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3 years ago

Which pendulum will.mobe faster

Engineering

1 answer:

Amiraneli [1.4K]3 years ago

5 0

Explanation:

The period T (i.e. time to make one complete swing)

of a pendulum of length L is

T = 2 pi sqrt(L/g)

where g=acceleration due to gravity.

Note that the period is independent (to first order) of mass.

This means that the shorter the string, the shorter is the time (i.e. faster) it takes to make a complete swring.

Since the 5 kg mass is attached to a shorter swing, it will "move" faster, or the period T is shorter.

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For a metal that has a yield strength of 690 MPa and a plane strain fracture toughness (KIc) of 32 MPa-m1/2, compute the minimum

Digiron [165]

Answer:

the minimum component thickness for which the condition of plane strain is valid is 0.005377 m or 5.38 mm

Explanation:

Given the data in the question;

yield strength σ $_y$ = 690 Mpa

plane strain fracture toughness K $_{Ic$ = 32 MPa- $m^{1/2$

minimum component thickness for which the condition of plane strain is valid = ?

Now, for plane strain conditions, the minimum thickness required is expressed as;

t ≥ 2.5( K $_{Ic$ / σ $_y$ )²

so we substitute our values into the formula

t ≥ 2.5( 32 / 690 )²

t ≥ 2.5( 0.0463768 )²

t ≥ 2.5 × 0.0021508

t ≥ 0.005377 m or 5.38 mm

Therefore, the minimum component thickness for which the condition of plane strain is valid is 0.005377 m or 5.38 mm

7 0

3 years ago

An insulated mixing chamber receives 0.5 kg/s of steam at 3 MPa and 300°C through one inlet, and saturated liquid water at 3 MPa

maxonik [38]

Answer:

$\dot m_{2} = 0.199\,\frac{kg}{s}$

Explanation:

The mixing chamber can be modelled by applying the First Law of Thermodynamics:

$\dot W_{in}+\dot m_{1}\cdot h_{1} +\dot m_{2} \cdot h_{2} - \dot m_{3}\cdot h_{3} = 0$

Since that mass flow rate of water at inlet 1 is the only known variable, the expression has to be simplified like this:

$\frac{\dot W_{in}}{\dot m_{1}} + h_{1}+ y\cdot h_{2} - z\cdot h_{3} = 0$

Besides, the following expression derived from the Principle of Mass Conservation is presented below:

$1 + y = z$

Then, the expression is simplified afterwards:

$\frac{\dot W_{in}}{\dot m_{1}} + h_{1}+ y\cdot h_{2} - (1+y)\cdot h_{3} = 0$

$\frac{\dot W_{in}}{\dot m_{1}} +h_{1} - h_{3} + y\cdot (h_{2}-h_{3}) = 0$

Specific enthalpies are obtained from steam tables and described as follows:

State 1 (Superheated vapor)

$h = 2994.3\,\frac{kJ}{kg}$

State 2 (Saturated liquid)

$h = 1008.3\,\frac{kJ}{kg}$

State 3 (Liquid-Vapor mixture)

$h = 2444.22\,\frac{kJ}{kg}$

The ratio of the stream at state 2 to the stream at state 1 is:

$y = \frac{\frac{\dot W_{in}}{\dot m_{1}}+h_{1}-h_{3}}{h_{3}-h_{2}}$

$y = \frac{\frac{10\,kW}{0.5\,\frac{kg}{s} }+2994.3\,\frac{kJ}{kg}-2444.22\,\frac{kJ}{kg} }{2444.22\,\frac{kJ}{kg}-1008.3\,\frac{kJ}{kg} }$

$y = 0.397$

The mass flow rate of the saturated liquid is:

$\dot m_{2} = y\cdot \dot m_{1}$

$\dot m_{2} = 0.397\cdot (0.5\,\frac{kg}{s} )$

$\dot m_{2} = 0.199\,\frac{kg}{s}$

5 0

3 years ago

An insulated 40 ft3 rigid tank contains air at 50 lbf/in2 and 120oF. A valve connected to the tank is now opened, and air is all

goldfiish [28.3K]

Answer:

The electrical work for the process is 256.54 Btu.

