Concept explainers
February 3, 2009, was a very snowy day along Interstate 69 just outside of Indianapolis, Indiana. As a result of the slippery conditions and low visibility (50 yards or less), there was an enormous accident involving approximately 30 vehicles, including cars, tractor-trailers, and even a fire truck. Many witnesses said that people were driving too fast for the conditions and were too close together. In this problem, we explore two rules of thumb for driving in such conditions. The first is to drive at a speed that is half of what it would be in ideal conditions. The other is the “8-second” rule: Watch the vehicle in front of you as it passes some object such as a street sign, and you should pass that same object 8 seconds later. On a dry road, the 8-second rule is replaced by a 3-second rule. a. Assume vehicles on a slippery interstate highway follow both rules. What is the distance between the vehicles? b. If a driver followed the first rule of thumb, driving at a lower speed, but used the 3-second rule instead of the 8-second rule, what is the distance between the vehicles? How does that distance compare with the visibility on the day of the accident? c. Suppose drivers do not follow either rule of thumb for slippery conditions. What is the distance between vehicles? How does that distance compare with the visibility on that day? d. Suppose a driver was not obeying either rule of thumb when she sees a tractor-trailer that stopped on the highway. She presses on her brakes, locking the wheels, and her car crashes into the truck. Estimate the magnitude of the impulse exerted on her car. e. Estimate the impulse on the car in part (d) had the driver followed both rules of thumb for slippery conditions instead of ignoring them.
(a)
The distance between the vehicles when running through the slippery road.
Answer to Problem 78PQ
The distance between the vehicles when running through the slippery road is
Explanation of Solution
Assume that the speed of the vehicles in highway is
Write the expression for the distance travelled by the vehicle (the distance between the vehicles).
Here,
Conclusion:
Substitute
Therefore, the distance between the vehicles when running through the slippery road is
(b)
The distance between the vehicles according to the
Answer to Problem 78PQ
The distance between the vehicles according to the
Explanation of Solution
Given that the visibility on the day of accident is
Equation (I) gives the distance between the vehicles.
When the
Conclusion:
Substitute
The visibility on the day of accident in the units of meters is,
This indicates that the distance between the vehicles when the
Therefore, the distance between the vehicles according to the
(c)
The distance between the vehicles according to the
Answer to Problem 78PQ
The distance between the vehicles according to the
Explanation of Solution
Given that the visibility on the day of accident is
Equation (I) gives the distance between the vehicles.
In this case the vehicle is moving with speed of
Conclusion:
Substitute
This indicates that the distance between the vehicles when moving with speed of
Therefore, the distance between the vehicles according to the
(d)
The magnitude of impulse on the car.
Answer to Problem 78PQ
The magnitude of impulse on the car is
Explanation of Solution
According to the energy conservation, the kinetic energy of the vehicle at the crash equals the initial energy minus the energy dissipated by friction after applying the brakes.
Here,
Write the expression for the kinetic energy of the car at the moment of crash.
Here,
Write the expression for the initial kinetic energy of the car.
Here,
Write the expression for the change in thermal energy.
Here,
Use equation (III), (IV), and (V) in (II) and solve for
The impulse on the car is equal to the change in momentum. Since the truck stops the car after collision, the final momentum is zero. Thus, the magnitude of impulse on the car will be equal to the momentum of the car at the moment of collision.
Here,
The mass of the car be
Conclusion:
Substitute
Substitute
Therefore, the magnitude of impulse on the car is
(e)
The magnitude of impulse on the car with rules for the slippery road is applied.
Answer to Problem 78PQ
The magnitude of impulse on the car with rules for the slippery road is applied is
Explanation of Solution
When the rules for the slippery road is applied, the initial speed of the car would be
Equation (VI) gives the speed of the car at the moment of crash.
Equation (VII) gives the magnitude of impulse on the car.
Conclusion:
Substitute
Substitute
Therefore, the magnitude of impulse on the car with rules for the slippery road is applied is
Want to see more full solutions like this?
