The momentum of the system of two cars after the collision will be [tex]\boxed{0.50\text{ kg.m/s}}[/tex].
Explanation:
Given:
The mass of each of the laboratory car is [tex]1\text{ kg}[/tex].
The velocity of the laboratory cart is [tex]0.50\text{ m/s}[/tex].
Concept:
The momentum of a body is defined as the amount of motion contained in the body at the particular instant. The momentum of the body is defined as the product of the mass and velocity of the body.
Write the expression for the momentum of the laboratory cart.
[tex]p_{1}=m\times{v}[/tex] ...... (1)
Here, [tex]p_1[/tex] is the momentum of the cart, [tex]m[/tex] is the amss of the cart and [tex]v[/tex] is the velocity of the cart.
The initial momentum of the laboratory cart which is in motion.
[tex]\begin{aligned}p_{i}&=(1\text{ kg})\times{(0.5\text{ m/s})}\\&=0.5\text{ kg.m/s}\end{aligned}[/tex]
As the cart collides and the surface is frictionless, the momentum of the system will remain conserved after the collision.
The two carts will stick to one another after the collision. So, the mass of the system will be [tex]2\text{ kg}[/tex] after the collision and the speed of the carts after collision is [tex]0.25\text{ m/s}[/tex].
Substitute the value of mass and velocity of the system in the equation of momentum.
[tex]\begin{aligned}p'&=(2\text{ kg})\times(0.25\text{ m/s})\\&=0.50\text{ m/s}\end{aligned}[/tex]
Thus, the momentum of the system of two cars after the collision will be [tex]\boxed{0.50\text{ kg.m/s}}[/tex].
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Momentum
Keywords:
laboratory cart, 0.50 m/s, east, collides, momentum, conserved, total momentum, similar cart, sticks, velocity.
