Need help with this one, don\'t know how to do it. Example 8.5 Kinetic Energy in

Question

Need help with this one, don't know how to do it.

Example 8.5 Kinetic Energy in a Perfectly Inelastic Collision Problem We claimed that the maximum amount of kinetic energy was transformed to other forms in a perfectly inelastic collision. Prove this statement mathematically for a one-dimensional two-particle collision Solution Conceptualize We will assume that the maximum kinetic energy is transformed and prove that the collision must be perfectly inelastic Categorize We categorize the system of two particles as an isolated system. We also categorize the collision as one-dimensional Analyze Find an expression for the ratio of the final kinetic energy after the collision to the initial kinetic energy m1V1 2 2 2 2 The maximum amount of energy transformed to other forms corresponds to the minimum value of f. For fixed initial conditions, imagine that the final velocities Vif and v2f are variables. Minimize the fraction f by taking the derivative of f with respect to vif and setting the result equal to zero: dv 2 2 dv2f From the conservation of momentum condition, we can evaluate the derivative in (1). Differentiate the conservation of momentum condition with respect to Vif. (m1V1f m2v2f) dv1f

Explanation / Answer

we should look for completely inelastic collision.
In completely inelastic collision, final velocity of masses be 0
so,
kf = 0
So, maximum loss = Ki- Kf = Ki
a)
maximum loss = 0.5*m*vi^2
= 0.5*3.9*(5.1)^2
= 50.72 J
b)
maximum loss = 0.5*m*vi^2
= 0.5*5.3*(5.1)^2
= 68.93 J

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