Momentum in Two Dimensions
Problems
practice
- Your consulting agency, with its extensive knowledge of physics, has been subpoenaed to provide expert testimony at an automobile accident case in civil court. The case involves a crash between a compact car, loaded with a driver and three passengers, and a tractor-trailer truck. Prior to your testimony you were provided with information from the local police department and the manufacturers of the car and truck.
- The police report stated that the force needed to drag a 130 N (29 lb) car tire across the pavement at a constant velocity at this location was no less than 100 N (22 lb). Specifications provided by the truck's manufacturer claim that, due to the manner in which the truck balances braking across its 3 axles, the effective coefficient of friction for truck tires is only 70% that of car tires. What is the coefficient of kinetic friction between the tires and the road for both the car and the truck?
- After colliding, the car and the truck skidded to a stop as shown in the diagram. The car skidded a distance of 8.2 m (27 ft) at 33° while the truck skidded 11 m (36 ft) at 7°. What was the speed of each vehicle immediately after the moment of impact?
- Before colliding, the car was traveling due north and the truck was traveling due west as shown in the diagram. What was the speed of each vehicle immediately before the moment of impact? The mass of the car is 1,380 kg (3,040 lb) and the mass of the truck is 7,120 kg (15,700 lb).
- At this intersection, the truck driver had a flashing yellow light while the car driver had a flashing red light. In situations like this, the driver with the flashing yellow is expected to be extra vigilant for cross traffic while the driver with the flashing red is expected to come to a complete stop and wait until the intersection is safe to enter.
- The truck driver claims that the car ran the flashing red light. He also claims to have begun braking in anticipation of a collision; traveling at only 6.7 m/s (15 mph) at the moment of impact.
- The car driver claims to have made a full stop at the light before entering the intersection. He also claims that the truck driver did not see him until after the collision.
- The police report stated that the distance from the traffic light to the collision point for the car was 14 m (46 ft).
- Specifications provided by the car's manufacturer claim that the maximum acceleration of a comparably loaded vehicle is about 3.0 m/s2 (10 ft/s2).
Adapted from Feldman, 1997
- Write something else.
- Write something different.
- Write something completely different.
numerical
- This activity was adapted from the Crash Reconstruction Proficiency Test administered by the Ohio State Highway Patrol in 1995. Read the police report of the accident and then answer the questions.
Highway patrol officers taking this exam are also given a table of frequently used equations. Most of the equations on this reference table can easily be found in the mechanics chapters of any introductory physics textbook; either in the general text or in the sample problems. One important exception was the velocity-distance formula for acceleration that changes abruptly from one constant value to another. This formula is shown below.
v2 = v02 + 2a1Δs1 + 2a2Δs2 + …
Report
Before the collision, vehicle #1 was traveling east on Main Street and vehicle #2 was traveling north on High Street. At this intersection, traffic on High Street is controlled by a stop sign while traffic on Main Street is uncontrolled.
- The driver of vehicle #1 states he was traveling 25 mph (11 m/s) as he approached the intersection. He continues to state that vehicle #2 ran the stop sign at High Street, pulling out in front of him and causing the crash.
- The driver of vehicle #2 states he stopped at the stop bar and carefully looked both left and right before pulling out to cross Main Street. (From the stop bar, vehicle #2 would have traveled 30 feet (9.1 m) to the point of impact.) He further states that he did not see the other car until the moment of impact. Confident that he had carefully looked both ways before pulling out, his only explanation for the crash is that vehicle #1 was speeding and concealed by a hill crest located on Main Street approximately 1,000 feet (300 m) west of the intersection.
After the collision, both vehicles experienced wheel lock due to crash damage and skidded over asphalt (μk = 0.72) followed by grass (μk = 0.35). Neither surface had any significant incline.
- Vehicle #1 skidded on 20 feet (6.1 m) of asphalt and 30 feet (9.1 m) of grass before coming to rest. The angle of departure for vehicle #1 was 45° north of east. The weight of vehicle #1 including load and occupants was 4,300 lb. (19,200 N).
- Vehicle #2 skidded on 25 feet (7.6 m) of asphalt and 35 feet (10.7 m) of grass before coming to rest. The angle of departure for vehicle #2 was 35° north of east. The weight of vehicle #2 including load and occupants was 3,150 lb. (14,000 N). An acceleration test was conducted with a vehicle similar in weight and performance to vehicle #2. It was found that the maximum acceleration rate for vehicle #2 would have been 2.0 m/s2 at the time of the accident.
Questions
- Sketch a diagram of the accident showing the path of each vehicle before and after collision. Includeall the relevant distances on the paths. Label each vehicle, label the streets, and label the differentsurfaces (asphalt and grass). Indicate the location of the stop sign, stop bar, and point of collision.
- What was the speed of each vehicle just after the collision?
- What was the speed of each vehicle just before the collision?
- Assess the claims of the two drivers. Justify your response with the appropriate calculations.
Adapted from Larabee, 2000
- an-elastic-collision-in-2d.pdf
Complete the table and verify that mechanical energy was conserved in the collision between the two hypothetical objects shown in the diagram.