Respuesta :
Suppose car A is moving with a velocity Va, and car b with a velocity Vb,
According the principle of conservation of momentum:
Va x Ma + Vb x Mb = (Ma + Mb) V
V = (Va x Ma + Vb x Mb)/(Ma +Mb)
V = speed of cars after coupling
V = (Va x 20 mg + Vb x 15 mg)/(20 mg + 15 mg)
Put in the values of Va and Vb, and get the V
The velocity of the freight cars A and B after they are coupled to each other will be [tex]\boxed{0.43\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}}[/tex] towards the left.
Further Explanation:
Given:
The velocity of the freight car A is [tex]1.5\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}[/tex] .
The velocity of the freight car B is [tex]3\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}[/tex] .
The mass of the freight car A is [tex]20\,{\text{Mg}}[/tex] .
The mass of the freight car B is [tex]15\,{\text{Mg}}[/tex] .
Concept:
The two freight cars are moving towards each other and they collide with each other and after collision, the two cars are coupled to each other. When the two cars collide, the momentum of the system remains conserved.
The momentum of the body is the amount of motion contained by the particular body. It is expressed as the product of the mass and velocity of the body. It is a vector quantity.
[tex]\boxed{\vec p=m\times v}[/tex]
Apply the conservation of momentum for the cars before and after collision.
[tex]{m_A}{v_A}+{m_B}{v_B}=\left({{m_A}+{m_B}}\right){v_f}[/tex]
Substitute the values in the above expression.
[tex]\begin{aligned}(20\times1.5)+(15\times(-3))&=(20+15)v_{f}\\v_{f}&=\dfrac{30-45}{35}\\&=-0.429\text{ m/s}\\&\approx4.3\text{ m/s towards the left}\end{aligned}[/tex]
Thus, the velocity of the freight cars A and B after they are coupled to each other will be [tex]\boxed{0.43\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}}[/tex] towards the left.
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Answer Details:
Grade: College
Subject: Physics
Chapter: Momentum
Keywords:
Freight cars, cars A and B, cars collide and couple together, momentum, conservation of momentum, vector, velocity of cars, after coupling.
