Rec11_Momentum_Auto_accident_2023

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Pennsylvania State University *

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211

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Physics

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Apr 3, 2024

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4

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Phys 211 MOMENTUM – THE ACCIDENT Readings: Knight Chap 11 The momentum of a system is 𝑝𝑝⃗ = 𝑚𝑚𝑣𝑣 ⃗ . The momentum of a whole system made of multiple objects is the vector sum of all the momenta 𝑃𝑃 �⃗ = 𝑝𝑝⃗ 1 + 𝑝𝑝⃗ 2 + ⋯ If there is an external force acting on the system, it will provide an impulse and change the momentum. 𝐽𝐽 𝑥𝑥 = � 𝐹𝐹 𝑥𝑥 ( 𝑡𝑡 ) 𝑑𝑑𝑡𝑡 𝑡𝑡 𝑓𝑓 𝑡𝑡 𝑖𝑖 = 𝛥𝛥𝑃𝑃 𝑥𝑥 and similarly, for y or z direction. If there is no external force acting on the system, the momentum of the whole system is conserved 𝑃𝑃 �⃗ 𝑓𝑓 = 𝑃𝑃 �⃗ 𝑖𝑖 Note that as a vector equation this equality must be true in all directions. THE AUTO ACCIDENT Your goal is to determine who caused an accident by careful observation of the aftermath. You will play the role of a police officer investigating the scene of an automobile accident. In this accident, a Porsche Carrera approached an intersection from a minor road while a Saturn SL approached the same intersection from a major road, traveling south (see figure 1). Your responsibility as an accident investigator (after you make sure that the accident victims have been tended to, of course) is to assign fault for the collision. In an effort to determine which driver was at fault, you have noted the following facts: a. 70-foot-long skid marks (21.3 m) exist going off at a 70-degree angle from the collision point, as shown in figure 1. The skids indicate that the two vehicles were locked together from the moment of impact until coming to rest. b. It is a dry, sunny day and the road is composed of asphalt. Based on this information, your fellow officer has already calculated that the force of friction between the road surface and the tires can provide a maximal acceleration or deceleration of 6.4 𝑚𝑚 / 𝑠𝑠 2 . Section #______________ Names: Recorder:____________________________ Checker:____________________________ Discussion Leader:____________________________
PHYS 211 RECITATION 2 c. The car on the minor road (Porsche) has a stop sign at the intersection and the major road has a speed limit of 45 mph = 20.1 m/s. The cars were presumably travelling straight just before the collision. The collision occurred towards the left-hand side of the major road roughly one quarter of the way across, as shown in figure 1. d. The two cars have the same mass. e. Porsche Carrera has an acceleration of 5.1 m/s 2 . Determine who was at fault and why. Answering the below questions might help with your analysis(Hint some will require thinking about kinematics while some are momentum conservation questions). 1. What was the velocity of the combined mass immediately after the collision?
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