5. (15 points) You have purchased two new examples of \"low-friction\" collision carts for your laboratory, and wish to characterize their behavior, so you arrange a collision between the two, producing the following graph: Velocty s - e e . - e Tirmwe (Secdnds) m_a is the purple {upper line that drops down) m_b is the green (lower line that moves up) {a) Describe the measurements you would have made to produce this graph, using standard laboratory cquipment, as well as the mitial conditions of this trial that would produce the given graph. {b) Derive an expression relating the inertias of the two carts, m_a and m_b, using physical constants as necessary and values determined from the graph (} Compute the slopes of the segments in the time intervals =(0,1) and t =(1.1.2) and offer a physical interpretation of their significance. {d) Based on the relationship between the masses, which cart should exhibit a greater force due to kinetic friction? Justify your answer. Cart A Cart B The mass does not atfect the force of friction {d) Which cart exhibits less acceleration due to kinetic friction? Derive expressions for the two friction coefficients, using physical constants as necessary and values determined from the graph. {e) Is this data consistent with the conservation of kinetic energy? Compute the coefficient of restitution from the observed data, and explain any observed discrepancies