Question

block 1 with mass m1 slides along an x axis across a frictionless floor and then undergoes an elastic collision with a stationary block 2 with mass m2. the figure shows a plot of position x versus time t of block 1 until the collision occurs at position xc and time tc.

Answer 1

The question deals with elastic and inelastic collisions on a frictionless surface, where final velocities and energy changes are analyzed using conservation laws in classical mechanics.

Step-by-step explanation:

The student's question pertains to collisions, focusing on elastic and inelastic collisions in one dimension on a frictionless surface.

In both cases, we analyze the dynamics of the system using concepts from classical mechanics, specifically linear momentum and kinetic energy conservation in the case of elastic collisions or momentum conservation alone in the case of inelastic collisions.

Elastic Collisions

In an elastic collision, both momentum and kinetic energy are conserved. Therefore, the final velocities of the masses can be determined by applying these conservation laws.

For example, when two masses of equal mass undergo an elastic collision, they typically exchange velocities if their initial velocities are equal in magnitude but opposite in direction.

The momentum p is equal to mass times velocity (mv) and kinetic energy KE is 1/2 mass times the square of the velocity (1/2 mv2).

Inelastic Collisions

For an inelastic collision, such as when two masses stick together after the collision, only momentum is conserved. The final common velocity of the combined mass can be found using the conservation of momentum.

In this scenario, the kinetic energy is not conserved and there is a loss of kinetic energy which is transformed into other forms of energy, such as heat or internal energy.