the body reaches a velocity of 6 m/s. Calculate the distance travelled by the object to reach this velocity.

The necessary steps in order for finding the molecular formula of an unknown compound from mass percent data are:

The correct answer is 1-2-3-4-5.

Let's start with the information provided in the issue, which is the weight in grams of each constituent. If percentages are provided, we'll assume that there is a total mass of 100 grams, making each element's mass equal to the specified percentage.

Convert each element's mass to a mole by using its molar mass from the periodic table. Multiply the lowest calculated number of moles by each mole value. To the nearest entire number, round up. The mole ratio of the elements is indicated by subscripts in the empirical formula.

If the number is too large to round off, multiply each response by the same factor to obtain the lowest whole number multiple (x.1 – x.9). Like multiplying each solution in the problem by 4 to get 5, if one solution is 1.25. Then multiply each subscript of the empirical formula by the integer multiple

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Answer:

0.00050, 0.000000000406, 36513

Answer:

a) the maximum shear stress τ\(_{max}\) the bar is 16T\(_{max}\) /πd³

b) the angle of twist between the ends of the bar is 16tL² / πGd⁴  

Explanation:

Given the data in the question, as illustrated in the image below;

d is the diameter of the prismatic bar of length AB

t is the intensity of distributed torque

(a) Determine the maximum shear stress tmax in the bar

Maximum Applied torque  T_max = tL

we know that;

shear stress τ = 16T/πd³

where d is the diameter

so

τ\(_{max}\) = 16T\(_{max}\) /πd³

Therefore, the maximum shear stress τ\(_{max}\) the bar is 16T\(_{max}\) /πd³

(b) Determine the angle of twist between the ends of the bar.

let theta (\(\theta\)) be the angle of twist

polar moment of inertia \(I_p}\) = πd⁴/32

now from the second image;

lets length dx which is at distance of "x" from "B"

Torque distance x

T(x) = tx

Elemental angle twist = d\(\theta\) = T(x)dx / G\(I_{p}\)

so

d\(\theta\) = tx.dx / G(πd⁴/32)

d\(\theta\) = 32tx.dx / πGd⁴

so total angle of twist \(\theta\) will be;

\(\theta\) =  \(\int\limits^L_0 \, d\theta\)

\(\theta\) =  \(\int\limits^L_0 \,\) 32tx.dx / πGd⁴

\(\theta\) = 32t / πGd⁴  \(\int\limits^L_0 \, xdx\)

\(\theta\) = 32t / πGd⁴ [ L²/2]

\(\theta\) = 16tL² / πGd⁴  

Therefore,  the angle of twist between the ends of the bar is 16tL² / πGd⁴  

answer yuo do not have it

Answer:

a)  B = 0.9375 T  -z, b)      B = 1.54 T

Explication

a) The magnetic force is

         F = q v x B

         f = q v B sin θ

bold indicates vectors

For direction let's use the right hand rule.

If the charge is positive

the flea in the direction of velocity, toward + x

the fingers extended in the direction of B

the palm the direction of the force + and

therefore the magnetic field goes in the direction of -z

           F = q v B

           2.25 10-16 = 1.6 10-19  1.50 103 B

           B = 2.25 10-16 / 2.4 10-16

           B = 0.9375 T  -z

b) now an electron

thumb speed direction, -z

opposite side of palm force + y

therefore the direction of the magnetic field is + x

            B = F / qv

            B = 8.5 10-16 / 1.16 10-19 4.75 103

             B = 1.54 T

R = ρ L/ A

Where;

ρ= resistivity = 1.68 x 10^-8 OHM m

L= lenght = 1 m

A = cross sectional area = 6.7 × 10-8 m2

R = resistance

R = 1.68 x 10^-8 OHM m ( 1 m/ 6.7 × 10-8 m2)

R = 0.25 OHM

OHM's LAW

V = IR

V= 9 V

I = V / R = 9 / 0.25 = 36 Ampere

Answer:

 Mg- 27   means isotope with 12 protons and 15 neutrons.

Also 27 is mass number which express sum of protons and neutrons.

In nucleus one neutrn decays to electron and proton. Mass number remain same but Al-27 nucleus contain 13 protons and 14 neutrons. Electron is ejected out from nucleus.

The net work done (in J) required to accelerate a 1500 kg car from 55 m/s to 65 m/s is 3127500 J

First, we shall obtain the initial kinetic energy. Details below:

KE₁ = ½mu²

= ½ × 1500 × 55²

= 41250 J

Next, we shall final kinetic energy. Details below:

KE₂ = ½mv²

= ½ × 1500 × 65²

= 3168750 J

Finally, we shall determine the net work done. Details below:

W = KE₂ - KE₁

= 3168750 - 41250

= 3127500 J

Thus, the net work done is 3127500 J

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Answer:

A quantity that has magnitude but no particular direction is described as scalar. A quantity that has magnitude and acts in a particular direction is described as vector.

The difference between scalar and vector quantities is simply the direction we always consider when dealing with vector quantities.

Scalar quantities are those quantities that have only magnitude but no direction. Examples are;

Vector quantities are those quantities that have both magnitude and direction. Examples are;

The difference between scalar and vector quantities is simply the direction we always consider when dealing with vector quantities.

Therefore, direction is the difference between them.

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Answer:

i = 0.00077A

Explanation:

Given:

loop radius, r = 3.0 cm = 0.03 m

Area, A = π x r² = π x 0.03² = 0.0028 m²

Magnetic Field, B = 0.75 T

Loop resistance, R = 18 Ω

time, t = 0.15 seconds

Now,

the induced emf is given as:

EMF = - BA/t .......1

Likewise,

EMF = iR.......2

Equate 1 and 2

iR = - BA/t

i = - BA/tR

i = 0.75×0.0028/0.15×18

i = 0.0021/2.7

i = 0.00077A

Answer:

60 kg m/s

Explanation:

F= Force = 6 N

m = Mass of object = 3 kg

u = Initial velocity = 15 m/s

t = Time = 10 s

v = Final velocity

\(\Delta p\) = Change in momentum

Force is given by

\(F=\dfrac{\Delta p}{t}\\\Rightarrow Ft=\Delta p\\\Rightarrow \Delta p=6\times 10\\\Rightarrow \Delta p=60\ \text{Ns}\)

The change in  momentum of the object is 60 kg m/s.

Answer:

10 N.m

Explanation:

Force * Perpendicular distance.

= 20 N * 0.5 m

= 10 N.m

Answer: They will be clear

Explanation:

When hydrochloric acid (HCl) is mixed with sodium hydroxide (NaOH), a neutralization reaction occurs, and the products of the reaction are sodium chloride (NaCl) and water (H2O).

The chemical equation for this reaction is:

HCl + NaOH → NaCl + H2O

Sodium chloride is a salt that is commonly used in cooking and as a de-icing agent, while water is a familiar and essential compound that we use every day.

NaCl and water  can be a clear solution but it is not coorrosive and a new salt is formed thus it does not retain any properties of the initial reactants.

The components of a 15 meters per second velocity at an angle of 60 above the horizontal are 13.05 m / s and 0.435 m / s

Resolving the velocity into its horizontal and vertical components, it makes a right angled triangle.

Hypotenuse = V = 15 m / s

θ = 60°

Opposite side = components = \(V_{y}\)

Adjacent side = Horizontal component = \(V_{x}\)

In a right angled triangle,

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

sin 60° = \(V_{y}\) / V

\(V_{y}\) = 15 * 0.87

\(V_{y}\) = 13.05 m / s

cos 60° = \(V_{x}\) / V

\(V_{x}\) = 0.5 * 0.87

\(V_{x}\) = 0.435 m / s

Therefore,

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Vector representation:

Let vector A be;

Vector B be;

Vector C be;

The resultant displacement vector R is given as,

The magnitude of the resultant displacement vector is given as,

Therefore, the magnitude of the football's resultant displacement is 40.79 yards.

Answer:

Steel is mostly composed of iron and carbon. It contains small amounts of manganese and even smaller amounts of silicon, phosphorous, oxygen, sulfur, and other elements.

...

Density of Steel.

carbon steel - 7.86

stainless steel - 7.9

Answer: 30 Years Old

Explanation: The constitution has around three qualifications for service in the U.S. Senate, Your age must be at least 30 years.

The frequency of f3 is approximately 716 Hz.

The frequency of a repeated event is its number of instances per unit of time. Hertz (Hz), which stands for the number of cycles per second, is a popular unit of measurement.

a. Given two frequencies, f1 and f2, the frequency ratio is as follows:

frequency ratio= \(\frac{f2}{f1}\)

Inputting the values provided yields:

frequency ratio = \(\frac{576}{320Hz}\) =1.8.

As a result, the difference in frequency between f1 = 320 Hz and f2 = 576 Hz is 1.8.

b. Since there are 12 half-steps in an octave and a fourth is a distance of 5 half-steps, going down a fourth requires dividing the frequency by \(2^{(4/12)}\). Hence, once a fourth is subtracted, the frequency ratio between f and f1 is:

frequency ratio= \(\frac{f}{ (f1 /f2 ) }\)=  \(\frac{f}{ (f1 / 1.3348) }\)

By dividing the numerator and denominator by 1.3348, we may make this more straightforward:

frequency ratio= (f × 1.33348)/f1

As a result, (f × 1.3348) / f1 is the frequency ratio between f and f1 after descending a fourth.

c. (c) To find the frequency of f3, we need to know the interval between f1 and f3. Let's assume that f3 is a fifth above f2. The frequency ratio for a fifth is given by: \(2^{(7/12)}\) = 1.49831

Therefore, the frequency of f3 is:

f3 = f1 × (\(2^{(7/12)}\)) × (\(2^{(7/12)}\)) = 320 Hz × 1.49831 ×1.49831 = 716 Hz

Therefore, the frequency of f3 is approximately 716 Hz.

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Given the statement:

The body will have zero momentum if its not in the motion.

Let's determine if the statement is true of false.

The momentum of a body can be expressed as:

momentum = mass x velocity

Since velocity depends on mass and velocity, if the body is not in motion, the velocity will be 0.

Hence, if the velocity is zero, the momentum will also be zero.

The momentum of any body at rest is always zero.

Therefore, the given statement is True.

ANSWER:

True.

It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.

2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.

3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.

4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.

5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.

6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".

7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).

8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).

9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.

10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.

11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).

12. Evaluating the expression, we find: t ≈ 546.

13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

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The distance between two objects of radius 6 cm and 2 cm is zero

To find the distance between two objects with radii of 6 cm and 2 cm, we need to consider the center-to-center distance between the objects and subtract the sum of their radii.

Let's denote the radii of the objects as r1 = 6 cm and r2 = 2 cm.

The distance between the centers of the objects can be represented as d = r1 + r2. Adding the radii ensures that we account for the space occupied by both objects.

Substituting the values, we have d = 6 cm + 2 cm = 8 cm.

Now, to find the actual distance between the objects, we subtract the sum of their radii from the center-to-center distance:

Distance = d - (r1 + r2) = 8 cm - (6 cm + 2 cm) = 8 cm - 8 cm = 0 cm.

The resulting distance is 0 cm, indicating that the objects are in direct contact with each other. This means that their surfaces are touching. When the distance between two objects is zero, it implies that they are overlapping or in physical contact. In this case, since the distance is equal to 0 cm, the two objects are touching each other, with their surfaces coming into contact.

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Move numbers to the boxes to show the factor pairs of 14:

Blank space 1: 1

Blank space 2: 1

Blank space 3: 2

Blank space 4: 7

A factor pair of a number is a pair of whole numbers that can be multiplied together to give the original number. For the number 14, the factor pairs are (1,14) and (2,7). So, we can put 1 in the first blank, 14 in the second blank, 2 in the third blank, and 7 in the fourth blank to show the factor pairs of 14.

To show the factor pairs of 14 in the given response area with 4 blank spaces, we need to find the two numbers that can be multiplied together to give 14. These two numbers are called factor pairs of 14.

To begin, we can start listing the factors of 14. The factors of 14 are 1, 2, 7, and 14. We can then use these factors to form factor pairs by multiplying them together. The factor pairs of 14 are (1, 14) and (2, 7).

To show these factor pairs in the given response area, we can put the first factor of each pair in the first and third blank spaces, and the second factor of each pair in the second and fourth blank spaces. Therefore, we can put 1 in the first blank, 14 in the second blank, 2 in the third blank, and 7 in the fourth blank to show the factor pairs of 14.

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Explanation:

it has no energy when considered with respect to earth ,as it has neither height (i e potential energy) nor velocity (i.e kinetic energy).

Answer:0.45m/sec

Explanation: Acceleration is defined as the rate of change of velocity with respect to time. The Magnitude of the acceleration is 0.45 m/sec².While the direction is downward.

Answer:

C: forces are equal but opposite in direction

Explanation:

If both objects are moving you know this is an elastic collision and therefore the bus and car will travel in opposite directions after the collision with equivalent forces.

if a car collides with a moving bus, the type of relationship exists between the force of the car and the force of the bus is  the forces are equal but opposite in direction.

Force can be defined as pushing or pulling of any object resulting from the object’s interaction or movement, without force the objects can not be moved, can be stopped or change the direction.

Force is a  quantitative interaction between two physical bodies, means an object and its environment, there are different types of forces in nature.

If an object in its moving state will be either static or motion, the position of the object will only be changed if it is pushed or pulled and The external push or pull upon the object called as Force.

The contact force types  are the force that occurs when we apply some effort on an object such as Spring Force, Applied Force, Air Resistance Force, Normal Force, Tension Force, Frictional Force

Non-Contact forces are another type of forces occur from a distance  such as Electromagnetic Force, Gravitational Force, Nuclear Force

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