GOAL Apply the work-energy theorem with a known force. PRO BLEM The driver of a
ID: 1323819 • Letter: G
Question
GOAL Apply the work-energy theorem with a known force. PRO BLEM The driver of a 1.00 X 10^3 kg car traveling on the interstate at 35.0 m/s (nearly 80.0 mph) slams on his brakes to avoid hitting a second vehicle In front of him, which had come to rest because of congestion ahead (see figure). After the brakes are applied, a constant kinetic friction force of magnitude 8.00 X 10^3 N acts on the car. Ignore air resistance. (a) At what minimum distance should the brakes be applied to avoid a collision with the other vehicle? (b) If the distance between the vehicles is initially only 30.0 m, at what speed would the collision occur? STRATEGY Compute the net work, which involves just the kinetic friction, because the normal and gravity forces are perpendicular to the motion. Then set the net work equal to the change in kinetic energy. To get the minimum distance in part (a), we take the final speed Vf to be zero just as the braking vehicle reaches the rear of the vehicle at rest. Solve for the unknown, delta x. For part (b) proceed similarly, except that the unknown is the final velocity vf. QUESTION Qualitatively, how would the answer for the final velocity change in part (b) if I'ts raining during the incident? PRACTICE IT Use the worked example above to help you solve this problem. The driver of a 1.15 X 10^3 kg car traveling on the interstate at 35.0 m/s (nearly 80.0 mph) slams on his brakes to avoid hitting a second vehicle in front of him, which had come to rest because of congestion ahead. After the brakes are applied, a constant kinetic friction force of magnitude 8.14 X 10^3 N acts on the car. Ignore air resistance. (a) At what minimum distance should the brakes be applied to avoid a collision with the other vehicle? (b) If the distance between the vehicles is initially only 30.0 m, at what speed would the collision occur? EXERCISE HINTS: GETTING STARTED I I?M STUCK! Use the values from PRACTICE IT to help you work this exercise. A police investigator measures straight skid marks 31.0 m long in an accident investigation. Assuming a friction force and car mass the same as in the problem above, what was the minimum speed of the car when the brakes locked?Explanation / Answer
Acceleration a = F / m = 8.14 * 103/ 1.15 * 103= 7.08 m/s2
time motion e = 1/2 a* t2
t2 = 2 e / a = 2 * 31 /7.08
t = 2.96 s
v= v0- a t = 35 - 7.08 * 2.96
= 14 m/s
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