Impulse and momentum of two particles

In summary, two particles with masses of 0.12kg and 0.08kg respectively, are initially at rest on a smooth horizontal table. Particle A is given an impulse in the direction AB, causing it to move with a speed of 3m/s directly towards B. After the particles collide, the speed of A is 1.2m/s, with its direction of motion unchanged. The magnitude of the impulse exerted on A in the collision is 0.216 Ns. The negative sign in the impulse indicates the direction of the average net force during the collision, which is opposite to the velocities of A. Therefore, the magnitude is taken as the answer, disregarding the negative sign.
  • #1
Pagey
19
0

Homework Statement



Two particles have mass 0.12kg and 0.08kg respectively. They are intially at rest on a smooth horizontal table. Particle A is then given an impulse in the direction AB so that it moves with speed 3m/s directly towards B.

Immediately after the particles collide the speed of A is 1.2m/s, its direction of motion being unchanged.

(c) find the magnitude of the impulse exerted on A in the collision.

Homework Equations



impulse = change in momentum (mv-mu)

The Attempt at a Solution



(c)

I get

impulse = mv-mu
= (0.12 x 1.2) - (0.12 x 3)
= - 0.216 Ns


But the mark scheme said the answer is + 0.216 Ns ... how can this be if the velocity after is less than the velocity before, i don't understand why??
 
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  • #2
Hi Pagey,

They asked for the magnitude of the impulse so they just need the absolute value.
 
  • #3
O so the maths is right. Ok it makes sense now, cheers!
 
  • #4
What is a negaitve impulse then, what does the - 0.216 mean? why is the answer negative (ingorning the fact it asks for magnitude)?
 
  • #5
Pagey said:
What is a negaitve impulse then, what does the - 0.216 mean? why is the answer negative (ingorning the fact it asks for magnitude)?

B consumed that momentum.
 
  • #6
The negative sign in the impulse indicates direction. The direction of the impulse is the same direction as the average net force during the collision.

So you called the velocities of particle A positive (they are both in the same direction in this problem). That set your coordinate system so that postive direction is in the direction of the velocities of A. But if A is slowing down, which direction is the average force on it? It is in the opposite direction of the velocities, and so since you already called the velocites positive, the average force and therefore the momentum must be negative.

(If particle A was moving to the right, then it needs a force to the left to slow it down.)
 

FAQ: Impulse and momentum of two particles

What is impulse and momentum?

Impulse and momentum are two related concepts in physics that describe the motion of objects. Momentum is a measure of an object's motion, while impulse is a measure of the change in an object's momentum over time.

How are impulse and momentum related?

Impulse and momentum are directly related through the equation p = mv, where p is momentum, m is mass, and v is velocity. This equation shows that an object's momentum is directly proportional to its mass and velocity.

How does the impulse-momentum theorem work?

The impulse-momentum theorem states that the change in an object's momentum is equal to the impulse applied to the object. Mathematically, this can be expressed as FΔt = Δp, where F is the force applied, Δt is the time over which the force is applied, and Δp is the change in momentum.

What is an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. This means that the objects involved in the collision bounce off each other without any loss of energy. In terms of impulse and momentum, this means that the total momentum before and after the collision is the same.

How does the conservation of momentum apply to two-particle systems?

The conservation of momentum applies to two-particle systems by stating that the total momentum of the system before and after the interaction between the two particles is the same. This means that the sum of the individual momenta of the two particles before the interaction is equal to the sum of their momenta after the interaction.

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