Suppose the wind is blowing with force vector F = (-y, 2x) in the vicinity of a straight road segment C from the point (0,0) to the point (4,3). A car moves along the straight road in two different scenarios: • there are traffic lights along the road segment causing the car to slow down and speed up again in such a way that its position along the road is given by r₁(t) = 2t 4 π sin 3t, 3t 2π sin 3t for 0 ≤ t ≤ 2π; • The traffic lights are broken and the car moves along the road segment at constant speed so that its position is given now by r₂(t) = (4t, 3t)

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics
Section: Chapter Questions
Problem 7.35P
icon
Related questions
icon
Concept explainers
Question
Suppose the wind is blowing with force vector F = (-y, 2x) in the vicinity of a
straight road segment C from the point (0,0) to the point (4,3). A car moves along the
straight road in two different scenarios:
there are traffic lights along the road segment causing the car to slow down and speed up
again in such a way that its position along the road is given by
for 0≤ t ≤ 2π;
• The traffic lights are broken and the car moves along the road segment at constant speed
so that its position is given now by
for 0 ≤ t ≤ 1.
4
3t
ri(t) - (²-sin 3f, 2-sin 3t)
3
r₂(t) = (4t, 3t)
Use each parametrization separately to determine the total work done by the wind on the car
during its journey and show that (strangely?) it is the same in both scenarios.
F. dr.
Remark: Recall that the work done by a vector field F along a path C is just the line integral
[F
Transcribed Image Text:Suppose the wind is blowing with force vector F = (-y, 2x) in the vicinity of a straight road segment C from the point (0,0) to the point (4,3). A car moves along the straight road in two different scenarios: there are traffic lights along the road segment causing the car to slow down and speed up again in such a way that its position along the road is given by for 0≤ t ≤ 2π; • The traffic lights are broken and the car moves along the road segment at constant speed so that its position is given now by for 0 ≤ t ≤ 1. 4 3t ri(t) - (²-sin 3f, 2-sin 3t) 3 r₂(t) = (4t, 3t) Use each parametrization separately to determine the total work done by the wind on the car during its journey and show that (strangely?) it is the same in both scenarios. F. dr. Remark: Recall that the work done by a vector field F along a path C is just the line integral [F
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Knowledge Booster
Gravitational Force
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
Physics
ISBN:
9780534408961
Author:
Stephen T. Thornton, Jerry B. Marion
Publisher:
Cengage Learning
University Physics Volume 1
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning