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1 year ago

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Hilda plans to display in a clear cube the needle betsy ross used to sew the first american flag. the needle will fit exactly as

the diagonal of the cube. if the side length of the clear cube is startroot 3 endroot inches, and the diagonal of a face of the cube is startroot 6 endroot inches, what is the length of the needle? startroot 6 endroot inches 3 inches 3 startroot 2 endroot inches 6 inches

2 answers:

inysia [295]1 year ago

8 0

Based on the length of side of the cube given, the length of the needle is 2.28 inches.

<h3>What is the length of the needle?</h3>

The length of the side of a cube and its diagonal are related by the formula below:

$Length \: of \: Diagonal = \sqrt{3s}$

where s is length of side

$Side \: Length \: of \: the \: Cube = \sqrt{3inches}$

$Diagonal \: of \: a \: face \: of \: the \: cube = \sqrt{6inches}$

$The \: length \: of \: the \: needle = \sqrt{3\sqrt{3}} = 2.28 \: inches \\$

Therefore, the length of the needle is 2.28 inches

Learn more about length of diagonal of cube at: brainly.com/question/800212

#SPJ4

Irina-Kira [14]1 year ago

7 0

Answer:

Its B 3in

Explanation:

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Arm ab has a constant angular velocity of 16 rad/s counterclockwise. At the instant when theta = 60

geniusboy [140]

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

<h3>How to determine the angular velocity of a collar</h3>

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

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

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

<h3>Velocities</h3>

$v_{D} + \omega_{BD}\cdot r_{BD}\cdot \sin \gamma = -\omega_{AB}\cdot r_{AB}\cdot \sin \theta$ (1)

$\omega_{BD}\cdot r_{BD}\cdot \cos \gamma = -\omega_{AB}\cdot r_{AB}\cdot \cos \theta$ (2)

<h3>Accelerations</h3>

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

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

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

<h3>Velocities</h3>

$v_{D}+3.402\cdot \omega_{BD} = -41.569$ (1)

$9.404\cdot \omega_{BD} = -24$ (2)

$v_{D} = -32.887\,\frac{in}{s}$ , $\omega_{BD} = -2.552\,\frac{rad}{s}$

<h3>Accelerations</h3>

$a_{D}+3.402\cdot \alpha_{BD} = -445.242$ (3)

$-9.404\cdot \alpha_{BD} = -687.264$ (4)

$a_{D} = -693.867\,\frac{in}{s^{2}}$ , $\alpha_{BD} = 73.082\,\frac{rad}{s^{2}}$

The <em>linear</em> acceleration of collar D when <em>θ = 60°</em> is - 693.867 inches per square second. $\blacksquare$

<h3>Remark</h3>

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

<em>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.</em>

To learn more on kinematics, we kindly invite to check this verified question: brainly.com/question/27126557

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1 year ago

The amount of WORK done is determined by 2 factors.

RUDIKE [14]

Explanation :

Work is done when a force is applied to create a displacement on an object.

Thus, the work done depends on the two factors i.e.

(1) Applied force (F)

(2) Distance or displacement (d)

Mathematically, work done is $W= F.s$

It also depends on the angle between the force and the displacement.

$W=Fs\ cos\ \theta$

For example,

A person carries a weight of 20 kg and lifts it on his head 1.5 m above the surface. So, the work done by him on the luggage will be:

$W= F\times s$

or

$W=m\times g \times s$

$W=20\ kg\times 9.8\ m/s^2\times 1.5\ m$

So, $W=294\ Joules$

Hence, the work done by him on the luggage is 294 Joules.

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tino4ka555 [31]

Answer: A. by analyzing and making inferences about them

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Two students designed an experiment to study the effect of solar radiations on four cities of Earth. They used a globe to repres

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Great experiment ! Everybody should try it if they can get the equipment.
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If the axis of the globe was tilted, then City-D had the least variation in
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