Determine the change in total mechanical energy. (B) Determine the change in tot

Question

Determine the change in total mechanical energy.

(B) Determine the change in total mechanical energy. While the forces that the two objects exert on each other cannot change their total momentum, they can change the total kinetic energy in an inelastic collision such as the one being considered. All of the mechanical energy in the problem is kinetic energy. The change in kinetic energy is then At this point, we can either substitute the numerical values to evaluate K, or we could substitute in Equation (1) for f into the expression for K and simplify the expression before doing the calculation. The first procedure is easier if only a numerical answer is needed, while the second is more useful in exploring how the loss ?n kinetic energy depends on the velocities and masses of the colliding objects. Directly substituting in numerical values gives Following the second procedure instead leads to This could be used to calculate the same numerical answer, but it also shows various features that you might examine in the simulation. For example, notice that the change ?n kinetic energy depends on velocity only through the relative initial velocity, or difference in initial velocity (V1 ? y2), of the two particles. FINALIZE For a given initial velocity with the second object initially at rest, does the solution to this problem suggest that a large ratio of m1 to m2 or a small ratio produces the largest possible final velocity? When the two objects initially have equal and oppositely-directed velocities, what does the momentum conservation equation indicate will happen? If the two particles are of equal mass, and the second particle is initially stationary, what simple relation applies between the initial velocity and the final velocity, and why?

Explanation / Answer

Given that m1 = 14 kg

m2 = 11 kg

v1 = - 13 m/s

v2 = 2 m/s

Delta K = - 0.5 ( m1 m1 / ( m1 + m2 ) ) (v1 - v2 )2

= - 0.5 * (14*11/(14+11))*(-13 - 2)^2 = - 693 J

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