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Systems with several particles or objects

Systems generally consist of more than one particle or object. However, the conservation of mechanical energy, in one of the forms in [link] or [link] , is a fundamental law of physics and applies to any system. You just have to include the kinetic and potential energies of all the particles, and the work done by all the non-conservative forces acting on them. Until you learn more about the dynamics of systems composed of many particles, in Linear Momentum and Collisions , Fixed-Axis Rotation , and Angular Momentum , it is better to postpone discussing the application of energy conservation to then.


  • A conserved quantity is a physical property that stays constant regardless of the path taken.
  • A form of the work-energy theorem says that the change in the mechanical energy of a particle equals the work done on it by non-conservative forces.
  • If non-conservative forces do no work and there are no external forces, the mechanical energy of a particle stays constant. This is a statement of the conservation of mechanical energy and there is no change in the total mechanical energy.
  • For one-dimensional particle motion, in which the mechanical energy is constant and the potential energy is known, the particle’s position, as a function of time, can be found by evaluating an integral that is derived from the conservation of mechanical energy.

Conceptual questions

When a body slides down an inclined plane, does the work of friction depend on the body’s initial speed? Answer the same question for a body sliding down a curved surface.

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Consider the following scenario. A car for which friction is not negligible accelerates from rest down a hill, running out of gasoline after a short distance (see below). The driver lets the car coast farther down the hill, then up and over a small crest. He then coasts down that hill into a gas station, where he brakes to a stop and fills the tank with gasoline. Identify the forms of energy the car has, and how they are changed and transferred in this series of events.

A car coasts down a hill up over a small crest, then down hill. At the bottom of the hill, it stops for gasoline.

The car experiences a change in gravitational potential energy as it goes down the hills because the vertical distance is decreasing. Some of this change of gravitational potential energy will be taken away by work done by friction. The rest of the energy results in a kinetic energy increase, making the car go faster. Lastly, the car brakes and will lose its kinetic energy to the work done by braking to a stop.

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A dropped ball bounces to one-half its original height. Discuss the energy transformations that take place.

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E = K + U constant is a special case of the work-energy theorem.” Discuss this statement.

It states that total energy of the system E is conserved as long as there are no non-conservative forces acting on the object.

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In a common physics demonstration, a bowling ball is suspended from the ceiling by a rope.

The professor pulls the ball away from its equilibrium position and holds it adjacent to his nose, as shown below. He releases the ball so that it swings directly away from him. Does he get struck by the ball on its return swing? What is he trying to show in this demonstration?

The figure is a drawing of a man pulling a bowling ball that is suspended from the ceiling by a rope away from its equilibrium position and holding it adjacent to his nose. In a second picture, the ball swings directly away from him.
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Questions & Answers

Suppose the master cylinder in a hydraulic system is at a greater height than the cylinder it is controlling. Explain how this will affect the force produced at the cylinder that is being controlled.
Louise Reply
Why is popo less than atmospheric? Why is popo greater than pipi?
The old rubber boot shown below has two leaks. To what maximum height can the water squirt from Leak 1? How does the velocity of water emerging from Leak 2 differ from that of Leak 1? Explain your responses in terms of energy.
David rolled down the window on his car while driving on the freeway. An empty plastic bag on the floor promptly flew out the window. Explain why.
Louise Reply
the pressure differential exerted a force on the bag greater than the gravitational force holding it on the floor.
what is angular velocity
Sthandazile Reply
The rate of change in angular displacement is defined as angular velocity.
a length of copper wire was measured to be 50m with an uncertainty of 1cm, the thickness of the wire was measured to be 1mm with an uncertainty of 0.01mm, using a micrometer screw gauge, calculate the of copper wire used
Nicole Reply
What is the answer please
If centripetal force is directed towards the center,why do you feel that you're thrown away from the center as a car goes around a curve? Explain
Maira Reply
if there is a centripetal force it means that there's also a centripetal acceleration, getting back to your question, just imagine what happens if you pull out of a car when it's quickly moving or when you try to stop when you are running fast, anyway, we notice that there's always a certain force..
... that tends to fight for its previous direction when you try to attribute to it an opposite one ou try to stop it.The same thing also happens whe a car goes around a curve, the car it self is designed to a"straight line"(look at the position of its tyres, mainly the back side ones), so...
... whenever it goes around a curve, it tends to throw away its the occupiers, it's given to the fact that it must interrupt its initial direction and take a new one.
Which kind of wave does wind form
Matthias Reply
calculate the distance you will travel if you mantain an average speed of 10N m/s for 40 second
Abdulai Reply
hw to calculate the momentum of the 2000.0 elephant change hunter at a speed of 7.50 m/s
Kingsley Reply
how many cm makes 1 inches
Hassan Reply
how do we convert from m/s to km/hr
Toni Reply
When paddling a canoe upstream, it is wisest to travel as near to the shore as possible. When canoeing downstream, it may be best to stay near the middle. Explain why?
SANA Reply
Explain why polarization does not occur in sound
one ship sailing east with a speed of 7.5m/s passes a certain point at 8am and a second ship sailing north at the same speed passed the same point at 9.30am at what distance are they closet together and what is the distance between them then
Kuber Reply
density of a subtance is given as 360g/cm,put it in it s.i unit form
Linda Reply
if m2 is twice of m1. find the ration of kinetic energy in COM system to lab system of elastic collision
Raman Reply
What is a volt equal to?
Clifton Reply
Practice Key Terms 3

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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