External Forces and Internal Energy Changes

External Forces and Internal Energy Changes

As the ice skater in pushes herself away from a railing, there is a force ii on her from the railing at angle 4> to the horizontal. This force accelerates her, increasing her speed until she leaves the railing . Thus, her kinetic energy is increased via the force. This example differs in two ways from earlier examples in which an object’s kinetic energy is changed via a force.

1. Previously, each part of an object moved rigidly in the same direction. Here the skater’s arm does not move like the rest of her body.

2. Previously, energy was transferred between the object (or system) and its  environment via an external force; that is, the force did work. Here the energy is transferred internally (from one part of the system to another) via the external force ii. In particular, the energy is transferred from internal biochemical energy of the skater’s muscles to kinetic energy of her body as a whole.

Next let us consider the energy transfers in the ice skater, which we now take as the system. Although an external force acts on the system, the force does not transfer energy to or from the system. Thus. the total energy £ of the system cannot change £ = O.

1

This equation means that as increases for the ice skater, decreases by just as much. Substituting.

As a skater pushe herself away from a railing, the fop, on her from the railing is F. (b) kbF the skater leaves the railing, he; center of mass has velocity v. (c) External force F is taken to act at the skater's center of mass, at angle cf> with a horizontal ..I' axis. ,When the center ~ mass goes through displacement d, its velocity is changed from Vo to v by the horizontal component {If
As a skater pushe herself
away from a railing, the fop, on her
from the railing is F. (b) kbF the
skater leaves the railing, he; center of
mass has velocity v. (c) External force
F is taken to act at the skater’s center
of mass, at angle cf> with a horizontal ..I’
axis. ,When the center ~ mass goes
through displacement d, its velocity is
changed from Vo to v by the horizontal
component 

If the driver applies the brakes, still holds. Now F due to the frictional forces is toward the rear . Energy is now transferred from kinetic energy of the car’s center of mass to thermal energy of the brakes.

A vehicle accelerates to the _ t using four- wheel drive. The road - ens four frictiogal forces (two of shown) on the bottom surfaces of tires. Taken together, these four es make up the net external force F ng on the car
A vehicle accelerates to the
 using four- wheel drive. The road
ens four frictional forces (two of
shown) on the bottom surfaces of
tires. Taken together, these four
es make up the net external force F
 on the car

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