You are a professional witness in a lawsuit. What do you tell the judge? What do
ID: 1446623 • Letter: Y
Question
You are a professional witness in a lawsuit. What do you tell the judge? What do you tell the Physicist (Read the following scenario.) You are on an RTD Stretch Bus (the long busses with the accordion in the middle. (This is called an articulating bus.)) The bus is fully loaded with fuel and people. You are traveling at 30 [mph] when a mini-Van in front of the bus pulls in front of the bus as it travels in a similar direction; the van is traveling 20 [mph]. The bus driver slams on the brakes, but there is black ice so the bus gracefully slides right into the van sending the van flying ahead. Three passengers riding the public transit bus, upon realizing their opportunity to make some quick cash, start crying of back and neck pain. Mass of bus + passengers + fuel is about 66,600 [lb] or 30,200 [kg]. Mass of van is about 2,000 [kg].
Forensics estimates from the bending of the light-pole that the van was moving at an uninhibited speed of about 35 [mph] when it hit the pole after sliding on ice. You are a professional witness; what is your statement to the judge and why? (Three other bus passengers tell the judge they didn't even feel the collision. They heard it and saw the van fly forward; but they claim they felt nothing.)
1) The Judge needs terms that are easy to understand. You need to include some "real world" examples to drive home your answer. The Judge needs to see concepts of momentum exchange and a final answer for change in speed for the bus in mph. 2) The Physicist needs to see calculations for momentum exchange and a final answer for change in velocity for the bus in m/s.
Explanation / Answer
Given,
Mb = 30200 kg ; Mv = 2000 kg ;
Ub = 30 mph = 13.41 m/s ; Uv = 20 mph = 8.94 m/s
Considering the collision is perfectly elastic, from conservation of linear momentum:
Pi = Pf
Mb Ub + Mv Uv = Mb Vb + Mv Vv
30200 x 13.41 + 2000 x 8.94 = 30200 Vb + 2000 Vv
30200 Vb + 2000 Vv = 422862
Vv + 15.1 Vb = 211.43 (1)
From the concept of relative velocity:
Vv - Vb = 13.41 - 8.94 = 4.47 m/s
Vv = 4.47 + Vb putting this in (1)
4.47 + Vb + 15.1 Vb = 211.43
16.1 Vb = 206.96 => Vb = 12.85 m/s = 28.7 mph
Vv = 4.47 + 12.85 = 17.32 = 38.74 mph
Considering if the collision was non elastic, so
Mb Ub + Mv Uv =( Mb + Mv )V
30200 x 13.41 + 2000 x 8.94 = (30200 + 2000) V
V = 422862/32200 = 13.13 m/s = 29.4 mph.
This suggests that no collision actually happened.
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