# Potential Energy and Conservation of Energy

## No Friction Involved

No Friction Involved To compete in a bowling-ball hurling contest, you first squat and cup your hands under the ball on the floor. Then you rapidly straighten up while also pulling your hands up sharply. launching the ball upward at about face level. During your upward motion, your applied force on the ball obviously does work: that is, …

## Work Done on a System by an External Force

Work Done on a System by an External Force We defined work as being energy transferred to or from an object by means of a force acting on the object. We can now extend that definition to an external force acting on a system of objects. Work is energy transferred to or from a system by means of …

## Equilibrium Points

Equilibrium Points Shows three different values for  superposed on the plot of the same potential energy function U(x). Let us see how they would change the situation. If  (purple line), the turning point shifts from XI to a point between XI and X.Also. at any point to the right of . the system’s mechanical energy is equal to its …

## Turning Points

Turning Points In the absence of a non conservative force, the mechanical energy E of the system has a constant value given by Tells us how to determine the kinetic energy K for any location x of the particle: On the U(x) curve, find U for that location x and then subtract. For example. if the particle …

## The Potential Energy Curve

The Potential Energy Curve  A plot of a potential energy function U(x) for a system in which a particle is in one-dimensional motion while a conservative force F(x) does work on it.

## Reading a Potential Energy Curve

Reading a Potential Energy Curve Once again we consider a particle that is part of a system in which a conservative force acts. This time suppose that the particle is constrained  along an x axis while the conservative force does work on it. Finding the Force Analytically We can check this result by putting , which is the …

## PROBLEM SOLVING TACTICS

PROBLEM SOLVING TACTICS Tactic 2: Conservation of Mechanical Energy Asking the following questions will help you to solve problems involving the conservation of mechanical energy. For what system is mechanical energy conserved? You should be able to separate your system from its environment. Imagine drawing a closed surface such that whatever is inside is your system and whatever is outside …

## Sample Problem

Sample Problem A 61.0 kg bungee-cord jumper is on a bridge 45.0 m above a river. The elastic bungee cord has a relaxed length of L = 25.0 m. Assume that the cord obeys Hooke’s law, with a spring constant of 160 N/m. .lf the jumper stops before reaching the water, what is the height h of her feet …

## Sample Problem

Sample Problem A child of mass m is released from rest at the top of a water slide, at height h = 8.S m above the bottom of the slide. SOLUTION: A Key Idea here is that we cannot find her speed at the bottom by using her acceleration along the slide as we might have in earlier …

## Sample Problem

Sample Problem (a) What is the gravitational potential energy U of the sloth Earth system if we take the reference point y = 0 to be (I) at the ground. SOLUTION: The Key Idea here is that once we have chosen the reference point for y = 0, we can calculate the gravitational potential energy U of the …