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A 2.0-kg ball moving eastward at 3.0 m/s suddenly collides with and sticks to a 4.0-kg ball moving northward at 2.0 m/s. What is the magnitude of the momentum of this system just after the collision?

Respuesta :

skyluke89

Answer:

10 kg m/s

Explanation:

Due to the law of conservation of momentum, the total momentum after the collision must be equal to the total momentum before the collision.

The momentum of each ball is given by:

p = mv

where m is the mass of the ball and v its velocity.

The momentum of ball 1 is:

p = mv = (2.0 kg)(3.0 m/s) = 6.0 kg m/s in the eastward direction

The momentum of ball 2 is:

p = mv = (4.0 kg)(2.0 m/s) = 8.0 kg m/s in the northward direction

The two momenta are in perpendicular directions, so the magnitude of the total momentum can be found as:

[tex]p=\sqrt{p_1^2 + p_2^2 }= \sqrt{(6.0 kg m/s)^2 + (8.0 kg m/s)^2}=10 kg m/s[/tex]

and due to the law of conservation of the momentum, this is also equal to the total momentum after the collision.

johanrusli

The magnitude of the momentum of this system just after the collision is about 10.0 kg.m/s

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Further explanation

Let's recall Impulse formula as follows:

[tex]\boxed {I = \Sigma F \times t}[/tex]

where:

I = impulse on the object ( kg m/s )

∑F = net force acting on object ( kg m /s² = Newton )

t = elapsed time ( s )

Let us now tackle the problem!

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Given:

mass of first ball = m₁ = 2.0 kg

velocity of first ball = v₁ = 3.0i m/s

mass of second ball = m₂ = 4.0 kg

velocity of second ball = v₂ = 2.0j m/s

Asked:

magnitude of the final momentum = p = ?

Solution:

We will use Conservation of Momentum formula to solve this problem:

[tex]\texttt{Total Momentum Before Collision = Total Momentum After Collision}[/tex]

[tex]m_1 v_1 + m_2 v_2 = \overrightarrow{p}[/tex]

[tex]2.0 ( 3.0\ \widehat{i} ) + 4.0 ( 2.0 \ \widehat{j} ) = \overrightarrow{p}[/tex]

[tex]\overrightarrow{p} = 6.0 \ \widehat{i} + 8.0 \ \widehat{j}[/tex]

[tex]|\overrightarrow{p}| = \sqrt{ 6.0^2 + 8.0^2 }[/tex]

[tex]|\overrightarrow{p}| = 10.0 \texttt{ kg.m/s}[/tex]

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Learn more

  • Velocity of Runner : https://brainly.com/question/3813437
  • Kinetic Energy : https://brainly.com/question/692781
  • Acceleration : https://brainly.com/question/2283922
  • The Speed of Car : https://brainly.com/question/568302
  • Average Speed of Plane : https://brainly.com/question/12826372
  • Impulse : https://brainly.com/question/12855855
  • Gravity : https://brainly.com/question/1724648

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

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