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3 years ago

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You are sitting in your car at rest at a traffic light with a bicyclist at rest next to you in the adjoining bicycle lane. As so

on as the traffic light turns green, your car speeds up from rest to 47.0 mi/h with constant acceleration 8.00 mi/h/s and thereafter moves with a constant speed of 47.0 mi/h. At the same time, the cyclist speeds up from rest to 23.0 mi/h with constant acceleration 12.00 mi/h/s and thereafter moves with a constant speed of 23.0 mi/h (a) For what time interval (in s) after the light turned green is the bicycle ahead of your car?
(b) What is the maximum distance (in ft) by which the bicycle leads your car during this time interval?

1 answer:

grigory [225]3 years ago

5 0

Answer:

Explanation:

Time duration during which acceleration exists in bicycle =

23 / 12 = 1.91 s

Time duration during which acceleration exists in car

= 47 / 8 = 5.875 s

Distance covered by bicycle during acceleration ( t = 1.91 s )

= 1/2 x 12 x (1.91)²

= 21.88 mi

Distance covered by car during this time ( t = 1.91 s )

= 1/2 x 8 x (1.91)²

7.64 mi ,

velocity of car after 1.91 s

= 8 x 1.91 = 15.28 mi/h

Let after time 1.91 , time taken by them to meet each other be t

Total distance covered by cycle = total distance covered by car

21.88 + 23 t = 7.64 + 15.28t + 4 t²

21.88 = 7.64 - 7.72t +4 t²

4 t² -7.72 t -14.24 = 0

t = 2.83 s

Total time taken

= 2.83 + 1.91

= 4.74 s

So after 4.74 s they will meet each other.

b ) Maximum distance occurs when velocity of both of them becomes equal .

Velocity after 1.91 s of bicycle

12 x 1.91 = 23 mi/h

Velocity after 1.91 s of car

8 x 1.91 = 15.28 mi/h . Let after time t , the velocity of car becomes 23

15.28 + 8t = 23

t = .965 s

So after time .965 s , car has velocity equal to that of bicycle.

The bicycle will travel a distance of

= 21.88 + .965 x 23 = 44.075 mi

car will travel a distance of

7.64 + 15.28 x .965 + .5 x 8 x .965²

= 7.64 + 14.75 + 3.72

= 26.11 mi

Distance between car and bicycle

= 44.075 - 26.11 = 17.965 mi

= 17.965 x 1760

= 31618.4 ft.

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<h3>Answer</h3><h3>7 Ns</h3><h3>Explanation</h3>

Given in the question,

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initial speed with which ball was hit with the bat = 30 m/s

final speed = 40 m/s

According to the scenario the whole scene is making a right angle triangle

So, to the solve the question we will use pythagorus theorem

<h3>Hypotenuse² = base² + height²</h3>

Here,

Hypotenuse= Magnitude of impulse

Base = 1st change of momentum

height = 2nd change of momentum

1st impulse (1st change of momentum)

p = m(1)v(1) = (0.14 kg)(40.0 m/s) = 5.6 kg m / s = 5.6 N s

2nd impulse (2nd change of momentum)

p = m(2)v(2) = (0.14 kg)(30.0 m/s) = 4.2 kg m / s = 4.2 N s

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3 years ago

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Answer:

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b. Power produced by the turbine = 2525.8kW

c. The rate of heat supply in the boiler = 6901.42Btu/s

d. Thermal efficiency of the cycle = 34.3%

Explanation:

In order to provide a solution, we must assume that ;

- The system is operating at a steady condition

- Kinetic and potential energy changes are negligible

Now from steam tables, we calculate specific volume $v$ and enthalpy $h$ as,

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( $S_f$ & $S_{fg}$ when pressure is 2psia)

$h_4S = h_f+x_4S*h_{fg}=95.96+(0.765)(1021.0)=877.025Btu/lb$

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Therefore,

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To calculate the mass flow rate of steam in the cycle, we use the formula

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where $1Kj = 0.947817 Btu$

The power output and the rate of heat addition are calculated thus,

$W_{T,out}=m(h_3-h_4)=(5.462lb/s)*(1364-925.7)Btu/lb*(\frac{1Kj}{0.94782Btu} )\\=5.462*438.3*1.055=2525.8KW$

$Q_{in}=mq_{in}=5.462(1263.54)=6901.46Btu/s$

The thermal efficiency of the cycle can be found thus;

$n_{th}=\frac{W_{net}}{Q_{in}} =\frac{2500}{6901.46}*(\frac{0.94782Btu}{1Kj} ) =0.343$

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2 years ago

Which of the following sets of properties leads to a high degree of thermal shock resistance? (A) High fracture strength High th

Rina8888 [55]

Answer:

The correct Answer is C) <u>High fracture strength,</u> <u>High Thermal Conductivity,</u> <u>Low modulus of elasticity,</u> <u>Low coefficient of thermal</u>

Explanation:

The ability of a solid to withstand sudden changes in temperature either during heating or cooling is known or referred to as Thermal Shock Resistance (TSR).

Thermal shock resistance is one of the most crucial factors of performance in solids for high temperature environments that can cause thermal stresses and risks for thermal shock damage.

Examples are as of such environments are energy conversion systems, electronic devices and cutting tools.

A common way to evaluate TSR is to look for maximum jump in surface temperature which a material can sustain without cracking. This is known as thermal conductivity.

Failure due to thermal shock can be prevented by;

Reducing the thermal gradient seen by the object, by changing its temperature more slowly or increasing the material's thermal conductivity
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upping its strength
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reducing its Young's modulus
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Thermal conductivity is an intensive physical property of a material that relates the heat flow through the material per unit area to temperature gradient across the material. The thermal conductivity of a material is basically a measure of its ability to conduct heat.

The other factor that contributes to a high degree of thermal shock is:

Fracture Strength: This is the ability of a material containing a crack to resist fracture or resist becoming brittle. For example, glass has a high strength, but the presence of a small fracture reduces the strength. Therefore, glass has low fracture resistance. Fracture toughness is an important consideration in hydraulic fracture design.

Modulus of Elasticity:

An object or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it is calculated or measured by a quantity known as Elastic Modulus (also known as Young modulus of elasticity)

A stiff material has a high Young's modulus and changes its shape only slightly under elastic loads (e.g. steel or diamond). A flexible material has a low Young's modulus and changes its shape considerably (e.g. rubbers).

Coefficient of thermal expansion (CTE) this refers to how the rate of change in the size of an object with respect of every degree change in temperature assuming that pressure remains the same. An object with low CTE is Fine Ceramics or Advanced Ceramics.

Cheers!

4 0

2 years ago