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
Bundle: Physics For Scientists And Engineers: Foundations And Connections, Advance Edition, Volume 1, Loose-leaf Version + Webassign Printed Access ... And Connections, 1st Edition, Multi-term
- A landscape architect is planning an artificial waterfall in a city park. Water flowing at 1.70 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 2.35 m high, and from there it will fall into a pool (Fig. P3.42). (a) Will the space behind the waterfall be wide enough for a pedestrian walkway? (b) To sell her plan to the city council, the architect wants to build a model to standard scale, which is one-twelfth actual size. How fast should the water flow in the channel in the model? Figure P3.42arrow_forwardA simple way of measuring a person's reaction time is to let the person catch a freely-falling ruler or meter stick and then measure the distance from the point where the fingers of the person was placed before the ruler is released to the point where the person's finger was located after the ruler was released. If the distance of fall is 19 cm, what is the person's reaction time? A. 19 s B. 1.9 s C. 0.2 s D. 0.1 sarrow_forwardFrogs, with their long, strong legs, are excellent jumpers. And thanks to the good folks of Calaveras County, California, who have a jumping frog contest every year in honor of a Mark Twain story, we have very good data as to just how far a determined frog can jump. The current record holder is Rosie the Ribeter, a bullfrog that made a leap of 2.2 m from a standing start. This compares favorably with the world record for a human, which is a mere 3.7 m. Typical data for a serious leap by a bullfrog look like this: The frog goes into a crouch, then rapidly extends its legs by 15 cm as it pushes off, leaving the ground at an angle of 30° to the horizontal. It’s in the air for 0.49 s before landing at the same height from which it took off. Given this leap, what is the acceleration while the frog is pushing off? How far does the frog jump?arrow_forward
- At night while it is dark, a driver inadvertently parks his car on a drawbridge. Some time later, the bridge must be raised to allow a boat to pass through. The coefficients of friction between the bridge and the car's tires are μs=0.820 and μk=0.470. If the bridge attendant sees the car suddenly start to slide and immediately turns off the bridge's motor, what will be the car's acceleration after it has begun to move? (Express your answer in meters per second squared.)arrow_forwardA student is testing the UAM equations by measuring the time it takes for light-weight plastic balls to fall to the floor from a height of 5 m in the lab. The student predicts the time to fall using g as 9.80 m/s^2 but finds the measured time to be 42.5% greater. Which of the following is the most likely cause of the large percent error? a. The acceleration due to gravity is 57.5% greater than 9.80 m/s^2 at this location. b. The acceleration due to gravity is 57.5% less than 9.80 m/s^2 at this location. c. Air resistance increases the downward acceleration. d. The acceleration of the plastic balls is not uniform. e. No Answerarrow_forwardWeddell seals make holes in sea ice so that they can swim down to forage on the ocean floor below. Measurements for one seal showed that it dived straight down from such an opening, reaching a depth of 0.30 km in a time of 5.0 min. What was the speed of the diving seal?A. 0.60 m/s B. 1.0 m/s C. 1.6 m/s D. 6.0 m/s E. 10 m/sarrow_forward
- The highest spot on Earth is Mt. Everest, which is 8850 m above sea level. If the radius of the Earth (to sea level) is 6370 km, how much does the magnitude of g change between sea level and the top of Mt. Everest? (G = 6.67 × 10-11 N m2/kg2, and the mass of the Earth is 5.98 × 1024 kg.)arrow_forwardA theme park is planning out a new free-fall ride. The drop is almost perfectly frictionless, with a distance of 190 meters. Assuming that the initial velocity was zero, what would be the speed at the bottom of the drop? 1 53 m/s 2 61 m/s 3 67 m/s 4 72 m/sarrow_forwardYour grandfather had to walk to school uphill, both ways, but one way he went at 5.0 km/hr, and the other he went at 4.0 km/hr. What is his average speed for the round trip? 0.50 km/hr 5.6 km/hr 9.5 km/hr 4.4 km/hrarrow_forward
- My sable-colored Siberian husky, Samba, loves to run after huge objects (for instance, tree branches). I decide to chunk a 6 foot long stick for her to run after and bring back to me. I throw the stick at 1.45 ft/s in 2.14 s. In feet and to two decimal places, how far away did the stick land?arrow_forwardIf a rocket in space is initially at rest and then accelerates at a rate of 50 m/s 2 for one minute (which is 60 seconds), how fast will it be going at that point? Your answer should be in units of m/s but you should only submit the number for your answer.arrow_forwardTowns A and B in Figure P4.64 are 80.0 km apart. A couple arranges to drive from town A and meet a couple driving from town B at the lake, L. The two couples leave simultaneously and drive for 2.50 h in the directions shown. Car 1 has a speed of 90.0 km/h. If the cars arrive simultaneously at the lake, what is the speed of car 2?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning