Work and Energy: Force, Displacement, and Angle
9 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the magnitude of the force applied on the body?

  • 10N
  • 0N
  • 2N
  • 5N (correct)
  • What is the displacement of the body?

  • 0m
  • 2m (correct)
  • 10m
  • 5m
  • The work done on the body is zero.

    True

    What is the angle between the force and displacement?

    <p>90 degrees</p> Signup and view all the answers

    Prove for n = 1: What does the equation 3 + 3 + 3 + 3n equal?

    <p>3 - 1</p> Signup and view all the answers

    The statement 31 = (31-1) is true.

    <p>False</p> Signup and view all the answers

    Assume it is true for n = k: What does the equation 3 + 3 + 3 + 3k equal?

    <p>3k - 1</p> Signup and view all the answers

    What is the next step in proving the equation for n = k + 1?

    <p>3 + 3 + 3 + 3k + 1</p> Signup and view all the answers

    The equation 3 + 3 + 3 + 3k + 1 can be transformed into ___(3k - 1) + (3k + 1 - 3k - 1).

    <p>3(3k - 1)</p> Signup and view all the answers

    Study Notes

    Mathematical Induction

    • The goal is to prove that 3 + 3 + 3 + 3n = 3n - 1 for all positive integers n.

    Base Case (n = 1)

    • The equation becomes 3 + 3 + 3 + 3(1) = 3(1) - 1
    • Simplifying the equation, we get 3 + 3 + 3 + 3 = 3 which is true

    Inductive Step (Assume true for n = k)

    • We assume that the equation is true for some integer k, i.e., 3 + 3 + 3 + 3k = 3k - 1

    Prove it is true for n = k+1

    • Start with the left-hand side of the equation: 3 + 3 + 3 + 3k + 3
    • Rewrite it as 3(3k - 1) + (3k + 1 - 3k - 1)
    • Simplify to get 9/4(3k - 1) - 3/2 + 3
    • Further simplify to get 9/4(3k - 1) + 3/4 + 9/4(3k - 1)
    • Combine like terms to get 9/4(3k) = 3/2(81k + 1) = (3k + 1) - 1
    • This shows that the equation is true for n = k + 1

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Description

    A body is subjected to a force of 5N, resulting in a displacement of 2m. However, the work done is zero. What is the angle between the force and displacement?

    More Like This

    Physics: Work and Energy
    10 questions

    Physics: Work and Energy

    IrresistiblePurple avatar
    IrresistiblePurple
    Physics: Work and Energy Quiz
    10 questions
    Physics Chapter: Work and Energy
    18 questions
    Physics Work and Energy Concepts
    24 questions
    Use Quizgecko on...
    Browser
    Browser