Particle A makes a perfectly elastic collision with another particle B at rest they fly apart in opposite direction with equal speeds the ratio of their masses mA/mB is?
3 Ma =Mb
To solve this problem, we can use the principle of conservation of momentum and the concept of elastic collisions.
In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum before the collision is equal to the total momentum after the collision, and the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
Let's assume that the masses of particle A and particle B are mA and mB, respectively. Since particle B is at rest initially, its momentum is zero.
Before the collision:
The momentum of particle A is given by mA * VA, where VA is the velocity of particle A.
The total momentum before the collision is just the momentum of particle A, since the momentum of particle B is zero: mA * VA.
After the collision:
Since the particles fly apart in opposite directions with equal speeds, the velocity of particle A after the collision is -VA (in the opposite direction), and the velocity of particle B is +VB (in the original direction). The magnitude of the velocities is the same, so |VA| = |VB|.
The momentum of particle A after the collision is -mA * |VA| (since it is in the opposite direction).
The momentum of particle B after the collision is mB * |VB|.
Applying the principle of conservation of momentum, we have:
Total momentum before the collision = Total momentum after the collision
mA * VA = -mA * |VA| + mB * |VB|
Since we know that |VA| = |VB|, we can simplify the equation:
mA * VA = -mA * VA + mB * VA
Now, let's solve for the ratio of their masses (mA/mB):
Divide both sides of the equation by VA:
mA = -mA + mB
Multiply both sides of the equation by -1:
-mA = mA - mB
Add mA to both sides of the equation:
0 = 2mA - mB
Multiply both sides of the equation by -1:
0 = mB - 2mA
Finally, divide both sides of the equation by 2mA:
mB / 2mA = 1
Thus, the ratio of their masses (mA/mB) is 1/2.
momentum (mv) is conserved.
So, if v is the same, m is the same.