Chapter 11 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- When visiting a friend in Atlanta you decide to drive around the city. You turn a corner and are driving up a steep hill. Suddenly, a small boy runs out on the street chasing a ball. You slam on the brakes and skid to a stop leaving a 50-foot-long skid mark on the street. The boy calmly walks away but a policemen watching from the sidewalk walks over and gives you a speeding ticket. He points out that the speed limit on this street is 25 mph. After you recover your wits, you begin to examine the situation. You determine that the street makes an angle of 25◦ with the horizontal and that the coefficient of static friction between your tires and the street is 0.80. You also find that the coefficient of kinetic friction between your tires and the street is 0.60. Your car’s information book tells you that the mass of your car is 1600 kg. You weigh 140 lbs. Will you fight the ticket in court? Please be as detailed as possible with your answer.arrow_forwardAs a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint concerns a stop sign at the corner of Pine Street and 1st Street. Residents complain that the speed limit in the area (89 km/h) is too high to allow vehicles to stop in time. Under normal conditions this is not a problem, but when fog rolls in visibility can reduce to only 47 meters. Because fog is a common occurrence in this region, you decide to investigate. The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.842 and 0.941, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.550 and 0.754. Vehicles of all types travel on the road, from small cars with a mass of 531 kg to large trucks with a mass of 3463 kg. Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the minimum and…arrow_forwardYou are a police officer examining the scene of a car crash that claimed the life of someone driving a Tesla. There was a collision involving them and a pickup truck. The truck driver, who survived, said he was travelling North into the intersection and the Tesla was travelling East into the intersection. The truck driver claims that he was not exceeding the speed limit when the accident occurred. You note the posted speed limit was 80 km/h. Like airplanes, Teslas have a black box that records various statistics in the event a collision occurs. After analyzing the data from the black box, you discover the Tesla was driving at a velocity of 64.6 km/h [E] when the collision occurred. You google the mass of both of the vehicles and find the Tesla should be about 2240 kg and the truck should be about 3060 kg. During the collision, the two vehicles crumpled and became entangled, the skid marks revealing that the two vehicles travelled E 62° N after impact. How fast, in km/h, was the truck…arrow_forward
- As a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint concerns a stop sign at the corner of Pine Street and 1st Street. Residents complain that the speed limit in the area (55 mph) is too high to allow vehicles to stop in time. Under normal conditions this is not a problem, but when fog rolls in visibility can reduce to only 155 ft. Since fog is a common occurrence in this region, you decide to investigate. The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.536 and 0.599, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.350 and 0.480. Vehicles of all types travel on the road, from small VW bugs weighing 1310 lb to large trucks weighing 8.40 x 10° lb. Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the minimum and maximum…arrow_forwardAs a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint concerns a stop sign at the corner of Pine Street and 1st Street. Residents complain that the speed limit in the area (55 mph) is too high to allow vehicles to stop in time. Under normal conditions this is not a problem, but when fog rolls in visibility can reduce to only 155 ft. Since fog is a common occurrence in this region, you decide to investigate. The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.536 and 0.599, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.350 and 0.480. Vehicles of all types travel on the road, from small VW bugs weighing 1410 lb to large trucks weighing 8250 lb. Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the minimum and maximum…arrow_forwardYou are an engineer in charge of designing a new generation of elevators for a prospective upgrade to the Empire State Building. Before the state legislature votes on funding for the project, they would like you to prepare a report on the benefits of upgrading the elevators. One of the numbers that they have requested is the time it will take the elevator to go from the ground floor to the 102nd floor observatory. They are unlikely to approve the project unless the new elevators make the trip much faster than the old elevators. If state law mandates that elevators cannot accelerate more than 23.90 m/s2 or travel faster than 19.3 m/s, what is the minimum time in which an elevator can travel the 373 m from the ground floor to the observatory floor? minimum travel time: ?arrow_forward
- As a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint concerns a stop sign at the corner of Pine Street and 1st Street. Residents complain that the speed limit in the area (55 mph) is too high to allow vehicles to stop in time. Under normal conditions this is not a problem, but when fog rolls in visibility can reduce to only 155 ft. Since fog is a common occurrence in this region, you decide to investigate. The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.689 and 0.770, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.450 and 0.617. Vehicles of all types travel on the road, from small VW bugs weighing 1210 lb to large trucks weighing 8640 lb. Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the minimum and maximum…arrow_forwardIn 1987, as a Halloween stunt, two sky divers passed a pumpkin back and forth between them while they were in free fall just west of Chicago.The stunt was great fun until the last sky diver with the pumpkin opened his parachute. The pumpkin broke free from his grip, plummeted about 0.5 km, ripped through the roof of a house, slammed into the kitchen floor, and splattered all over the newly remodeled kitchen. From the sky diver’s viewpoint and from the pumpkin’s viewpoint, why did the sky diver lose control of the pumpkin?arrow_forwardA Deadly Virus. On your flight out of South America your cargo plane emergency-lands on a deserted island somewhere in the South Pacific. Because it was a beach landing, the pilot skids the plane on its belly rather than lowering the landing gear. The landing is rough: an initial vertical drop followed by an abrupt horizontal deceleration. When the dust settles, the pilot and your scientist colleagues are all okay, but you know there might be a big problem. Your team is transporting samples of a deadly virus from a recent breakout in a small village. The samples were packed in a cryogenically cooled container that has a special seal that may leak if it exceeds an acceleration greater than 10g. The container has a mechanical accelerometer gauge that measures the maximum vertical deceleration in case the container is dropped. It reads a value of a -7.00g. However, you are still worried: there was another component of the acceleration. You get out of the plane and measure the length of…arrow_forward
- As you drive your car along a country road at night, a deer jumps out of the woods and stands in the middle of the road ahead of you. This occurs just as you are passing from a 55-mi/h zone to a 50-mi/h zone. At the 50-mi/h speed-limit sign, you slam on the car’s brakes, causing them to lock up, and skid to a stop inches from the startled deer. As you breathe a sigh of relief, you hear the sound of a police siren. The policeman proceeds to write you a ticket for driving 56 mi/h in 50-mi/h zone. Because of your preparation in physics, you are able to use the 25-m-long skid marks that your car left behind as evidence that you were not speeding. What evidence do you present? You must use work/energy methods to solve this problem!The coefficientsof friction between car tires and dry concrete are (s=1.0, k=0.80).arrow_forwardI've been moonwalking for hours, and I'm getting tired. Explain why, as I come to a stop, my velocity is increasing while my speed is decreasing.arrow_forwardIn 1992, a 14-kg meteorite struck a car in Peekskill, NY, leaving a 20-cm-deep dent in the trunk. If the meteorite was moving at 500 m/s before striking the car, what was the magnitude of its acceleration while stopping? Find the time it takes for the meteorite to come to a complete stop.arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON