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forsale [732]
2 years ago
5

A 4kg and 5kg bodies moving on a frictionless horizontal surface at a velocity of ( -6i )m/s and ( +3 )m/s respectively. Collide

a head on elastic collision. What is the velocity ( magnitude and direction) of the each body after collision?
Physics
1 answer:
Vladimir [108]2 years ago
3 0

Answer:

4 kg → +4 m/s

5 kg → -5 m/s

Explanation:

The law of conservation of momentum states that:

  • m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
  • left side → velocities before collision
  • right side → velocities after collision

You'll notice that we have two missing variables: v₁' & v₂'. Assuming this is a perfectly elastic collision, we can use the conservation of kinetic energy to set the initial and final velocities of the individual bodies equal to each other.

  • v₁ + v₁' = v₂ + v₂'  

Let's substitute all known variables into the first equation.

  • (4)(-6) + (5)(3) = (4)v₁' + (5)v₂'
  • -24 + 15 = 4v₁' + 5v₂'
  • -9 = 4v₁' + 5v₂'  

Let's substitute the known variables into the second equation.

  • (-6) + v₁' = (3) + v₂'
  • -9 = -v₁' + v₂'
  • 9 = v₁' - v₂'  

Now we have a system of equations where we can solve for v₁ and v₂.

  • -9 = 4v₁' + 5v₂'
  • 9 = v₁' - v₂'  

Use the elimination method and multiply the bottom equation by -4.

  • -9 = 4v₁' + 5v₂'
  • -36 = -4v₁' + 4v₂'

Add the equations together.

  • -45 = 9v₂'
  • -5 = v₂'

<u>The final velocity of the second body (5 kg) is -5 m/s</u>. Substitute this value into one of the equations in the system to find v₁.  

  • 9 = v₁' - v₂'
  • 9 = v₁' - (-5)
  • 9 = v₁' + 5
  • 4 = v₁'

<u>The final velocity of the first body (4 kg) is 4 m/s.</u>

<u></u>

We can verify our answer by making sure that the law of conservation of momentum is followed.

  • m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
  • (4)(-6) + (5)(3) = (4)(4) + (5)(-5)
  • -24 + 15 = 16 - 25
  • -9 = -9

The combined momentum of the bodies before the collision is equal to the combined momentum of the bodies after the collision. [✓]

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Soloha48 [4]

Answer:

Should be B

Explanation:

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6 0
3 years ago
The current in a series circuit is 19.3 A. When an additional 7.40-Ω resistor is inserted in series, the current drops to 13.4 A
Bogdan [553]

Answer:

16.8ohms

Explanation:

According to ohm's law which states that the current passing through a metallic conductor at constant temperature is directly proportional to the potential difference across its ends.

Mathematically, V = IRt where;

V is the voltage across the circuit

I is the current

R is the effective resistance

For a series connected circuit, same current but different voltage flows through the resistors.

If the initial current in a circuit is 19.3A,

V = 19.3R... (1)

When additional resistance of 7.4-Ω is added and current drops to 13.4A, our voltage in the circuit becomes;

V = 13.4(7.4+R)... (2)

Note that the initial resistance is added to the additional resistance because they are connected in series.

Equating the two value of the voltages i.e equation 1 and 2 to get the resistance in the original circuit we will have;

19.3R = 13.4(7.4+R)

19.3R = 99.16+13.4R

19.3R-13.4R = 99.16

5.9R = 99.16

R= 99.16/5.9

R = 16.8ohms

The resistance in the original circuit will be 16.8ohms

5 0
3 years ago
1. The resistance of an electric device is 40,000 microhms. Convert that measurement to ohms.
lidiya [134]

Answer:

The answer would be 0.04ohms.

Explanation:

Hopefully this helps

4 0
2 years ago
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Calculate the electric field at one corner of a square 50 cm on a side if the other corners are occupied by 250x10-7C (charges)
SIZIF [17.4K]

The electric field at one corner of a square is 1614217 N/C.

Explanation:

The distance between x and y direction diagonals.

As per the given details the distance between diagonals is calculated as

0.5² + 0.5² = c²  =>  c = 0.707 m

Charge to the right:  In x direction

In order to find the electric charge towards x direction

we use e = kq/r² formula

As 'k' is coulomb's constant it's value is 9 x 10^{9} N m²/C²

e = (9 x 10^{9})(250 x 10^{-7}) / (0.5)²

e = 9 x 10^{5} N/C

Charge diagonal:

e = kq/r²

e = [(9 x 10^{9})(250 x 10^{-7}) / (0.707)²] cos 45

e = 225000√2 N/C

X direction sum = 1218198 N/C.

Similarly as shown in x direction the charge is same for y direction also

Charge below:  For y direction

e = kq/r²

e = (9 x 10^{9})(250 x 10^{-7}) / (0.5)²

e = 9 x 10^{5} N/C

Charge diagonal:

e = kq/r²

e = [(9 x 10^{9})(250 x 10^{-7}) / (0.5)²] sin 45

e = 159099 N/C

Y direction sum = 1059099 N/C

Resultant electric field strength:

1218198 ² + 1059099² = e²

e = 1614217 N/C [45 degrees below the horizontal]

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Answer:

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3 years ago
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