Conservation of Momentum in a explosion

[mvl46566]

Homework Statement

A firecracker, initially at rest, explodes into two fragments. The first, of mass 14g, moves in the positive x direction at 48m/s. The second moves at 32m/s. Find the mass and direction of its motion.

Homework Equations

p=mv

The Attempt at a Solution

So I know momentum is conserved in this situation. I set m1v1 equal to m2v2 and found the mass of the second fragment to be .041 kg or 41 grams. I think this goes in the negative x direction because the initial momentum is zero and so the sum of all momentums would have to be zero, but I am not sure.

 

[Astronuc]

Homework Statement

A firecracker, initially at rest, explodes into two fragments. The first, of mass 14g, moves in the positive x direction at 48m/s. The second moves at 32m/s. Find the mass and direction of its motion.

Homework Equations

p=mv

The Attempt at a Solution

So I know momentum is conserved in this situation. I set m1v1 equal to m2v2 and found the mass of the second fragment to be .041 kg or 41 grams. I think this goes in the negative x direction because the initial momentum is zero and so the sum of all momentums would have to be zero, but I am not sure.

Correct. In the conservation of momentum, the momentum after the explosion = momentum before the explosion. What is the momentum before the explosion?

Remember that momentum is a vector, which has magnitude and direction. We can have to vectors of the same magnitude, but opposite direction, so the sum is zero.

 

[kerimek]

Your solution is correct. The conservation of momentum principle states that the total momentum before and after a collision or explosion remains constant. In this case, the initial momentum is zero since the firecracker was at rest. Therefore, the total momentum after the explosion must also be zero. Since one fragment is moving in the positive x direction, the other fragment must have an equal but opposite momentum in the negative x direction to balance out the total momentum to zero. This is why the mass of the second fragment is negative and its direction of motion is in the negative x direction. Great job using the conservation of momentum principle to solve this problem!