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2 years ago

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The driveshaft of an automobile is being designed to transmit 134 hp at 2900 rpm. Determine the minimum diameter d required for

a solid steel shaft if the allowable shear stress in the shaft is not to exceed 6100 psi.

1 answer:

Misha Larkins [42]2 years ago

4 0

Answer:

The minimum diameter is 1.344 in

Explanation:

The angular speed of the driveshaft is equal to:

$w=\frac{2\pi N}{60}$

Where

N = rotational speed of the driveshaft = 2900 rpm

$w=\frac{2\pi *2900}{60} =303.69rad/s$

The torque in the driveshaft is equal to:

$\tau=\frac{P}{w}$

Where

P = power transmitted by the driveshaft = 134 hp = 73700 lb*ft/s

$\tau=\frac{73700}{303.69} =242.68lb*ft$

The minimum diameter is equal to:

$d_{min} =(\frac{16T}{\pi *\tau } )^{1/3}$

Where

T = shear stress = 6100 psi

τ = 242.68 lb*ft = 2912.16 lb*in

$d_{min} =(\frac{16*2912.16}{\pi *6100} )^{1/3} =1.344in$

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The amplitudes of the displacement and acceleration of an unbalanced motor were measured to be 0.15 mm and 0.6*g, respectively.

ehidna [41]

Answer:

The speed of shaft is 1891.62 RPM.

Explanation:

given that

Amplitude A= 0.15 mm

Acceleration = 0.6 g

So

we can say that acceleration= 0.6 x 9.81

$acceleration,a=5.88\ \frac{m}{s^2}$

We know that

$a=\omega ^2A$

So now by putting the values

$a=\omega ^2A$

$5.88=\omega ^2 \0.15\times 10^{-3}$

$\omega =198.09\ \frac{rad}{s}$

We know that

ω= 2πN/60

198.0=2πN/60

N=1891.62 RPM

So the speed of shaft is 1891.62 RPM.

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2 years ago

A lake has a carrying capacity of 10,000 fish. At the current level of fishing, 2,000 fish per year are taken with the catch uni

arlik [135]

Answer:

The population size would be $p' = 5000$

The yield would be $MaxYield = 2082 \ fishes \ per \ year$

Explanation:

So in this problem we are going to be examining the application of a population dynamics a fishing pond and stock fishing and objective would be to obtain the maximum sustainable yield and and the population of the fish at the obtained maximum sustainable yield, so basically we would be applying an engineering solution to fishing

So the current yield which is mathematically represented as

$\frac{dN}{dt} = \frac{2000}{1 \ year }$

Where dN is the change in the number of fish

and dt is the change in time

So in order to obtain the solution we need to obtain the rate of growth

For this we would be making use of the growth rate equation which is

$r = \frac{[\frac{dN}{dt}] }{N[1-\frac{N}{K} ]}$

Where N is the population of the fish which is given as 4,000 fishes

and K is the carrying capacity which is given as 10,000 fishes

r is the growth rate

Substituting these values into the equation

$r = \frac{[\frac{2000}{year}] }{4000[1-\frac{4000}{10,000} ]} =0.833$

The maximum sustainable yield would be dependent on the growth rate an the carrying capacity and this mathematically represented as

$Max Yield = \frac{rK}{4} = \frac{(10,000)(0.833)}{4} = 2082 \ fishes \ per \ year$

So since the maximum sustainable yield is 2082 then the the population need to be higher than 4,000 so in order to ensure a that this maximum yield the population size denoted by $p'$ would be

$p' = \frac{K}{2} = \frac{10,000}{2} = 5000\ fishes$

7 0

3 years ago

Read 2 more answers

A vector AP is rotated about the Z-axis by 60 degrees and is subsequently rotated about X-axis by 30 degrees. Give the rotation

Musya8 [376]

Answer:

R = $\left[\begin{array}{ccc}1&0&0\\0&cos30&-sin30\\0&sin30&cos30\end{array}\right]$ $\left[\begin{array}{ccc}cos 60&-sin60&0\\sin60&cos60&60\0&0&1\end{array}\right]$

Explanation:

The mappings always involve a translation and a rotation of the matrix. Therefore, the rotation matrix will be given by:

Let $\theta$ and $\alpha$ be the the angles 60⁰ and 30⁰ respectively

that is $\theta$ = 60⁰ and

$\alpha$ = 30⁰

The matrix is given by the following expression:

$\left[\begin{array}{ccc}1&0&0\\0&cos30&-sin30\\0&sin30&cos30\end{array}\right]$ $\left[\begin{array}{ccc}cos 60&-sin60&0\\sin60&cos60&60\0&0&1\end{array}\right]$

The angles can be evaluated and left in the surd form.

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2 years ago

What statement exemplifies the role of archeology in architecture?

horrorfan [7]

The answer is B because an architect designs buildings

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2 years ago

The product life cycle defines the stages that new products move through as they enter, are established in, and ultimately leave

Bas_tet [7]

Answer:

The four marketing mix of every new business are:

1. Product

2. Place

3. Price

4. Promotion

For each of the stages of product life cycle, those 4p should be use appropriately.

Explanation:

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1. Product

2. Place

3. Price

4. Promotion

the product life cycle are directly proportional to the 4p of marketing. the product life cycle stages are introduction, growth, maturity and decline.

For each of the stages of product life cycle, those 4p should be use appropriately.

Stages of product life cycle and how the 4p fit into it.

The introduction stage:

at this stage, a new product just want to be introduced to the consumers. the product stage has being developed. The place where the product will fit in will also be consider. the location of people who consume this product. Pricing strategy consider a low price at the introduction stage, the business owner may not get any profit at this stage. then, continuous advertisement to create awareness of the product to the environment.

The growth stage:

the product will continuing to be move to different locations. the standard of the product quality will be maintained. the Pricing will start increasing. then, continuous advertisement to create awareness of the product and working on improving the product to suit the consumer.

the Mature stage:

At this stage, the consumer are fully aware of the product. wide range of location are reach. the pricing has reach its peak. Profit have been maximized. And, competitors of the product are in the market. Corporate social responsibility (CSR) will be the promotional value at this stage.

The Declining stage:

The business product have fully grown to its peak, and its only constant promotional values like CSR, advertisement, bonuses, can sustain it in the market. At this stage also, price comparison with other competitor should be carefully look into.

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3 years ago