Two carts collide and bounce apart. Cart 1 had a momentum of [tex]$-6 kg \cdot m / s$[/tex] before the collision. Cart 2 had a momentum of [tex]$10 kg \cdot m / s$[/tex] before the collision.

What is the total momentum of the carts after the collision?
A. [tex]$-16 kg \cdot m / s$[/tex]
B. [tex]$-10 kg \cdot m / s$[/tex]
C. [tex]$4 kg \cdot m / s$[/tex]
D. [tex]$10 kg \cdot m / s$[/tex]

Calculate the total momentum before the collision by adding the individual momenta of the two carts: − 6 k g "." m / s + 10 k g "." m / s = 4 k g "." m / s .
Apply the law of conservation of momentum, which states that the total momentum before the collision equals the total momentum after the collision.
Therefore, the total momentum after the collision is 4 k g "." m / s .
The total momentum of the carts after the collision is 4 k g "." m / s ​ .

Explanation

Understanding the Problem We are given the momentum of two carts before a collision and asked to find the total momentum of the carts after the collision. The key principle here is the conservation of momentum.

Conservation of Momentum The law of conservation of momentum states that the total momentum of a closed system remains constant if there are no external forces acting on the system. In simpler terms, the total momentum before a collision is equal to the total momentum after the collision.

Calculating Initial Total Momentum To find the total momentum before the collision, we add the individual momenta of the two carts: Cart 1: − 6 k g "." m / s and Cart 2: 10 k g "." m / s .

Summing the Momenta Total momentum before collision = ( − 6 k g "." m / s ) + ( 10 k g "." m / s ) = 4 k g "." m / s .

Applying Conservation of Momentum Since momentum is conserved, the total momentum after the collision is the same as the total momentum before the collision. Therefore, the total momentum after the collision is 4 k g "." m / s .

Final Answer The total momentum of the carts after the collision is 4 k g "." m / s ​ .


Examples
Imagine two billiard balls colliding on a pool table. The total momentum of the two balls before they hit is the same as the total momentum after they bounce off each other (assuming we ignore friction and other external forces). This principle helps predict the motion of objects after collisions, from car crashes to subatomic particle interactions. Understanding momentum conservation is crucial in physics and engineering for designing safer vehicles and understanding the behavior of systems in motion.

Answered by GinnyAnswer | 2025-07-08

The total momentum of the carts before the collision is 4 kg ⋅ m/s . According to the conservation of momentum, the total momentum after the collision remains the same at 4 kg ⋅ m/s . The correct answer is C .
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Answered by Anonymous | 2025-07-27