Chapter 8. Potential Energy and Energy Conservation. 8.1. What is Physics? 8.2. Work and Potential Energy 8.3. Path Independence of Conservative Forces 8.4. Determining Potential Energy Values 8.5. Conservation of Mechanical Energy
8.1. What is Physics?
8.2. Work and Potential Energy
8.3. Path Independence of Conservative Forces
8.4. Determining Potential Energy Values
8.5. Conservation of Mechanical Energy
8.6. Reading a Potential Energy Curve
8.7. Work Done on a System by an External Force
8.8. Conservation of Energy
In Chapter 7 we introduced the concepts of work and kinetic energy. We then derived a net work-kinetic energy theorem to describe what happens to the kinetic energy of a single rigid object when work is done on it. In this chapter we will consider a systems composed of several objects that interact with one another.
(2) The system consists of two crates and a floor. This system is rearranged by a person (again, outside the system) who pushes the crates apart by pushing on one crate with her back and the other with her feet
(1) The system consists of an Earth–barbell system that has its arrangement changed when a weight lifter (outside of the system) pulls the barbell and the Earth apart by pulling up on the barbell with his arms and pushing down on the Earth with his feet
There is an obvious difference between these two situations. The work the weight lifter did has been stored in the new configuration of the Earth-barbell system, and the work done by the woman separating the crates seem to be lost rather than stored away.
The net work done on the skier as she travels down the ramp is given by
It does not depend on the shape of the ramp but only on the vertical component of the gravitational force and the initial and final positions of her center of mass.
Figure a shows a 2.0 kg block of slippery cheese that slides along a frictionless track from point 1 to point 2. The cheese travels through a total distance of 2.0 m along the track, and a net vertical distance of 0.80 m. How much work is done on the cheese by the gravitational force during the slide?
Consider a particle-like object that is part of a system in which a conservative force acts. When that force does work W on the object,
the change in the potential energy associated with the system is the negative of the work done
we choose the reference configuration to be when the spring is at its relaxed length and the block is at .
A 2.0 kg sloth hangs 5.0 m above the ground (Fig. 8-6).
The mechanical energy is the sum of kinetic energy and potential energies:
In a system where (1) no work is done on it by external forces and (2) only conservative internal forces act on the system elements, then the internal forces in the system can cause energy to be transferred between kinetic energy and potential energy, but their sum, the mechanical energy Emec of the system, cannot change.
An isolated system: is a system that there is no net work is done on the system by external forces.
Some of the following situations are consistent with the principle of conservation of mechanical energy, and some are not. Which ones are consistent with the principle?
(a) An object moves uphill with an increasing speed.
(b) An object moves uphill with a decreasing speed.
(c) An object moves uphill with a constant speed.
(d) An object moves downhill with an increasing speed.
(e) An object moves downhill with a decreasing speed.
(f) An object moves downhill with a constant speed.
A motorcyclist is trying to leap across the canyon shown in Figure by driving horizontally off the cliff at a speed of 38.0 m/s. Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side.
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. If the jumper stops before reaching the water, what is the height h of her feet above the water at her lowest point?
Since Newton's Third Law tells us that
the internal work is given by the integral of y
the internal work on a system is not zero in general
Solving for F(x) and passing to the differential limit yield
A 2.00 kg particle moves along an x axis in one-dimensional motion while a conservative force along that axis acts on it. The potential energy U(x) associated with the force is plotted in Fig. 8-10a. That is, if the particle were placed at any position between x=0 and x=7m , it would have the plotted value of U. At x=6.5m , the particle has velocity v0=(-4.0m/s)i . (a) determine the particle’s speed at x1=4.5m. (b) Where is the particle’s turning point located? (c) Evaluate the force acting on the particle when it is in the region 1.9m<x<4.0m.
THE PRINCIPLE OF CONSERVATION OF ENERGY: Energy can neither be created nor destroyed, but can only be converted from one form to another.
For a isolated system where Wext is zero, it energy is conserved.
In Fig. 8-58, a block slides along a path that is without friction until the block reaches the section of length L=0.75m, which begins at height h=2.0m on a ramp of angle θ=30o . In that section, the coefficient of kinetic friction is 0.40. The block passes through point A with a speed of 8.0 m/s. If the block can reach point B (where the friction ends), what is its speed there, and if it cannot, what is its greatest height above A?