Learning Objectives
- Understand the Work-Energy Theorem and its application in calculating the change in kinetic energy as equivalent to the work done by net forces.
- Calculate the scalar product of vectors and apply it to solve problems involving vector quantities in physics.
- Analyze conservative forces and derive potential energy functions, understanding the path independence of work done by these forces.
- Apply the principle of conservation of mechanical energy in systems where only conservative forces are acting, ensuring the total mechanical energy remains constant.
- Differentiate between elastic and inelastic collisions, focusing on the conservation of momentum and kinetic energy in elastic collisions.
- Integrate variable forces over displacement to determine the work done, using calculus to handle non-constant forces.
- Compute the potential energy stored in a spring using Hooke's Law and relate it to the displacement from equilibrium.
- Calculate power as the rate of work done or energy transfer, utilizing the relationship between force and velocity.
- Solve problems involving two-dimensional collisions by conserving momentum in both x and y components.
- Evaluate the work done by constant forces, considering the angle between force and displacement, and apply this to scenarios involving friction, gravity, and normal forces.
- Determine kinetic energy changes using the formula and relate it to speed and mass.
- Examine the effects of non-conservative forces like friction on energy loss and modify energy conservation equations accordingly.
- Analyze one-dimensional collisions for head-on elastic and inelastic interactions, using final velocity formulas and considering special mass cases.