1. Examine the graph of final kinetic energy vs. initial kinetic energy during a

Question

1. Examine the graph of final kinetic energy vs. initial kinetic energy during an inelastic collision between a moving cart "m" and a stationary cart of mass "M" at different initial speeds. From the slope of the graph, how big is "M" compared to "m"? The slope of the graph is about 1/3.

graph>>>> http://tinypic.com/view.php?pic=2aigal2&s=8#.U-FZ9FZycpE

2. The slope of a plot of final kinetic energy to initial kinetic energy is found to be 0.44 for the inelastic collision between a stationary cement truck of Mass 9,182 (kg) and a moving car of mass 1,030 (kg). What is the ratio (in decimal notation) of the final velocity of the two to the initial velocity of the car?

Please remember significant figures.

Explanation / Answer

so Final KE = 1/2 ( M + m) v^2

and initial KE = 1/2 m v0^2

we know that m v0 = ( M + m )v

so v = m v0/( M + m)

so final KE = 1/2 (M + m) m^2 v0^2/ (M + m)^2

final KE = 1/2 m^2/( M + m) v0^2

so final KE/initial KE = 1/2 m^2/( M + m) v0^2/1/2 m v0^2

= m/( M + m)

so since slope is 0.33
m/(M + m) = 0.33

m = 0.33 M + 0.33 m

0.67 m = 0.33 M

M = 2 m

2)

so final KE/initial KE = 1/2 ( M + m) v^2/ 1/2 m v0^2

(9182 + 1030)/1030 (v/v0)^2 = 0.44

v/v0 = sqrt( 0.44*1030/(9183+1030))= 0.21

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