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For the simplest case, where the force is constant and the motion takes place in a straight line in the direction of the force we define the work done on an object by applied force as a product of the force and the distance through which the object is moved. In shorter form Work = force x distance
More generally, work is a product of only the component of force that acts in the direction of motion and the distance moved. For example, when a force acts at right angles to the direction of motion, with no force component in the direction of motion, no work is done!
Conceptual Question Does Earth do work on Moon?
Important: Definition of work involves both a force and a distance.
Units of Work 1 J = 1 N m
Power Power = work done/time interval
Units of Power 1 W = 1J/s
Question Are the collisions of billiard balls perfectly elastic?
The net work done on an object is equal to the change in its kinetic energy.
Conceptual Example:Work to Stop a car An automobile traveling 60 km/h brake to a stop within a distance of 20 m. If the car is going twice as fast, 120 km/h, what is its stopping distance? The maximum braking force is approximately independent of speed.
Questions Can an object have energy? Can an object have work?
Potential energy is the energy associated with forces that depend on the position or configuration of a body (or bodies) and the surroundings.
PE of Gravity We will define the potential energy of a body as the product of gravitational force mg acting on a body and its height h above some reference level.
Important: The change in potential energy between any two points does not depend on the choice of reference level. Important: The changes in gravitational potential energy depend only on the change in vertical height and not on the path taken.
Equation Fs = - kx is known as spring equation and also as Hooke’s law.
Important: Potential energy belongs to a system, and not to a single object alone!!!! The potential energy is a property of a system as a whole.
If no frictional (or other dissipative) forces are involved, the total mechanical energy of a system neither increases nor decreases in any process. It stays constant – it is conserved.
Total energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes.
Problem Solving Using Conservation of Mechanical Energy If the original height of the stone is y1 = h = 3.0m, calculate the stone’s speed when it has fallen to 1.0m above the ground.
Conceptual Example: Speeds on Two Water Slides • Two water slides at a pool are shaped differently, but have the same length and start at the same height h. Two riders, Paul and Kathleen, start from rest at the same time on different slides. • Which rider, Paul or Kathleen, is traveling faster at the bottom? • Which rider makes it to the bottom first?
Questions • You have been asked to analyze a collision at a traffic intersection. Will you be better off to begin your analysis using conservation of momentum or conservation of kinetic energy? Why? • If a system has zero kinetic energy, does it necessarily have zero momentum? Give an example to illustrate your answer. • An object has a velocity toward the south. If a force is directed toward the north, will the kinetic energy of the object initially increase, decrease, or stay the same? Explain.
In tryouts of the national bobsled team, each competing team pushes a sled along a level, smooth surface for 5 meters. One team brings a sled that is much lighter than the others. Assuming that this team pushes with the same force as the others, compare the kinetic energy of the light sled to that of the others after 5 meters . Compare the momentum of the light sled to that of the others after 5 meters. • Suppose the rules were changed in previous question so that the teams pushed for a fixed time of 5 seconds rather that a fixed distance of 5 meters. Compare the momentum of the light sled to that of the others after 5 seconds. Compare the kinetic energy of the sled to that of the others after 5 seconds.
