An object at rest explodes into three fragments. FIGURE EX11.32 shows the momentum vectors of two of the fragments. What is the momentum of the third fragment? Write your answer using unit vectors.

Question

Momentum vectors P1 and P2 of two fragments from an explosion, showing their directions and magnitudes.

Accepted Answer

Hey everyone. So this problem is dealing with conservation of momentum. Let's see what it's asking us. The stationary body undergoes an explosion, breaking into three fragments, determine the momentum of the third fragment. If the momentum of the two parts is as depicted in the figure below, then you can see in this graph, we have power P one and P two uh vectors where P one is in the negative X positive Y direction and P two is in the positive X positive Y direction. Our multiple choice answers here are a negative one common negative 10 B one comma negative 10 C negative one, comma 10 or D one comma negative 10. And all of those answers are in units of kilograms times meters per second, which is what we would expect for uh momentum. And so the key here is to recall the conservation of momentum theorem which states that our initial momentum is equal to our final momentum where our final momentum is the combined momentum of each of the three pieces that break apart. Our initial momentum is going to be zero because the um stationary body undergoes an explosion. So we can recall that momentum is given by mass multiplied by velocity. So if our initial velocity is zero, then our initial momentum is also zero. And so knowing that, and given the fact that we have a graph, we're using vectors, we can sum the X components to be equal to zero and the Y components to be equal to zero to find our X and Y components of this third part. So the way that looks is you can say P one X plus P two, X plus P three X equals zero. And then we look at our grass. So P one X, it's going to be negative four, P two X see that's three. So positive three and then we will take P three X subtract both sides. So we can isolate that variable and then divide both sides by negative one. So we have P three X is equal to one. And so that's our component of this um factor. And so when we go into our multiple choice answers, we can eliminate a and see we're going to do the same thing in the Y direction. So P one, Y plus P two, Y plus P three, Y equals zero. So P one Y is four positive four, P two, Y is positive six plus P three Y that all equals zero. So P three, Y equals negative 10, some four and six equals 10, subtract that from both sides. So P three, Y is negative 10. And so our correct answer written in vector notation is T three equals sorry, one or positive one, comment negative. And so that is the correct answer and that aligns with answer choice B so that's all we've got for this one, we'll see you in the next video.

An object at rest explodes into three fragments. FIGURE EX11.32 shows the momentum vectors of two of the fragments. What is the momentum of the third fragment? Write your answer using unit vectors.

Verified Solution

Key Concepts

Conservation of Momentum

Vector Addition

Unit Vectors