The x-component of the velocity of the third piece = -16.87 m/s

[aszymans]

Explosion of ball!

Homework Statement

An object with total mass mtotal = 16.6 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.9 kg moves up and to the left at an angle of θ1 = 18° above the –x axis with a speed of v1 = 25.5 m/s. A second piece with mass m2 = 5.5 kg moves down and to the right an angle of θ2 = 23° to the right of the -y axis at a speed of v2 = 23.9 m/s.

What is the x-component of the velocity of the third piece

Homework Equations

I know the final P=0 and the mass of the third object = 6.2kg

The Attempt at a Solution

I tried finding the x component for m2 which I got to be 10.144 by tan(23)*23.9, and we know the x component of m1, so I multiplied these x components by their masses and added them, since P=0 I then subtracted them to the other side of the = sign to give me the opposite. I don't know if I am on the right track or not. I have tried every way I can think of to do this problem, can't get the right answer.

 

[ehild]

You are on the right track that the sum of the momentums is zero. Show your calculations in detail. I can not follow you from that you have. How do you get the x component of a vector?

ehild

 

[aszymans]

I was doing it wrong, and then I thought I was doing it correctly now, but am still getting the wrong answer. I am finding the x and y of each piece that we are given theta by taking the cos(theta)=x/v then found x(cm) by taking the x value and multiplying it mass then dividing by total mass, once I got both x's for both thetas given I found the difference between the two , I did this because I know P=0 so I want them to sum to 0, since I have one piece that goes in the negative x direction I made that negative and still can't figure out what I am doing wrong.

 

[ehild]

Write out the calculation with formulas. What are the x components of the momentum of both pieces?

ehild

 

[asteriatic]

I would approach this problem by first setting up a coordinate system and labeling the initial and final velocities of each piece. I would then use the conservation of momentum equation (P_initial = P_final) to solve for the x-component of the third piece's velocity.

P_initial = 0 (since the object is initially at rest)
P_final = m1v1x + m2v2x + m3v3x
We know the values for m1, v1x, m2, and v2x, so we can plug those in and solve for v3x.

m1v1x + m2v2x + m3v3x = 0
(4.9)(25.5cos18) + (5.5)(23.9cos23) + (6.2)v3x = 0
v3x = -16.87 m/s

Therefore, the x-component of the velocity of the third piece is -16.87 m/s. This indicates that the third piece is moving to the left, which makes sense since the other two pieces are moving in opposite directions. The negative sign indicates that the third piece is moving in the negative x direction.

As for the explosion of the ball, this problem is an example of an inelastic collision, where the total momentum of the system is conserved but the total kinetic energy is not. The explosion causes the object to break into multiple pieces and each piece has its own velocity, direction, and mass. By using the conservation of momentum equation, we can calculate the velocities of each piece after the explosion.