a particle a of mass 2kg and particle b of mass 1kg are connected by alight elastic string c, and initially held at rest 0.9m apart on a smooth horizontal table with the string in tension. they are then simultaneously released . the string releases 12j of energy as it contracts to its natural length. calculate the velocity acquired by each of the particles. Where do the particles collide

the two particles experience the same force (the tension in the string)

since A has twice the mass of B, its acceleration will be half of B's

so A's final velocity will be half of B's

(1/2 * 2kg * v^2) + (1/2 * 1kg * (2v)^2) = 12J

2 v^2 + 4 v^2 = 24

v^2 = 4 ___ v = 2 ___ 2v = 4

because B's acceleration and final velocity are twice that of A, B travels twice the distance of A

A + 2A = .9m

A = .3m , B = .6m

To calculate the velocity acquired by each particle, we can use the principle of conservation of energy.

Initially, both particles are at rest, so the total initial energy of the system is zero. As the string contracts, it releases 12J of energy. This energy is divided between the kinetic energy of both particles.

Let's denote the velocity acquired by particle A as vA and particle B as vB.

The kinetic energy of a particle can be calculated using the formula: KE = (1/2)mv^2, where m is the mass of the particle and v is its velocity.

Let's calculate the kinetic energy of each particle.

For particle A:
KEA = (1/2)(2kg)(vA^2)

For particle B:
KEB = (1/2)(1kg)(vB^2)

Since the total energy released by the string is divided between the particles, we have the equation:

KEA + KEB = 12J

Substituting the equations for KEA and KEB, we get:

(1/2)(2kg)(vA^2) + (1/2)(1kg)(vB^2) = 12J

Simplifying the equation:

2vA^2 + vB^2 = 24J

Since the particles are connected by a light elastic string, they will have the same velocity after collision. Hence, vA = vB = v.

Substituting v for vA and vB:

2v^2 + v^2 = 24J

Simplifying:

3v^2 = 24J

v^2 = 8J

Taking the square root of both sides:

v = √8J

v ≈ 2.83 m/s

Therefore, each particle acquires a velocity of approximately 2.83 m/s.

To determine where the particles collide, we need more information about the system, such as the length or geometry of the table, or any other constraints. Without this additional information, it is not possible to determine the exact collision point.