Center of momentum frame question:

[Michael12]

Homework Statement

An 8.0-kg object is sliding across the ice at 2.34 m/s in the positive x direction. An internal explosion occurs, splitting the object into two equal chunks and adding 16 J of kinetic energy to system. The explosive separation takes place over a 0.16-s time interval. Assume that the one of the chunks after explosion moves in the positive x direction. The x component of the average acceleration of this chunk during the explosion is a(front,x), the x component of the average acceleration of the other chunk during the explosion is a(rear,x). What are the x components of the average accelerations of the two chunks during the explosion?

Homework Equations

V[cm] = (m[1]v[1]+m[2]v[2]) / (m[1]+m[2]) = v[1] for this problem since there is only one initially moving mass
K[e,cm] = 1/2 * m[total] * v^2[cm]
probably more equations but I'm not sure

The Attempt at a Solution

I honestly don't even know where to begin with this problem. I'm really lost in this class so far and I don't understand how to work in the 16 joules or how kinetic energy changes in a center of mass reference frame. Please help

 

[kuruman]

Welcome to PF.

You can view an explosion as a perfectly inelastic collision with time running backwards. What is common to all collisions? The same is common to all explosions. As for the 16 J, you know that energy is lost in an inelastic collision. This means that KE_after < KE_before. When you reverse time and have an explosion, KE_after > KE_before. Can you see where to begin now?

 

[Andrew Mason]

Homework Statement

An 8.0-kg object is sliding across the ice at 2.34 m/s in the positive x direction. An internal explosion occurs, splitting the object into two equal chunks and adding 16 J of kinetic energy to system. The explosive separation takes place over a 0.16-s time interval. Assume that the one of the chunks after explosion moves in the positive x direction. The x component of the average acceleration of this chunk during the explosion is a(front,x), the x component of the average acceleration of the other chunk during the explosion is a(rear,x). What are the x components of the average accelerations of the two chunks during the explosion?

1. The analysis is simplest in the centre of mass (COM) frame, where the initial momentum is 0. After explosion, the momentum of each chunk is $p_i = \frac{m}{2}v_i$ and the two momenta must sum to 0 (conservation of momentum). Write out the equation for total momentum in the COM frame after the collision in terms of mass and velocity of each chunk. How are the magnitudes of the velocities (ie. speeds) related?

2. Next, write out the equation for kinetic energy in the COM frame after the collision in terms of the velocities $v_i$. (hint: How much KE did the explosion add?). From this (and knowing the relationship between the speeds of each chunk) you should be able to determine the final velocities in the COM frame.

3. Finally, you must relate these velocities to the average acceleration and time to find the average accelerations. How are they related? (hint: watch the signs).

AM