A block of mass 3. 0 kg is hung from a spring, causing it to stretch 12 cm at equilibrium, as shown above. The 3. 0 kg block is then replaced by a 4. 0 kg block, and the new block is released from the position shown above, at which the spring is unstretched. How far will the 4. 0 kg block fall before its direction is reversed?.

The linear acceleration of collar D when θ = 60° is - 693.867 inches per square second.

In this question we have a system formed by three elements, the element AB experiments a pure rotation at constant velocity, the element BD has a general plane motion, which is a combination of rotation and traslation, and the ruff experiments a pure translation.

To determine the linear acceleration of the collar ([tex]a_{D}[/tex]), in inches per square second, we need to determine first all linear and angular velocities ([tex]v_{D}[/tex], [tex]\omega_{BD}[/tex]), in inches per second and radians per second, respectively, and later all linear and angular accelerations ([tex]a_{D}[/tex], [tex]\alpha_{BD}[/tex]), the latter in radians per square second.

By definitions of relative velocity and relative acceleration we build the following two systems of linear equations:

[tex]v_{D} + \omega_{BD}\cdot r_{BD}\cdot \sin \gamma = -\omega_{AB}\cdot r_{AB}\cdot \sin \theta[/tex]   (1)

[tex]\omega_{BD}\cdot r_{BD}\cdot \cos \gamma = -\omega_{AB}\cdot r_{AB}\cdot \cos \theta[/tex]   (2)

[tex]a_{D}+\alpha_{BD}\cdot \sin \gamma = -\omega_{AB}^{2}\cdot r_{AB}\cdot \cos \theta -\alpha_{AB}\cdot r_{AB}\cdot \sin \theta - \omega_{BD}^{2}\cdot r_{BD}\cdot \cos \gamma[/tex]   (3)

[tex]-\alpha_{BD}\cdot r_{BD}\cdot \cos \gamma = - \omega_{AB}^{2}\cdot r_{AB}\cdot \sin \theta + \alpha_{AB}\cdot r_{AB}\cdot \cos \theta - \omega_{BD}^{2}\cdot r_{BD}\cdot \sin \gamma[/tex]   (4)

If we know that [tex]\theta = 60^{\circ}[/tex], [tex]\gamma = 19.889^{\circ}[/tex], [tex]r_{BD} = 10\,in[/tex], [tex]\omega_{AB} = 16\,\frac{rad}{s}[/tex], [tex]r_{AB} = 3\,in[/tex] and [tex]\alpha_{AB} = 0\,\frac{rad}{s^{2}}[/tex], then the solution of the systems of linear equations are, respectively:

[tex]v_{D}+3.402\cdot \omega_{BD} = -41.569[/tex]   (1)

[tex]9.404\cdot \omega_{BD} = -24[/tex]   (2)

[tex]v_{D} = -32.887\,\frac{in}{s}[/tex], [tex]\omega_{BD} = -2.552\,\frac{rad}{s}[/tex]

[tex]a_{D}+3.402\cdot \alpha_{BD} = -445.242[/tex]   (3)

[tex]-9.404\cdot \alpha_{BD} = -687.264[/tex]   (4)

[tex]a_{D} = -693.867\,\frac{in}{s^{2}}[/tex], [tex]\alpha_{BD} = 73.082\,\frac{rad}{s^{2}}[/tex]

The linear acceleration of collar D when θ = 60° is - 693.867 inches per square second. [tex]\blacksquare[/tex]

The statement is incomplete and figure is missing, complete form is introduced below:

Arm AB has a constant angular velocity of 16 radians per second counterclockwise. At the instant when θ = 60°, determine the acceleration of collar D.

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Explanation:

velocity = frequency × wave length

velocity = 440 × 0.78

velocity = 343 m/sec

can you please mark my answer brainliest ♥️

Answer:

is 200 J

Explanation:

hope this is the right answer

The true statement about the blocks momentum is : The momentum of the block has increased by approximately 1/2 F₀t₁  ( B )

Given that the change in momentum is equivalent to the Area which is under the force time graph

where :

Area under the force time graph = 1/2 F₀t₁ . Therefore we can conclude that the momentum of the block has increased by an equivalent value of the are under the time graph.

Hence we can conclude that the true statement about the blocks momentum is The momentum of the block has increased by approximately 1/2 F₀t₁ .

