Chapter 7: Kinetic Energy and Work

Energy and WorkKinetic energy

Work done by a constant force

Work–kinetic energy theorem

Work Done by a Gravitational Force

Work done by gravitational force

Change in kinetic energy

Tomato thrown upward

Lifting/lowering an object

Work Done by a Spring ForceHooke’s law

Work done by a spring force

Work Done by a General Variable Force

Work: variable force

Calculus

Divide area under curve

Add increments of W (numerically)

Analytical form?

Integration!!!

Sample Problem 7-8

Chapter 8: Potential Energy and Conservation of Energy

Introduction

Potential Energy and Conservation of EnergyConservative ForcesGravitational and Elastic Potential EnergyConservation of (Mechanical) EnergyPotential Energy CurveExternal Forces

Work and Potential EnergyPotential Energy

General Form

Gravitational Potential Energy

Elastic Potential Energy

(Non-)Conservative Forces

The system consists of two or more objects.A force acts between a particle–like object in the

system and the rest of the system.When the system configuration changes, the force

does work W1 on the particle–like object, transferring energy between the kinetic energy K of the object and some other form of energy of the system.

When the configuration change is reversed, the force reverses the energy transfer, doing work W2 in the process.

W1 = –W2 conservative force

Path Independence of Conservative Forces

The net work done by a conservative force on a particle moving around every closed path is zero.

The work done by a conservative force on a particle moving between two points does not depend on the path taken by the particle.

Sample Problem 8-1: A 2.0 kg block of cheese that slides along a frictionless track from a to point b. The cheese travels through a total distance of 2.0 m, and a net vertical distance of 0.8 m. How much work is done on the cheese by the gravitational force?

Conservation of Mechanical Energy

Mechanical Energy

Conservation of Mechanical Energy

In an isolated system where only conservative forces cause energy changes, the kinetic and potential energy can change, but their sum, the mechanical energy Emec of the system, cannot change.

Potential Energy Curve

Turning Points Equilibrium Points

– Neutral Equilibrium

– Unstable Equilibrium

– Stable Equilibrium

A plot of U(x), the potential energy function of a system containing a particle confined to move along the x axis. There is no friction, so mechanical energy is conserved.

1D Motion

Conservation of Energy

The total energy of a system can change only by amounts of energy that are transferred to or from the system.

The total energy E of an isolated system cannot change.

Thermal Energy/Friction

Sample Problem 8-8