Introduction to Collisions Learning Goal: To understand how to find the velociti

Question

Introduction to Collisions Learning Goal: To understand how to find the velocities of objects after a collision. There are two main types of collisions that you will study: perfectly elastic collisions and perfectly inelastic collisions. When two objects collide elastically, both total kinetic energy and total momentum are conserved. These two conservation laws allow the final motion of the two objects to be determined. When two objects collide inelastically, total momentum is conserved, but the total kinetic energy is not conserved. After an inelastic collision the two objects are stuck together, and thus travel with the same final velocity; this fact, together with conservation of momentum, allows the final motion of the two objects to be calculated. In reality, there is a range of collision types, with elastic and perfectly inelastic at the extreme ends. These extreme cases allow for a more straightforward analysis than the in-between cases. The applet at the end of the problem will give you a chance to explore the "in-between" collisions. Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary...

Explanation / Answer

Here

part A)

Using conservation of momentum

m * v1 + m2 * v2 = m * v

v1 + v2 = v ----(1)

as the collision is elastic

v2 - v1 = v

solving both

v2 = v

v1 = 0

(v1 , v2) = (0 , v)

part B)

as this collision is inelastic

v2 = v1

Now , Using conservation of momentum

(m + m) * v1 = (m * v)

v1 = v/2

the velocities are

(v1 , v2) = (v/2 , v/2)

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