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Fantom [35]
3 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]3 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]3 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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A certain amplifier has an open-circuit voltage gain of unity, an input resistance of 1 \mathrm{M} \Omega1MΩ and an output resistance of 100 \Omega100Ω The signal source has an internal voltage of 5 V rms and an internal resistance of 100 \mathrm{k} \Omega.100kΩ. The load resistance is 50 \Omega.50Ω. If the signal source is connected to the amplifier input terminals and the load is connected to the output terminals, find the voltage across the load and the power delivered to the load. Next, consider connecting the load directly across the signal source without the amplifier, and again find the load voltage and power. Compare the results. What do you conclude about the usefulness of a unity-gain amplifier in delivering signal power to a load?

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The voltage produced by the voltage-controlled source is:

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We can find voltage across the load, again by using voltage-divider principle:  

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P_l = V_o^2/R_l

     = 125*10^-9 W

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