Bumper cars A and B undergo a collision during which the momentum of the combined system is conserved.

Which equation(s) correctly states the principle of conservation of momentum?

1. P⃗ A, i+P⃗ B, i=P⃗ A, f+P⃗ B, f

2. P⃗ A, i+P⃗ A, f=P⃗ B, i+P⃗ B, f

3. ΔP⃗ A=ΔP⃗ B

4. ΔP⃗ A+ΔP⃗ B=0

The correct statement to state the principle of conservation of momentum is PiA + PiB = PfA+PfB. Hence, option (1) is correct.

According law of conservation of momentum which states that the sum or momentum of two bodies before collision is equal to the momentum of the bodies after collision.

Given two bumper cars A and B that undergoes collision during which momentum is conserved, the type of collision that exists between the bumpers is inelastic collision

Let initial momentum of A is PiA and initial momentum of B is PiB, the sum of their momentum before collision is expressed as;

PiA + PiB (1)

If final momentum of A is PfA and initial momentum of B is PfB, the sum of their momentum after collision is expressed as;

PfA+PfB (2)

According to the law of conservation of linear momentum,  

 PiA + PiB = PfA+PfB

Thus, we can conclude that the correct statement to state the principle of conservation of momentum is PiA + PiB = PfA+PfB. Hence, option (1) is correct.

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1. P⃗ A,i+P⃗ B,i=P⃗ A,f+P⃗ B,f

Explanation:

Collision occurs when two bodies moving at different velocities exert force on each other through colliding. Collision can either be elastic or inelastic.

For elastic collision, both energy and momentum of the bodies is conserved i.e they separates after collision.

For inelastic collision, only momentum is conserved but not energy. The body sticks together after colliding and moves with a common velocity.

According law of conservation of momentum which states that the sum or momentum of two bodies before collision is equal to the momentum of the bodies after collision.

Given two bumper cars A and B that undergoes collision during which momentum is conserved, the type of collision that exists between the bumpers is inelastic collision

.

If initial momentum of A is PiA and initial momentum of B is PiB, the sum of their momentum before collision is expressed as;

PiA + PiB ... (1)

If final momentum of A is PfA and initial momentum of B is PfB, the sum of their momentum after collision is expressed as;

PfA+PfB ... (2)

According to the law, equation 1 is equal to equation 2

The fore the formula that states the law is expressed as;

PiA + PiB = PfA+PfB

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