Conservation of energy and momentum Problem

AI Thread Summary
The problem involves a 16 kg block that explodes into two fragments, with a total kinetic energy increase of 76.8 joules. Using conservation of momentum, the relationship between the velocities of the two fragments is established, leading to the calculation of the kinetic energy for each fragment. The first fragment, weighing 10 kg, slides 1.47 meters before stopping, while the second fragment's distance is calculated using the work-energy principle, factoring in friction. The equations used derive from the conservation of energy and the work done by friction. The final distance the 6 kg fragment slides before coming to rest is determined to be approximately 4.08 meters.
rzn972
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Homework Statement



A 16 kg block is initially at rest on a rough horizontal surface (uk= .2). The block has a small explosive charge inside it. The charge explodes, splinting the block into two fragments and adding 76.8 joules of kinetic energy. The other 10kg slides 1.47m along the rough surface before coming to Rest. How far does the other 6kg fragment slide along the rough surface before it comes to rest?
Must be solved using conservation laws.

Homework Equations





The Attempt at a Solution


Using conservation of momentum:
6va = 10vb
vb= .6 va
line 1: 76.8 = .5 * 6 *va^2 + .5* 10 * vb^2
va = 4
line 2: .5 * 6 * 4^2 + -.2 * 6 * g * da= 0
da= 4.08
I am not sure where the equation from line 1 and 2 came from.
Is line 1 using work = change in kinetic energy?
I am not sure what equation is used for line 2.
 
Physics news on Phys.org
line 1 computes total kinetic energy after explosion
line 2 uses the work of friction force and sets it equal to the change in kinetic energy
 

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