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Attached below is the missing part of your question

missing options

Answer:

the answer is. C.

Explanation:

[tex] 0.36 \times 30 = 10.8[/tex]

the solution

Objects with the same charge repel each other, and objects with opposite charges attract each other

According to Coulomb, the electric force for charges at rest has the following properties: Like charges repel each other; unlike charges attract. Thus, two negative charges repel one another, while a positive charge attracts a negative charge. The attraction or repulsion acts along the line between the two charges.

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Answer:

Rolling friction

Explanation:

Option B is correct

Answer:

126 / 2 = 63 = angle between one rope and the direction of the resultant force

t = F cos 73 = .45 F      force on stump due to one horse

T = 2 t = .90 F       force on stump due to both horses - T would be the resultant of the two horses each pulling with force F

Answer: They Are all gas giants.

Explanation:

Answer:

solar

Explanation:

this is a form of solar panel

Earth would be an icy wasteland if greenhouse gases were not present. Greenhouse gases keep our planet livable by retaining some of the Earth's heat energy, preventing it from escaping into space. The greenhouse effect refers to the trapping of heat.

Answer:

the answer is white they combine to give white

Answer:

they are primary colors of light.

(pls don't delete this answer because I am just trying to help)

The resulting positive amplitude of the two waves after the superimposition is 4.30 cm.

The amplitude of the waves is the maximum displacement of the wave. This is the vertical position of the wave measured from the zero origin.

After the superimposition of the two similar waves, the resulting amplitude will be less than the initial amplitude of the wave with the highest vertical height since the superimposition creates destructive interference.

Resulting amplitude of the two waves is calculated as;

A = 5.4 cm - 1.10 cm

A = 4.30 cm

Thus, the resulting positive amplitude of the two waves after the superimposition is 4.30 cm.

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Answer:

Vaccum

Explanation:

You can test it .

One source error is deliberate deception and one of its solutions is having a lie scale inserted into the assessment.]

An error is a mistaken or erroneous action. In some contexts, an error is interchangeable with a mistake.

The discrepancy between the calculated value and the correct value is referred to as an "error" in statistics.

When a person is completely aware of what they are doing, they are engaging in deception. They are concealing the truth and making a deliberate decision to tell someone something that is false.

When describing a magic trick, such as a sleight of hand, the term deception can also be used.

When there are repetitive questions that ask the same questions over and over with different formats to check if the responses are constant over time, lie scales are utilized.

Hence one source error is deliberate deception and one of its solutions is having a lie scale inserted into the assessment.

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The destructive interference formula for diffraction grating problems is [tex]d sin \theta = (n+\frac{1}{2})\lambda[/tex].

Destructive interference happens when the maxima of two waves are 180° out of phase a positive displacement of one wave is canceled exactly by a negative displacement of the other wave.

The formula for brighter patches resulting from constructive interference and darker patches resulting from destructive interference in a diffraction grating is:

[tex]\rm d sin \theta = n \lambda[/tex]

The grating spacing is denoted by d, the angle of light is denoted by a the fringe order is denoted by n, and the wavelength is denoted by [tex]\rm \lambda[/tex].

The destructive interference formula is now based on the fact that destructive interference occurs between the fringes.

Hence the destructive interference formula for diffraction grating problems is [tex]d sin \theta = (n+\frac{1}{2})\lambda[/tex].

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Answer:

A. dsin  =

Explanation:

The object's velocity accelerating from rest from the applied force and time is closest to 4 m/s.

The velocity of the object can be determied by applying Newton's second law of motion as shown below;

F = ma

where;

The acceleration of the object is calculated as follows;

a = F/m

at time, t 4.0 s, the corresponding force = 2 N

a = 2/2

a = 1 m/s²

Velocity of the object is calculated as;

v = u + at

v = 0 + 1 x 4

v = 4 m/s

Thus, the object's velocity accelerating from rest from the applied force and time is closest to 4 m/s.

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Answer:

a thunder

Explanation:

It's because the difference in speed of light and sound

So we hear thunder later

Answer:

C

Explanation:

Therefore, Thunder Follows The Easiest Part. And it is not (A) because Thunder Follows A Lightening Not Vice Versa.

