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ruslelena [56]
1 year ago
8

Glider‌ ‌A‌ ‌of‌ ‌mass‌ ‌0.355‌ ‌kg‌ ‌moves‌ ‌along‌ ‌a‌ ‌frictionless‌ ‌air‌ ‌track‌ ‌with‌ ‌a‌ ‌velocity‌ ‌of‌ ‌0.095‌ ‌m/s.‌

‌It‌ ‌collides‌ ‌with‌ ‌glider‌ ‌B‌ ‌of‌ ‌mass‌ ‌0.710‌ ‌kg‌ ‌moving‌ ‌in‌ ‌the‌ ‌same‌ ‌direction‌ ‌at‌ ‌a‌ ‌speed‌ ‌of‌ ‌0.045‌ ‌m/s.‌ ‌After‌ ‌the‌ ‌collision,‌ ‌glider‌ ‌A‌ ‌continues‌ ‌in‌ ‌the‌ ‌same‌ ‌direction‌ ‌with‌ ‌a‌ ‌velocity‌ ‌of‌ ‌0.035‌ ‌m/s.‌ ‌What‌ ‌is‌ ‌the‌ ‌velocity‌ ‌of‌ ‌glider‌ ‌B‌ ‌after‌ ‌the‌ ‌collision?
Physics
1 answer:
NemiM [27]1 year ago
7 0

Answer:

vB' = 0.075[m/s]

Explanation:

We can solve this problem using the principle of linear momentum conservation, which tells us that momentum is preserved before and after the collision.

Now we have to come up with an equation that involves both bodies, before and after the collision. To the left of the equal sign are taken the bodies before the collision and to the right after the collision.

(m_{A}*v_{A})+(m_{B}*v_{B})=(m_{A}*v_{A'})+(m_{B}*v_{B'})

where:

mA = 0.355 [kg]

vA = 0.095 [m/s] before the collision

mB = 0.710 [kg]

vB = 0.045 [m/s] before the collision

vA' = 0.035 [m/s] after the collision

vB' [m/s] after the collison.

The signs in the equation remain positive since before and after the collision, both bodies continue to move in the same direction.

(0.355*0.095)+(0.710*0.045)=(0.355*0.035)+(0.710*v_{B'})\\v_{B'}=0.075[m/s]

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Consider an optical cavity of length 40 cm. Assume the refractive index is 1, and use the formula for Icavity vs wavelength to p
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Answer:

Diode Lasers  

Consider a InGaAsP-InP laser diode which has an optical cavity of length 250  

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4. The optical gain bandwidth (as measured between half intensity points) will  

normally depend on the pumping current (diode current) but for this problem  

assume that it is 2 nm.  

(a) What is the mode integer m of the peak radiation?  

(b) What is the separation between the modes of the cavity? Please express your  

answer as Δλ.  

(c) How many modes are within the gain band of the laser?  

(d) What is the reflection coefficient and reflectance at the ends of the optical  

cavity (faces of the InGaAsP crystal)?  

(e) The beam divergence full angles are 20° in y-direction and 5° in x-direction  

respectively. Estimate the x and y dimensions of the laser cavity. (Assume the  

beam is a Gaussian beam with the waist located at the output. And the beam  

waist size is approximately the x-y dimensions of the cavity.)  

Solution:  

(a) The wavelength λ of a cavity mode and length L are related by  

n

mL

2

λ = , where m is the mode number, and n is the refractive index.  

So the mode integer of the peak radiation is  

1290

1055.1

10250422

6

6

= ×

××× == −

−

λ

nL

m .  

(b) The mode spacing is given by nL

c f 2

=Δ . As

λ

c f = , λ

λ

Δ−=Δ 2

c f .  

Therefore, we have nm

nL f

c

20.1

)10250(42

)1055.1(

2 || 6

2 2 26

= ×××

× ==Δ=Δ −

− λλ λ .  

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For mode integer of 1290, nm

m

nL 39.1550

1290

10250422 6

= ××× ==

−

λ

Take m = 1291, nm

m

nL 18.1549

1291

10250422 6

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λ

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m

nL 59.1551

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10250422 6

= ××× ==

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λ .

Explanation:

8 0
2 years ago
the brightest , hottest, and most massive stars are the brilliant blue stars designated as spectral class O. if a class O star w
4vir4ik [10]

The speed is 0.956 m / s.

<u>Explanation</u>:

The kinetic energy is equal to the product of half of an object's mass, and the square of the velocity.

                   K.E = 1/2 \times m \times v^{2}

where K.E represents the kinetic energy,

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            v represents the velocity.

                  K.E = 1/2 \times m \times v^{2}

    1.10 \times 10^42 = 1/2 \times 3.26 \times 10^31 \times v^{2}

                     v^{2} = (1.10 \times 10^42 \times 2) / (3.26 \times 10^31)

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6 0
2 years ago
A transverse wave is traveling on a string stretched along the horizontal x-axis. The equation for the
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Answer:

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Wavenumber (k)=47.12 and wavelength  ( λ )  =  0.133 m

Time period(T)=0.0385 s and angular frequency  ( ω )  =  52 π  rad/s

Maximum speed of the string is given by  aw

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2 years ago
. Suppose you have a device that extracts energy from ocean breakers in direct proportion to their intensity. If the device prod
slava [35]

Answer:

4.988kW

Explanation:

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E = kI where k is the constant of proportionality.

From the formula; k = E/I

This shows that increase in energy extracted will lead to increase in its intensity and vice versa.

If the device produces 10.0 kW of power on a day when the breakers are 1.20 m high

E = 10kW and I = 1.20m

k = 10/1.20

k = 8.33kW/m

To know how much energy E that will be produced when they are 0.600 m high, we will use the same formula

k = E/I where;

k = 8.33kW/m

I = 0.600m

E = kI

E = 8.33 × 0.6

E = 4.998kW

The device will produce energy of 4.998kW when they are 0.600m high.

3 0
2 years ago
Read 2 more answers
A solid steel bar of circular cross section has diameter d 5 2.5 in., L 5 60 in., and shear modulus of elasticity G 5 11.5 3 106
8090 [49]

Answer:

A) θ = 4.9 x 10^(-3) rad

B) τ_max = 1.173 ksi

C) τ_a = 4.786 ksi

Explanation:

We are given;

diameter; d = 2.5 inches = 0.2083 ft

Length; L = 60 inches = 5 ft

Torque; T = 300 lb.ft

Shear modulus; G = 11.5 x 10^(6) psi = 11.5 x 144 x 10^(6) lb/ft² = 1.656 x 10^(9) lb/ft²

A) Now, formula to determine angle of twist is given as;

T/I_p = Gθ/L

Where I_p is polar moment of inertia

θ is angle of twist.

Now I_p = πd⁴/32 = π(0.2083)⁴/32 = 1.85 x 10^(-4) ft⁴

Thus, making θ the subject, we have;

TL/GI_p = θ

θ = (300 x 5)/(1.656 x 10^(9) x 1.85 x 10^(-4))

θ = 4.9 x 10^(-3) rad

B) Maximum shear stress is given by the formula ;

τ_max = (Gθ/L)(d/2)

From earlier, (Gθ/L) = T/I_p

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Thus,

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Converting to ksi = 168891.89/144000 ksi = 1.173 ksi

C) Shear stress at radial distance is given as;

τ_a = (Gθ/L)•r_a

r_a is given as 5.1 inches = 0.425m

τ_a = 1621621.6216 x 0.425 = 689189.189 lbf/ft²

Converting to ksi = 689189.189/144000 ksi = 4.786 ksi

7 0
2 years ago
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