8.1 8.2 Potential Energy of a System The Isolated System—Conservation of Mechanical Energy Conservative and Nonconservative Forces Changes in Mechanical Energy for Nonconservative Forces Relationship Between Conservative Forces and Potential Energy Energy Diagrams and the Equilibrium of a System
ANSWERS TO QUESTIONS
Q8.1 The final speed of the childrenwill not depend on the slide length or the presence of bumps if there is no friction. If there is friction, a longer slide will result in a lower final speed. Bumps will have the same effect as they effectively lengthen the distance over which friction can do work, to decrease the total mechanical energy of the children. Total energy is the sum of kinetic and potential energies. Potential energy canbe negative, so the sum of kinetic plus potential can also be negative. Both agree on the change in potential energy, and the kinetic energy. They may disagree on the value of gravitational potential energy, depending on their choice of a zero point.
mgh is provided by the muscles. No further energy is supplied to the object-Earthsystem, but some chemical energy must be supplied to the muscles as they keep the weight aloft. The object loses energy mgh, giving it back to the muscles, where most of it becomes internal energy.
Lift a book from a low shelf to place it on a high shelf. The net change in its kinetic energy is zero, but the book-Earth system increases in gravitational potential energy. Stretch arubber band to encompass the ends of a ruler. It increases in elastic energy. Rub your hands together or let a pearl drift down at constant speed in a bottle of shampoo. Each system (two hands; pearl and shampoo) increases in internal energy. Three potential energy terms will appear in the expression of total mechanical energy, one for each conservative force. If you write an equation with initialenergy on one side and final energy on the other, the equation contains six potential-energy terms.
It does if it makes the object’s speed change, but not if it only makes the direction of the velocity change. Yes, according to Newton’s second law.
The original kinetic energy of the skidding can be degraded into kinetic energyof random molecular motion in the tires and the road: it is internal energy. If the brakes are used properly, the same energy appears as internal energy in the brake shoes and drums. All the energy is supplied by foodstuffs that gained their energy from the sun. Elastic potential energy of plates under stress plus gravitational energy is released when the plates “slip”. It is carried away bymechanical waves. The total energy of the ball-Earth system is conserved. Since the system initially has gravitational energy mgh and no kinetic energy, the ball will again have zero kinetic energy when it returns to its original position. Air resistance will cause the ball to come back to a point slightly below its initial position. On the other hand, if anyone gives a forward push to the ballanywhere along its path, the demonstrator will have to duck. Using switchbacks requires no less work, as it does not change the change in potential energy from top to bottom. It does, however, require less force (of static friction on the rolling drive wheels of a car) to propel the car up the gentler slope. Less power is required if the work can be done over a longer period of time. There is no workdone since there is no change in kinetic energy. In this case, air resistance must be negligible since the acceleration is zero. There is no violation. Choose the book as the system. You did work and the earth did work on the book. The average force you exerted just counterbalanced the weight of the book. The total work on the book is zero, and is equal to its overall change in kinetic energy....
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