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Fantom [35]
2 years ago
5

three balls each have a mass m if a has a speed v just before a direct collision with B determine the speed of C after collision

the coefficient of restitution between each pair of balls is e. neglect the size of each ball
Engineering
2 answers:
ratelena [41]2 years ago
8 0

Answer:

Vc2= V(l+e) ^2/4

Vg2= V(l-e^2)/4

Explanation:

Conservation momentum, when ball A strikes Ball B

Where,

M= Mass

V= Velocity

Ma(VA)1+ Mg(Vg)2= Ma(Va)2+ Ma(Vg)2

MV + 0= MVg2

Coefficient of restitution =

e= (Vg)2- (Va)2/(Va)1- (Vg)1

e= (Vg)2- (Va)2/ V-0

Solving equation 1 and 2 yield

(Va)2= V(l-e) /2

(Vg)2= V(l+e)/2

Conservative momentum when ball b strikes c

Mg(Vg)2+Mc(Vc)1 = Mg(Vg)3+Mc(Vc)2

=> M[V(l+e) /2] + 0 = M(Vg)3 + M(Vc) 2

Coefficient of Restitution,

e= (Vc)2 - (Vg)2/(Vg)2- (Vc)1

=> e= (Vc)2 - (Vg)2/V(l+e) /2

Solving equation 3 and 4,

Vc2= V(l+e) ^2/4

Vg2= V(l-e^2)/4

puteri [66]2 years ago
5 0

Answer:

(vb)_3 = [v(1 - e)²]/4

(vc)_2 = [v(1 + e)²]/4

Explanation:

From conservation of momentum, when ball A strikes ball B, we have;

ma(va)_1 + mb(vb)_1 = ma(va)_2 + mb(vb)_2

Ball B is at rest before being hit. so (vb)_1 = 0 m/s

Thus, after being hit, we now have;

mv = m(va)_2 + m(vb)_2 - - - (eq1)

Coefficient of restitution is given as;

e =[((vb)_2) - ((va)_2)]/[((va)_1) - ((vb)_1)]

(vb)_1 = 0 m/s

Thus,we now have;

ve =[((vb)_2) - ((va)_2)] - - - (eq2)

If we divide each term in eq 1 by m, we have;

v = (va)_2 + (vb)_2 - - - - eq3

Now, let's put add eq 3 to eq 2 to obtain ;

v + ve = 2(vb)_2

v(1 + e) = 2(vb)_2

(vb)_2 = [v(1 + e)]/2 - - - - - eq(4)

Now let's subtract eq 2 from eq 3 to obtain;

v - ve = (va)_2 + (va)_2

v(1 - e) = 2(va)_2

(va)_2 = [v(1 - e)]/2

Now let's repeat the same process for conservation of momentum when ball B strikes ball C;

mb(vb)_2 + mc(vc)_1 = mb(vb)_3 + mc(vc)_2

Ball C is at rest before being hit. so (vc)_1 = 0 m/s

Thus, after being hit, we now have;

m(vb)_2 = m(vb)_3 + m(vc)_2

From earlier, (vb)_2 = [v(1 + e)]/2

Thus, we now have;

m[v(1 + e)]/2] = m(vb)_3 + m(vc)_2

Divide through by m;

[v(1 + e)]/2] = (vb)_3 + (vc)_2 - - - eq5

Coefficient of restitution is given as;

e =[(vc)_2) - ((vb)_3)]/[((vb)_2) - ((vc)_1)]

(vc)_1 = 0 m/s, so

e =[(vc)_2) - ((vb)_3)]/[((vb)_2)]

From earlier, (vb)_2 = [v(1 + e)]/2

Thus,

e =[(vc)_2) - ((vb)_3)]/ [v(1 + e)]/2]

e[v(1 + e)/2] = [(vc)_2) - ((vb)_3)]

- - - eq6

Let's add eq 5 to eq6;

[v(1 + e)/2](1 + e) = 2(vc)_2

2(vc)_2 = [v(1 + e)²]/2

(vc)_2 = [v(1 + e)²]/4

Also,let's subtract eq 6 from eq5 to obtain;

[v(1 + e)]/2](1-e)= 2(vb)_3

2(vb)_3 = [v(1 - e)²]/2

(vb)_3 = [v(1 - e)²]/4

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Answer:

Control mechanisms

Explanation:

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4 0
2 years ago
Six years ago, an 80-kW diesel electric set cost $160,000. The cost index for this class of equipment six years ago was 187 and
exis [7]

Answer:

new boiler total cost = $229706.825

new boiler total cost = $127512

Explanation:

given data

power p1 = 80 kW

cost C = $160000

cost index CI 1 = 187

cost index CI 2= 194

cost capacity factor f = 0.6

power p2 = 120 kW

current cost = $18000

to find out

total cost and cost of 40 kW

solution

we consider here CN cost for new boiler and CO cost for old boiler

and x is capacity of new boiler

first we find old boiler current cost that is

current cost CO = C × \frac{CI 1 }{CI 2 }   .............1

put here value

current cost = 160000 × \frac{194 }{187 }

new current cost = $165989.304

and

use here power sizing technique for 124 kW

CN/CO = (\frac{p2}{p1} )^{f}    ...............2

put here value and find CN

CN/CO = (\frac{p2}{p1} )^{f}  

CN / 165989.304 = (\frac{120}{80} )^{0.6}  

CN = 211706.825

so new cost = $211706.825

so

total cost for new boiler is

total cost = new cost + current cost

total cost = 211706.825 + 18000

new boiler total cost = $229706.825

and

for 40 kW new cost will be

use equation 2

CN/CO = (\frac{p2}{p1} )^{f}

CN / 165989.304 = (\frac{40}{80} )^{0.6}  

CN = 109512

so new cost is $109512

so

total cost for new boiler is

total cost = new cost + current cost

total cost = 109512 + 18000

new boiler total cost = $127512

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2 years ago
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Elza [17]
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3 0
2 years ago
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The air contained in a room loses heat to the surroundings at a rate of 50 kJ/min while work is supplied to the room by computer
Artemon [7]

Answer:

net amount of energy change of the air in the room during a 30-min period = 660KJ

Explanation:

The detailed calculation is as shown in the attached file.

4 0
2 years ago
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A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the
morpeh [17]

The magnitude of applied stress in the direction of 101 is 12.25 MPA and in the direction of 011, it is not defined.                                          

<u>Explanation</u>:        

<u>Given</u>:

tensile stress is applied parallel to the [100] direction

Shear stress is 0.5 MPA.

<u>To calculate</u>:

The magnitude of applied stress in the direction of [101] and [011].

<u>Formula</u>:

zcr=σ cosФ cosλ

<u>Solution</u>:

For in the direction of 101

cosλ = (1)(1)+(0)(0)+(0)(1)/√(1)(2)

cos λ = 1/√2

The magnitude of stress in the direction of 101 is 12.25 MPA

In the direction of 011

We have an angle between 100 and 011

cosλ = (1)(0)+(0)(-1)+(0)(1)/√(1)(2)

cosλ  = 0

Therefore the magnitude of stress to cause a slip in the direction of 011 is not defined.                                                                                                                                                                      

                                                                                   

                                                                                                                                                   

                                                                                                                                                             

5 0
2 years ago
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