General physics a1 week 4 work – mechanical energy

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  ˆj and B  iˆ  ˆj   ❑ Determine the scalar product: A  B  ?   A  B  Ax Bx  Ay B y   (-1)    -2   ❑ Find the angle θ between these two vectors: A  Ax2  Ay2  22  32  13   4 A B cos     AB 13 65   cos1  60.3 65 B  Bx2  By2  ( 1)  2  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°< 