4 Week 4 Work Energy - Pham Tan Thi PDF

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General Physics A Week 4: Work – Mechanical EnergyVietnam National University Ho Chi Minh City Ho Chi Minh City University of TechnologyContents❑ Scalar Product ❑ Work ❑ Kinetic Energy and the Work-Energy Theorem ❑ Power ❑ Gravitational Potential Energy ❑ Elastic (Spring) Potential Energy ❑ Conserva...

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Vietnam National University Ho Chi Minh City Ho Chi Minh City University of Technology

General Physics A1 Week 4: Work – Mechanical Energy

Contents ❑ Scalar Product ❑ Work ❑ Kinetic Energy and the Work-Energy Theorem ❑ Power ❑ Gravitational Potential Energy ❑ Elastic (Spring) Potential Energy ❑ Conservative and Nonconservative Forces ❑ Conservation of Energy

Scalar Product of Two Vectors  The

scalar product of two vectors is written as



It is also called the dot product



θ is the angle between A and B

Scalar Product is a Scalar  Not

a vector  May be positive, negative, or zero

Scalar Product: An Example 

❑ The vectors: A  2iˆ  3 ˆj and B  iˆ  2 ˆj   ❑ Determine the scalar product: A  B  ?   A  B  Ax Bx  Ay B y  2  (-1)  3  2  -2  6  4

❑ Find the angle θ between these two vectors: A  Ax2  Ay2  22  32  13   4 4 A B cos     AB 13 5 65 4   cos1  60.3 65

B  Bx2  By2  ( 1) 2  2 2  5

Contents ❑ Scalar Product ❑ Work ❑ Kinetic Energy and the Work-Energy Theorem ❑ Power ❑ Gravitational Potential Energy ❑ Elastic (Spring) Potential Energy ❑ Conservative and Nonconservative Forces ❑ Conservation of Energy

Definition of Work W 

The work, W, done by a constant force on an object is defined as the scalar (dot) product of the component of the force along the direction of displacement and the magnitude of the displacement

  



is the magnitude of the force is the the object’s displacement Φ is the angle between

SI Unit  

N•m=J J = ( kg • m / s2 ) • m

and

Work: Positive or Negative 

Work can be positive, negative, or zero. The sign of the work depends on the direction of the force relative to the displacement



Work Work Work Work Work

   

positive: if 0°<  < 90° negative: if 90°< ...