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maks197457 [2]
3 years ago
13

Applying the Law of Conservation of Momentum

Physics
1 answer:
IgorC [24]3 years ago
6 0

answer

the final velocity is half of train car B's initial velocity

explanation

the conservation of momentum states that the initial and final total momentum are equal

m1v1 + m2v2 for initial momentum

(m1 + m2)v3 for final momentum because both cars stick together so their masses are combined

m1v1 + m2v2 = (m1 + m2)v3

since the mass of both are the same, m1 = m2

m1v1 + m1v2 = (m1 + m1)v3

m1(v1 + v2) = 2m1v3

divide both sides by m1

v1 + v2 = 2v3

since train car A is initially at rest, v1 = 0

v2 = 2v3

v3 = v2 * 1/2

the final velocity is half of train car B's initial velocity

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A car accelerates from rest for 8.0 s, and reaches a speed of 66 m/s. How far will the
PSYCHO15rus [73]

Answer: C

Explanation:

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Now use this kinematic equation to find the displacement:

v_f^2=v_i^2+2a*d\\66^2=0^2+2(8.25)d\\4356=16.5d\\d=264m

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3 years ago
At a rock concert, the sound intensity 1.0 m in front of the bank of loudspeakers is 0.10 W/m². A fan is 30 m from the loudspeak
Klio2033 [76]

To solve this problem we will apply the concepts related to the Area, the power and the proportionality relationships between intensity and distance.

The expression for sound power is,

P = AI

Here,

A = Area

I = Intensity

P = Power

At the same time the area can be written as,

A = \frac{\pi d^2}{4}

Now the intensity is inversely proportional to the square of the distance from the source, then

I \propto \frac{1}{r^2}

The expression for the intensity at different distance is

\frac{I_1}{I_2}= \frac{r^2_2}{r_1^2}

Here,

I_1 = Intensity at distance 1

I_2 = Intensity at distance 2

r_1 = Distance 1 from light source

r_2 = Distance 2 from the light source

If we rearrange the expression to find the intensity at second position we have,

I_2 = I_1 (\frac{r_1^2}{r_2^2})

If we replace with our values at this equation we have,

I_2 = (0.10W/m^2)(\frac{1.0m^2}{30.0m^2})

I_2 = 1.11*10^{-4} W/m^2

Now using the equation to find the area we have that

A = \frac{\pi (8.4*10^{-3}m)^2}{4}

A = 5.5*10^{-5}m^2

Finally with the intensity and the area we can find the sound power, which is

P = AI

P = (5.5*10^{-5}m^2)(1.11*10^{-4}W/m^2)

P = 6.1*10^{-9}J/s

Power is defined as the quantity of Energy per second, then

E = 6.1*10^{-9}J

8 0
3 years ago
Three charges are located at a different position in a plane: q1= 10μC at →r1=(5,6)cm q2=−27μC at →r2=(−6,10)cm and q3=−12μC at
sasho [114]

Answer:

 E = (2.29 i ^ - 0.917 j ^) 10⁶ N / C

 E_{total} = 2,467 10⁶ N / A       θ = -21.8      

Explanation:

For this exercise we will use that the electric field is a vector quantity, so the total field is

        E_total = E₁₃ + E₂₃

bold font vectors .  We can work with the components of the electric field in each axis

X- axis

       E_ total x = E₁₃ₓ + E_{23x}

y-axis  

      E_{total y} = E_{13y} + E_{23y}

the expression for the electric field is

       E = k q / r²

where r is the distance between the charge and the positive test charge

       

in this exercise

Let's find the field created by charge 1

q₁ = 10 μC = 10 10⁻⁶ C

x₁ = 5 cm = 0.05 m

x₃ = 21 cm = 0.21 m

         E_{13x} = 9 10⁹ 10 10⁻⁶ / (0.21 -0.05)²

         E_{13x} = 3.516 10⁶ N / C

y₁ = 6 cm = 0.06 cm

y₃ = -12 cm = -0.12 m

        E_{13y} = 9 10⁹ 10 10⁻⁶ / (-0.12 - 0.06)²

        E_{13y} = 2,777 10⁶ N / C

let's find the field produced by charge 2

q₂ = -27 μC = - 27 10⁻⁶ C

x₂ = -6 cm = -0.06 m

x₃ = 0.21 m

        E_{23x} = 9 10⁹ 27 10⁻⁶ / (0.21 + 0.06)²

        E_{23x} = 1.23 10⁶ N / A

y₂ = 10 cm = 0.10 m

y₃ = -0.12 m

        E_{23y} = 9 10⁹ 27 10⁻⁶ / (-0.12 - 0.10)²

        E_{23y} = 1.86 10⁶ N / C

Taking the components we can calculate the total electric field, we must use that charge of the same sign repel and attract the opposite sign, remember that the test charge is always considered positive.

       E_{total x} = E_{13x} - E_{23x}

       E_{total x} = (3.516 - 1.23) 10⁶

       E_{total x} = 2.29 10⁶ N / A

       

       E_{total y} = -E_{13y} + E_{23y}

       E_{total y} = (-2.777 +1.86) 10⁶ N / A

       E_{total y} = -0.917 10⁶ N / A

we can give the result in two ways

         E = (2.29 i ^ - 0.917 j ^) 10⁶ N / C

or in the form of modulus and angle, let's use the Pythagorean theorem to find the modulus

                E_{total} = √ (E_{total x}^2 + E_{total y}^ 2)

                 E_{total} = √ (2.29² + 0.917²) 10⁶

                E_{total} = 2,467 10⁶ N / A

let's use trigonometry for the angle

                tan θ = E_total and / E_totalx

                θ = tan⁻¹ E_{total y} / E_{total x}

                θ = tan⁻¹ (-0.917 / 2.29)

                θ = -21.8

The negative sign indicates that the angle is measured with respect to the x-axis in a clockwise direction.

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How will frost on the wings of an airplane affect takeoff performance?
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Frost will disturb the smooth flow of air over the wing, unpleasantly distressing its lifting competence. In other words, this spoils the even flow of air over the wings, by this means decreasing lifting capability. Also, frost may avoid the airplane from becoming flying at normal departure speed.

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