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larisa86 [58]
3 years ago
8

The flexural strength or MOR of a ceramic is 310 MPa. A block of the ceramic, which is 20 mm wide, 15 mm high, and 300 mm long,

is supported between two rods 150 mm apart. Determine the force required to fracture the material, assuming no plastic deformation occurs.

Engineering
1 answer:
Alja [10]3 years ago
3 0

Answer:

F=6200\ \text{N}\\

Explanation:

In this problem you need to define the force that acts upon a beam in a 3 point bending problem. I put a picture of the problem taken from Wikipedia:

In this problem the flexural strength is defined with the following formula:

\sigma=\cfrac{3FL}{2bd^2}

where F is the force applied, L the length between the two rods, b the width of the ceramic block and d it's height.

The force is then defined as:

F=\cfrac{2\sigma bd^2}{3L}=6200\ \text{N}

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A race car is travelling around a circular track. The velocity of the car is 20 m/s, the radius of the track is 300 m, and the m
Zielflug [23.3K]

Answer:

μ = 0.136

Explanation:

given,

velocity of the car = 20 m/s

radius of the track = 300 m

mass of the car = 2000 kg

centrifugal force

F_c = \dfrac{mv^2}{r}

F_c = \dfrac{2000\times 20^2}{300}

F c = 2666. 67 N

F f= μ N

F f = μ m g

2666.67  =  μ × 2000 × 9.8

μ = 0.136

so, the minimum coefficient of friction between road surface and car tyre is equal to μ = 0.136

5 0
3 years ago
A microwave transmitter has an output of 0.1W at 2 GHz. Assume that this transmitter is used in a microwave communication system
Len [333]

Answer:

gain = 353.3616

P_r = 1.742*10^-8 W

Explanation:

Given:

- The output Power P_o = 0.1 W

- The diameter of the antennas d = 1.2 m

- The frequency of signal f = 2 GHz

Find:

a. What is the gain of each antenna?

b. If the receiving antenna is located 24 km from the transmitting antenna over a free space path, find the available signal power out of the receiving antenna.

Solution:

- The gain of the parabolic antenna is given by the following formula:

                            gain = 0.56 * 4 * pi^2 * r^2 / λ^2

Where, λ : The wavelength of signal

            r: Radius of antenna = d / 2 = 1.2 / 2 = 0.6 m

- The wavelength can be determined by:

                            λ = c / f

                            λ = (3*10^8) / (2*10^9)

                            λ = 0.15 m

- Plug in the values in the gain formula:

                            gain = 0.56 * 4 * pi^2 * 0.6^2 / 0.15^2

                            gain = 353.3616

- The available signal power out from the receiving antenna is:

                            P_r = (gain^2 * λ^2 * W) / (16*pi^2 * 10^2 * 10^6)

                            P_r = (353.36^2 * 0.15^2 * 0.1) / (16*pi^2 * 10^2 * 10^6)

                            P_r = 1.742*10^-8 W

4 0
3 years ago
In this problem set, you will implement multidimensional scaling (MDS) from scratch. You may use standard matrix/vector librarie
EleoNora [17]

Features of Multidimensional scaling(MDS) from scratch is described below.

Explanation:

Multidimensional scaling (MDS) is a way to reduce the dimensionality of data to visualize it.  We basically want to project our (likely highly dimensional) data into a lower dimensional space and preserve the distances between points.  

If we have some highly complex data that we project into some lower N dimensions, we will assign each point from our data a coordinate in this lower dimensional space, and the idea is that these N dimensional coordinates are ordered based on their ability to capture variance in the data.  Since we can only visualize things in 2D, this is why it is common to assess your MDS based on plotting the first and second dimension of the output.  

If you look at the output of an MDS algorithm, which will be points in 2D or 3D space, the distances represent similarity. So very close points = very similar, and points farther away from one another = less similar.

Working of MDS

The input to the MDS algorithm is our proximity matrix.  There are  two kinds of classical MDS that we could use:  Classical (metric) MDS is for data that has metric properties, like actual distances from a map or calculated from a vector .Nonmetric MDS is for more ordinal data (such as human-provided similarity ratings) for which we can say a 1 is more similar than a 2, but there is no defined (metric) distance between the values of 1 and 2.

Uses

Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of n objects or individuals" into a configuration of n points mapped into an abstract Cartesian space.

8 0
3 years ago
A 35 ft simply supported beam is loaded with concentrated loads 15 ft in from each support. On one end, the dead load is 8 kips
agasfer [191]

Answer: ASD = 306 kips-ft

               LRSD = 1387.5 k-ft

Explanation:

To begin, we will take a step by step process to solving this problem.

Attached below is a picture to guide us to solving this.

To begin, we have that to reaction of the support

ΣMд = 0

where;

RB * 35 - (8+18)15 - (4+9)20 = 0

RB = 18.57k

also Ey = 0;

RA + RB = 18 + 8 + 9 +4 = 20.43 k

taking the maximum moment at mid point;

Mc = RA * 35/2 - (8 +18) (35/2 -15)

Mc = 292.525

therefore, MD = RA * 15 = 20.43 * 15 = 306.45 k.ft

MD = 306.45 k.ft

ME = 279 k.ft i.e 18.57 * 15

considering the unsupported  length; 35 - (15*2 = 5ft

now we have that;

Lb = Lp = 5ft

where Lp = 1.76 ry(√e/fy)

Lp = 1.76 ry √29000/50 ......

ry = 1.4 inch

so we have that Mr = Mp for Lb = Lp where

Mp = 2 Fy ≤ 1.5 sx Fy

Recall from the expression,

RA + RB = (8+4) * 1.2 + (18+9) * 1.6 = 57.6

RA * 35 = 4 * 1.2 * 15 + 9 *1.6 * 15 + 8 * 1.2 * 20 + 18 * 1.6 * 20

RA = 30.17 k

the maximum moment at D = 30.17 * 15 = 452.55 k.ft

Zrequired = MD/Fy = 452.55 * 12 / 50 = 108.61 inch³

so we have Sx = 452.55 * 12 / 1.5 * 50 = 72.4 inch³

also r = 1.41 in

Taking LRFD solution:

where the design strength ∅Mn = 0.9 * Zx * Fy

given r = 2.97

Zx = 370 and Sx = 81.5, we have

∅Mn = 0.9 * 370 * 50 = 16650 k-inch = 1387.5 k-ft

this tells us it is safe.

ASD solution:

for Lb = Lp, and where Mn = Mp = Fcr Sx

we already have value for Sx as 81.5 so

Fcr = ZxFy/Sx

Fcr = 370 * 50 / 81.5 = 227 ksi

considering the strength;

Strength = Mn / Ωb = (0.6 * 81.5 * 50) * (1.5) / 12 = 306 kips-ft

This justifies that it is safe because is less than 306

cheers i hope this helps.

4 0
3 years ago
Which of the following is caused by coccidiosis?
Vanyuwa [196]

Answer:

I believe it is a not 100 percent sure

8 0
2 years ago
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