An object initially at rest on a horizontal OX axis explodes into two pieces . One piece moves just after explosion along the axis OX with a speed of 6m/s. What are the direction and the magnitude of the velocity of the second piece whose mass is three times that of the first?
momentum is conserved
the 2nd (larger) piece moves in the opposite direction at 1/3 the speed
I want to be good in physics
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the explosion and after the explosion should be the same.
Let's denote the mass of the first piece (moving along the OX axis with a speed of 6 m/s) as m1, and the mass of the second piece as m2 (which is three times the mass of the first piece, so m2 = 3m1).
The initial momentum (before the explosion) is zero since the object is at rest. After the explosion, the total momentum should still be zero (conservation of momentum).
The initial momentum is given by:
Initial momentum = m1 * v1 + m2 * v2
where v1 and v2 are the velocities of the first and second pieces, respectively.
Since the first piece is moving along the OX axis with a speed of 6 m/s, we have:
v1 = 6 m/s
Using the conservation of momentum, we can set up the equation:
0 = m1 * v1 + m2 * v2
Substituting v1 = 6 m/s and m2 = 3m1, we get:
0 = m1 * 6 + 3m1 * v2
Combining the terms, we have:
0 = 6m1 + 3m1 * v2
Simplifying the equation:
0 = 6 + 3 * v2
Rearranging the equation:
3 * v2 = -6
Dividing both sides by 3:
v2 = -2 m/s
Therefore, the magnitude of the velocity of the second piece is 2 m/s, and the direction is in the negative direction along the OX axis.