Energy Sharing.? An object with mass ?m?, initially at rest, explodes into two fragments, one with mass ?mA? and the other with mass ?mB?, where ?mA? + ?mB? = ?m?. (a) If energy ?Q? is released in the explosion, how much kinetic energy does each fragment have immediately after the explosion? (b) What percentage of the total energy released does each fragment get when one fragment has four times the mass of the other?
Solution 100P Step 1 of 3: Let the final speed of the two fragments be v and v . They must move in opposite A B directions after the explosion. Momentum is conserved in the explosion. Step 2 of 3: (a) Since the initial momentum of the system is zero, conservation of momentum says m v = m v A A A A mA vB= ( m )vA B K A K =BQ............................(1) 1m v + m (1 mA ) v = Q 2 A A 2 B mB A m 1m v (1 + A) = Q 2 A A mB K = Qm A 1+mB m B = ( mA+mB)Q Substitute in (1) find K B K A K =BQ K B Q K A m = Q ( B )Q m Am B m = Q(1 B m Am B m A = ( m +m )Q A B