The mechanism for the given reaction by adding the missing bonds, charges, nonbonding electrons, and curved arrows is as represented in the attached image.

The representation of an organic reaction mechanism typically includes designation of the overall reaction type (which may be substitution, addition, elimination, oxidation, reduction, or rearrangement), the presence of any reactive intermediates, the nature of the reagent that initiates the reaction, the presence of any catalysis as facilitated by a catalyst, and ultimately it's stereochemistry.

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The mechanism for the given reaction is depicted in the attached picture by adding missing bonds, charges, nonbonding electrons, and curved arrows.

The existence of any reactive intermediates, the nature of the reagent that begins the reaction, the presence of any catalysis as helped by a catalyst.

Finally the stereochemistry of an organic reaction mechanism are all included in the depiction of an organic reaction mechanism.

Hence the mechanism for the given reaction is depicted in the attached picture by adding missing bonds, charges, nonbonding electrons, and curved arrows.

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Answer:

B. where tectonic plates meet

Explanation:

Most volcanoes occur near tectonic plate boundaries. For example, a large amount are found on the Ring of Firez connecting several plates.

Answer:

the same as the initial launch velocity (7.59 m/s)

Explanation:

vf^2 = vi^2 + 2ad

d = displacement = 0, so vf^2 = vi^2, so vf = vi = 7.59m/s

Torque:-

[tex]\\ \rm\Rrightarrow \tau =14(0.018)[/tex]

[tex]\\ \rm\Rrightarrow \tau=0.25Nm[/tex]

option B

A light-year is a unit of measurement which is used to measure distance between the Earth and the sun.

This is defined as the distance light travels in the time it takes the Earth to orbit the Sun.

It is also the distance a beam of light travels in a single earth year which is why option C was chosen as the most appropriate choice.

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The magnitude of the work done by force experience by the object is (2a²b + 3b²)J.

The magnitude of the work done by force experience by the object is calculated as follows;

W = f.d

where;

The work done by the force is determined from the dot product of the force and the displacement of the object.

F = (2xyi + 3yj).(a + b)

W = (2abi + 3bj).(ai + bj)

W = (2a²b + 3b²)J

Thus, the magnitude of the work done by force experience by the object is (2a²b + 3b²)J.

The complete question is below:

The particle moves from the origin to the point with coordinates (a, b) by moving first along the x-axis to (a, 0), then parallel to the y-axis.

How much work does the force do?

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The total work done  for an object moving in the xy-plane is subjected to the force f⃗ =(2xyı^ 3yȷ^)n, where x and y are in m is 3ab N.

Work done is the force applied on a body to move it over a distance. Work done for inclined plane can be given as,

[tex]W=F\times d[/tex]

Here (F) is the magnitude of force and (d) is the distance traveled.

An object moving in the xy-plane is subjected to the force

[tex]\vec f =(2xy\hat i +3y\hat j)[/tex]

Here, x and y are in meter.

The particle moves from the origin to the point with coordinates (a, b) by moving first along the x-axis to (a, 0), then parallel to the y-axis.

For the first part, the particle moves along x-axis. It moves zero along x-axis. Thus, the force, as y=0.

[tex]W_1=\int\limits^a_0 {2xy\hat i} \, dx =0\\[/tex]

Now, when the object moves along y-axis,

[tex]W_2=\int\limits^a_0 {3y\hat j} \, dx \\W_2=3\int\limits^b_0 {y\hat j} \, dx\\W_2=3y(a-0)\\W_2=3ba\\W_2=3ab[/tex]

Total work done,

[tex]W=0+3ab\\W=3ab\rm\; N[/tex]

Thus, the total work done  for an object moving in the xy-plane is subjected to the force f⃗ =(2xyı^ 3yȷ^)n, where x and y are in m is 3ab N.

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Answer:

M a = Fc -M g

Use up as positive - a is the acceleration upwards

Fc = M (a + g)       force exerted by chair

Fc = 19.8 M m/s^2      where M is the mass of the astronaut

The force exerted by the astronaut accelerating straight up with an acceleration of 10 m/s² is m/5 Newton.

If you want to accelerate a body of mass 'm' with acceleration 'a' than a force of magnitude given by the product of mass and acceleration is needed.

Given is an astronaut accelerating straight up with an acceleration of 10 m/s².

