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Olin [163]
3 years ago
13

A(n) 12500 lb railroad car traveling at 7.8 ft/s couples with a stationary car of 7430 lb. The acceleration of gravity is 32 ft/

s 2 . What is their velocity after the collision
Physics
1 answer:
navik [9.2K]3 years ago
7 0

To solve this problem we will apply the concepts related to the conservation of momentum. That is, the final momentum must be the same final momentum. And in each state, the momentum will be the sum of the product between the mass and the velocity of each object, then

\text{Initial Momentum} = \text{Final Momentum}

m_1u_1 +m_2u_2 = m_1v_1+m_2v_2

Here,

m_{1,2}= Mass of each object

u_{1,2}= Initial velocity of each object

v_{1,2}= Final velocity of each object

When they position the final velocities of the bodies it is the same and the car is stationary then,

m_2u_2 = (m_1+m_2)v_f

Rearranging to find the final velocity

v_f = \frac{m_2u_2}{ (m_1+m_2)}

v_f = \frac{ 12500*7.8}{ 12500+7430}

v_f = 4.8921ft/s

The expression for the impulse received by the first car is

I = m_1 (v-u)

I = \frac{W}{g} (v-u)

Replacing,

I = \frac{12500}{32.2}(4.89-7.8)

I = -1129.65lb\cdot s

The negative sign show the opposite direction.

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An insulated rigid tank initially contains 1.4-kg saturated liquid water and water vapor at 200°C. At this state, 25 percent of
Elan Coil [88]

Solution:

Mass of liquid water and water vapor in the insulated tank initially = 1.4 kg

Temperature = 200 °C

And 25% of the volume by liquid water is steam.

State 1

$m=\frac{V}{v}$

$m=m_f+m_g$

$1.4=\frac{0.25V}{v_f}+\frac{0.75V}{v_g}$

$1.4=\frac{0.25V}{1.1565 \times 10^{-3}}+\frac{0.75V}{0.1274}$       (taking the value of $v_g$ and $v_g$ at 200°C  )

$V=6.304 \times 10^{-3}$

Now quality of vapor

$x=\frac{m_g}{m}$

  $=3.377 \times 10^{-3}$

Internal energy at state 1 can be found out by

$u_1=u_f+xu_{fg}$

    $=850.65+3.377\times10^{-3}\times 1744.65$

    = 856.54 kJ/kg

After heating with the resistor for 20 minutes, at state 2, the tank contains saturated water vapor $v_2=v_g \text { and }\ x=1$

Tank is rigid, so volume of tank is constant.

$v_g=v_2=\frac{V}{m}$

$v_g=\frac{6.304\times 10^{-3}}{1.4}$

$v_g=4.502 \times 10^{-3} \ m^3 /kg$

Now interpolate the value to get temperature at state 2 with specific volume value to get final temperature

$T_2=360+(374.14-360)\left(\frac{0.004502-0.006945}{0.003155-0.006945}\right)$

   = 369.11° C

Internal energy at state 2

$u_2=2154.9 \ kJ/kg$

Now power rating of the resistor

$P=\frac{m(u_2-u_1)}{t}$

$P=\frac{1.4(2154.9-856.54)}{20 \times 60}$

  = 1.51 kW

6 0
3 years ago
What is a formula unit​
Nana76 [90]

A formula unit is the empirical formula for an ionic compound. It is the lowest possible ratio of the cations and anions of a given ionic compound.

3 0
3 years ago
A pilot in a small plane encounters shifting winds. He flies 26.0 km northeast, then 45.0 km due north. From this point, he flie
cluponka [151]

Answer:

a) v₃ = 19.54 km, b)  70.2º north-west

Explanation:

This is a vector exercise, the best way to solve it is finding the components of each vector and doing the addition

vector 1 moves 26 km northeast

let's use trigonometry to find its components

         cos 45 = x₁ / V₁

         sin 45 = y₁ / V₁

         x₁ = v₁ cos 45

         y₁ = v₁ sin 45

         x₁ = 26 cos 45

         y₁ = 26 sin 45

         x₁ = 18.38 km

         y₁ = 18.38 km

Vector 2 moves 45 km north

        y₂ = 45 km

Unknown 3 vector

          x3 =?

          y3 =?

Vector Resulting 70 km north of the starting point

           R_y = 70 km

we make the sum on each axis

X axis

      Rₓ = x₁ + x₃

       x₃ = Rₓ -x₁

       x₃ = 0 - 18.38

       x₃ = -18.38 km

Y Axis

      R_y = y₁ + y₂ + y₃

       y₃ = R_y - y₁ -y₂

       y₃ = 70 -18.38 - 45

       y₃ = 6.62 km

the vector of the third leg of the journey is

         v₃ = (-18.38 i ^ +6.62 j^ ) km

let's use the Pythagorean theorem to find the length

         v₃ = √ (18.38² + 6.62²)

         v₃ = 19.54 km

to find the angle let's use trigonometry

           tan θ = y₃ / x₃

           θ = tan⁻¹ (y₃ / x₃)

           θ = tan⁻¹ (6.62 / (- 18.38))

           θ = -19.8º

with respect to the x axis, if we measure this angle from the positive side of the x axis it is

          θ’= 180 -19.8

          θ’= 160.19º

I mean the address is

          θ’’ = 90-19.8

          θ = 70.2º

70.2º north-west

3 0
3 years ago
Two resistors of 12Ω and 2Ω are connected in parallel to a battery of 4 V. Current through 12Ω resistor will be _____________ an
Alex

Answer:

0.33  Amp

8 Watts

Explanation:

The current through the 12 Ω resistor will be given by Ohm's law:

4 V / 12 Ω = 1/3 Amp ≈ 0.33  Amp

The power dissipated on the 2 Ω resistor can be calculated via the formula: \frac{V^2}{R}  which gives:

4^2 / 2 = 8 Watts

6 0
3 years ago
Yoga not only builds flexibility, but strength and balance.<br><br> True or False
azamat

Answer:

True

Explanation:

I just know.

3 0
2 years ago
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