Explanation:

From the ideal gas equation:

n = PV/RT

n is the number of moles of air in the tank

P is initial pressure of air = 50 lbf/in^2 = 50 lbf/in^2 × 4.4482 N/1 lbf × (1 in/0.0254m)^2 = 344736.2 N/m^2

V is volume of the tank = 40 ft^3 = 40 ft^3 × (1 m/3.2808 ft)^3 = 1.133 m^3

T is initial temperature of air = 120 °F = (120-32)/1.8 + 273 = 321.9 K

R is gas constant = 8.314 J/mol.k

n = 344736.2×1.133/8.314×321.9 = 145.94 mol

The thermodynamic process is an isothermal process because the temperature is kept constant.

W = nRTln(P1/P2) = 145.94×8.314×321.9×ln(50/25) = 145.94×8.314×321.9×0.693 = 270669 J = 270669 J × 1 Btu/1055.06 J = 256.54 Btu

5 0

3 years ago

Read 2 more answers

transformer has 26 turns on the primary coil and 720 turns on the secondary coil. If this transformer is to produce an output of

hram777 [196]

<h2>Corrected Question:</h2>

A step-up transformer has 26 turns on the primary coil and 720 turns on the secondary coil. If this transformer is to produce an output of 4100 V with a 16-mA current, what input current and voltage are needed?

<h2>Answer:</h2>

The input current and voltage needed are 443 mA and 148 V respectively.

<h2>Explanation:</h2>

In a step-up transformer, the relationship between the number of turns in its primary coil ( $N_{p}$ ), the number of turns in its secondary coil ( $N_{s}$ ), the input voltage ( $V_{p}$ ), the output voltage ( $V_{s}$ ), the input current ( $I_{p}$ ), and the output current ( $I_{s}$ ) is given by;

$\frac{N_{s} }{N_{p} }$ = $\frac{V_{s} }{V_{p} }$ = $\frac{I_{p} }{I_{s} }$

This implies that;

$\frac{N_{s} }{N_{p} }$ = $\frac{V_{s} }{V_{p} }$ ---------------------(i)

$\frac{N_{s} }{N_{p} }$ = $\frac{I_{p} }{I_{s} }$ ---------------------(ii)

From the question;

$N_{p}$ = 26 turns

$N_{s}$ = 720 turns

$V_{s}$ = 4100V

$I_{s}$ = 16mA = 16 x 10⁻³A

(a) Substitute these values into equation (ii) as follows;

$\frac{720}{26}$ = $\frac{I_{p} }{16*10^{-3}}$

Solve for $I_{p}$ ;

$I_{p}$ = 720 x 16 x 10⁻³ / 26

$I_{p}$ = 443 x 10⁻³

$I_{p}$ = 443 mA

Therefore the input current needed is 443mA

(b) Also, substitute those values into equation (i) as follows;

$\frac{720}{26}$ = $\frac{4100 }{V_{p} }$

Solve for $V_{p}$ ;

$V_{p}$ = 4100 x 26 / 720

$V_{p}$ = 148 V

Therefore, the input current needed is 148 V

5 0

3 years ago

Consider the smoothie example given in class: Write down the production function of Tutti Frutti Smoothie example given in class

mart [117]

Answer:

Production Function : TFSq = f { ingredient 1 ...... ing. i }

Increasing/ Constant/ Increasing Returns to Scale :

Output change > / = / < Input change respectively

Explanation:

Production Function is the relationship between production inputs & outputs, given technology. It denotes the maximum output that can be generated with given inputs.

Tutti Frutti Smoothie [TFS] quantity = Function of {Ingredient1.....ingredient i}

Returns to Scale represents change in output when all inputs change in same proportion.

Constant Returns to Scale [CRS] : Output Change = All inputs change
Increasing Returns to Scale [IRS] : Output Change > All inputs change
Negative Returns to Scale [NRS] : Output Change < All inputs change

When all inputs (ingredients) change by same proportion i.e get twice 2X :- If output of Tutti Frutti Smoothie increases by > 2X i.e 3X - IRS. If it increases equal ie 2X - CRS. If it increases lesser i.e 1.5X - CRS.

6 0

4 years ago

Which pendulum will.mobe faster​

Which pendulum will.mobe faster