Since the astronaut is moving in upward direction, the resultant resultant force is in upward direction. Now, assume that the force exerted by the astronaut on the chair is F[A].  The normal reaction force on the astronaut will also be same. Mathematically -

F[N] = F[A]

Now, we can write the resultant normal reaction force as -

ma - mg = F[N]

F[N] = m(a - g)

F[N] = m(10 - 9.8)

F[N] = m(0.2)

F[N] = m/5

F[A] = F[N] = m/5

where m is the mass of astronaut.

Therefore, the force exerted by the astronaut accelerating straight up with an acceleration of 10 m/s² is m/5 Newton.

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In a vacuum all colors of light travel with same speed and this is the reason a white ray travels through the vacuum without going through any dispersion..

Speed of light is the distance per time light waves propagate through different materials. The value for the speed of light in a vacuum is now defined as exactly 299,792,458 metres per second.

Therefore, In a vacuum all colors of light travel with same speed and this is the reason a white ray travels through the vacuum without going through any dispersion

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The wavelength of the radio waves emitted by the radio galaxies which have twin radio jets that emanate from a central core is determined as 15 m.

The wavelength of the radio waves is the distance traveled by the radio waves. The magnitude of the wavelength is determined from the ratio of speed of radio waves to the frequency of the radio waves.

v = fλ

where;

Radio wave is an example of electromagnetic radiation, and it travels at the same speed as light (3 x 10⁸ m/s).

λ = v/f

λ = (3 x 10⁸ ) / (20 x 10⁶)

λ = 15 m

Thus, the wavelength of the radio waves emitted by the galaxy is 15 m.

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Hi there!

We can use the work-energy theorem and apply it to this situation.

At the top of the ramp, the ball only has gravitational potential energy, and at the bottom of the ramp, the ball has BOTH translational and rotational kinetic energy.

We must use the following equations:
[tex]GPE = mgh \\KE_T = \frac{1}{2}mv^2\\\\KE_R = \frac{1}{2}I \omega^2[/tex]

m = mass of sphere (kg)
g = acceleration due to gravity (m/s²)

h = height of ramp (m)

v = final velocity (m/s)
I = Moment of Inertia (kgm²)

ω = angular velocity (rad/sec)

Since:
[tex]E_i = E_f\\\\mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega ^2[/tex]

In order to make things easier, since the ball is not slipping, we can relate angular velocity to translational velocity:
[tex]\omega = \frac{v}{r}[/tex]

Also, recall the equation for the moment of inertia for a solid sphere:
[tex]I = \frac{2}{5}mr^2[/tex]

We can use these to simply our equation:
[tex]KE_R = \frac{1}{2}(\frac{2}{5}mr^2)(\frac{v}{r})^2 = \frac{1}{5}mv^2[/tex]

Now, we can rewrite the equation and solve for 'v'.

[tex]mgh = \frac{1}{2}mv^2 + \frac{1}{5}mv^2\\\\mgh = \frac{7}{10}mv^2\\\\v = \sqrt{\frac{10gh}{7}} = \sqrt{\frac{10(9.8)(2.2 - 1.87)}{7}} = 2.149\frac{m}{s}[/tex]

a)

We can begin by solving for the time taken for the ball to land on the ground. The ball only has a horizontal velocity, so this is essentially a free-fall situation. Use the rearranged kinematic equation:
[tex]t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2(1.87)}{9.8}} = .6178 s[/tex]

Now, use the following equation to solve for horizontal distance given horizontal velocity and time:
[tex]d_x = v_x t\\\\d_x = 2.149 * .6178 = \boxed{1.328 m}[/tex]

b)
We can use the previously-stated relationship between translational and angular velocity to solve for the angular velocity.

[tex]\omega = \frac{v}{r}[/tex]
It is given that the diameter is 0.14 m, so the radius is 1/2th the diameter, or 0.07 m.

Solve for the angular velocity:
[tex]\omega = \frac{2.149}{0.07} = 30.706 \frac{rad}{sec}}[/tex]

Using the above fall time and dimensional analysis to convert from rad/sec to revolutions, we can solve for the # of revolutions made by the ball:
[tex]\frac{30.706rad}{sec} * .6178 sec * \frac{1 rev}{2\pi rad} = \boxed{3.019 rev}[/tex]